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  • + + + + + diff --git a/v0.0.x/api/sdr.MLPED.A_received/index.html b/v0.0.x/api/sdr.MLPED.A_received/index.html new file mode 100644 index 000000000..0d658b55f --- /dev/null +++ b/v0.0.x/api/sdr.MLPED.A_received/index.html @@ -0,0 +1,9728 @@ + + + + + + + + + + + + + + + + sdr.MLPED.A_received - sdr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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    +property sdr.MLPED.A_received : float
    +

    (Settable) The received signal RMS amplitude \(A_{rx,rms}\).

    +
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    + + + + + + + + + + + + \ No newline at end of file diff --git a/v0.0.x/api/sdr.MLPED.A_reference/index.html b/v0.0.x/api/sdr.MLPED.A_reference/index.html new file mode 100644 index 000000000..8f4c1108e --- /dev/null +++ b/v0.0.x/api/sdr.MLPED.A_reference/index.html @@ -0,0 +1,9728 @@ + + + + + + + + + + + + + + + + sdr.MLPED.A_reference - sdr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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    +property sdr.MLPED.A_reference : float
    +

    (Settable) The reference signal RMS amplitude \(A_{ref,rms}\).

    +
    + + + + + + + + + + +
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    + + + + + + + + + + + + \ No newline at end of file diff --git a/v0.0.x/api/sdr.MLPED.__call__/index.html b/v0.0.x/api/sdr.MLPED.__call__/index.html new file mode 100644 index 000000000..d6568ce48 --- /dev/null +++ b/v0.0.x/api/sdr.MLPED.__call__/index.html @@ -0,0 +1,9846 @@ + + + + + + + + + + + + + + + + sdr.MLPED.__call__ - sdr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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    + + + +
    +
    +sdr.MLPED.__call__(received: ArrayLike, reference: ArrayLike) ndarray
    +

    Detects the phase error.

    +
    +
    Parameters:¶
    +
    +
    received: ArrayLike¶

    The received complex symbols \(\tilde{a}[k]\).

    +
    +
    reference: ArrayLike¶

    The reference complex symbols, either the known transmitted complex symbols \(a[k]\) +or the complex symbols decisions \(\hat{a}[k]\).

    +
    +
    +
    +
    Returns:¶
    +

    The detected phase error \(\theta_e[k]\) in radians.

    +
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    + + + + + + + + + + + + \ No newline at end of file diff --git a/v0.0.x/api/sdr.MLPED.__init__/index.html b/v0.0.x/api/sdr.MLPED.__init__/index.html new file mode 100644 index 000000000..b59ea630d --- /dev/null +++ b/v0.0.x/api/sdr.MLPED.__init__/index.html @@ -0,0 +1,9828 @@ + + + + + + + + + + + + + + + + sdr.MLPED.__init__ - sdr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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    + + + +
    +
    +sdr.MLPED(A_received: float = 1, A_reference: float = 1)
    +

    Initializes the ML-PED.

    +
    +
    Parameters:¶
    +
    +
    A_received: float = 1¶

    The received signal RMS amplitude \(A_{rx,rms}\).

    +
    +
    A_reference: float = 1¶

    The reference signal RMS amplitude \(A_{ref,rms}\).

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    + + + + + + + + + + + + \ No newline at end of file diff --git a/v0.0.x/api/sdr.MLPED.data_aided_error/index.html b/v0.0.x/api/sdr.MLPED.data_aided_error/index.html new file mode 100644 index 000000000..863059a1b --- /dev/null +++ b/v0.0.x/api/sdr.MLPED.data_aided_error/index.html @@ -0,0 +1,9846 @@ + + + + + + + + + + + + + + + + sdr.MLPED.data_aided_error - sdr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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    +sdr.MLPED.data_aided_error(modem: LinearModulation, n_points: int = 1000) tuple[NDArray[float_], NDArray[float_]]
    +

    Measures the average phase error of the data-aided PED using the specified modulation scheme.

    +
    +
    Parameters:¶
    +
    +
    modem: LinearModulation¶

    The linear modulation scheme.

    +
    +
    n_points: int = 1000¶

    The number of points to use to measure the phase error.

    +
    +
    +
    +
    Returns:¶
    +

      +
    • The true phase error in radians.

    • +
    • The detected phase error in radians.

    • +
    +

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    + + + + + + + + + \ No newline at end of file diff --git a/v0.0.x/api/sdr.MLPED.decision_directed_error/index.html b/v0.0.x/api/sdr.MLPED.decision_directed_error/index.html new file mode 100644 index 000000000..104d7f430 --- /dev/null +++ b/v0.0.x/api/sdr.MLPED.decision_directed_error/index.html @@ -0,0 +1,9846 @@ + + + + + + + + + + + + + + + + sdr.MLPED.decision_directed_error - sdr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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    +sdr.MLPED.decision_directed_error(modem: LinearModulation, n_points: int = 1000) tuple[NDArray[float_], NDArray[float_]]
    +

    Measures the average phase error of the decision-directed PED using the specified modulation scheme.

    +
    +
    Parameters:¶
    +
    +
    modem: LinearModulation¶

    The linear modulation scheme.

    +
    +
    n_points: int = 1000¶

    The number of points to use to measure the phase error.

    +
    +
    +
    +
    Returns:¶
    +

      +
    • The true phase error in radians.

    • +
    • The detected phase error in radians.

    • +
    +

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    + + + + + + + + + \ No newline at end of file diff --git a/v0.0.x/api/sdr.MLPED.gain/index.html b/v0.0.x/api/sdr.MLPED.gain/index.html new file mode 100644 index 000000000..fe2dc8989 --- /dev/null +++ b/v0.0.x/api/sdr.MLPED.gain/index.html @@ -0,0 +1,9728 @@ + + + + + + + + + + + + + + + + sdr.MLPED.gain - sdr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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    + + + +
    +
    +property sdr.MLPED.gain : float
    +

    The gain of the phase error detector \(K_p\).

    +
    + + + + + + + + + + +
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    + + + + +
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    + + + + + + + + + + + + \ No newline at end of file diff --git a/v0.0.x/api/sdr.MLPED/index.html b/v0.0.x/api/sdr.MLPED/index.html new file mode 100644 index 000000000..87acb41f6 --- /dev/null +++ b/v0.0.x/api/sdr.MLPED/index.html @@ -0,0 +1,10046 @@ + + + + + + + + + + + + + + + + sdr.MLPED - sdr + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
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    + + + +
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    + + + +
    +
    +class sdr.MLPED(sdr.PED)
    +

    Implements a maximum-likelihood phase error detector (ML-PED).

    +

    Notes¶

    +

    The data-aided ML-PED is computed using the received complex symbols \(\tilde{a}[k]\) and the known +transmitted complex symbols \(a[k]\).

    +

    +\[\theta_{e,DA}[k] = \Im(\tilde{a}[k]) \cdot \Re(a[k]) - \Re(\tilde{a}[k]) \cdot \Im(a[k])) \]
    +

    +

    The data-aided ML-PED is computed using the received complex symbols \(\tilde{a}[k]\) and the complex +symbol decisions \(\hat{a}[k]\).

    +

    +\[\theta_{e,DA}[k] = \Im(\tilde{a}[k]) \cdot \Re(\hat{a}[k]) - \Re(\tilde{a}[k]) \cdot \Im(\hat{a}[k]) \]
    +

    +

    References¶

    +
      +
    • Michael Rice, Digital Communications: A Discrete-Time Approach, Section 7.2.2.

    • +
    +

    Examples¶

    +

    Compare the data-aided and decision-directed ML-PEDs on QPSK modulation.

    +
    In [1]: qpsk = sdr.PSK(4)
    +
    +In [2]: A_rx, A_ref = 5, 3
    +
    +In [3]: ped = sdr.MLPED(A_rx, A_ref)
    +
    +
    +
    In [4]: error, da_error = ped.data_aided_error(qpsk); \
    +   ...: error, dd_error = ped.decision_directed_error(qpsk)
    +   ...: 
    +
    +In [5]: plt.figure(figsize=(8, 4)); \
    +   ...: plt.plot(error, da_error, label="Data-aided"); \
    +   ...: plt.plot(error, dd_error, label="Decision-directed"); \
    +   ...: plt.grid(True); \
    +   ...: plt.legend(); \
    +   ...: plt.xlabel("Phase of received symbols (radians)"); \
    +   ...: plt.ylabel("Phase error (radians)"); \
    +   ...: plt.title("Comparison of data-aided and decision-directed ML-PEDs on QPSK"); \
    +   ...: plt.tight_layout();
    +   ...: 
    +
    +
    +../../_images/sdr_MLPED_1.png +

    Observe that the slope of the phase error \(K_p = A_{rx,rms} A_{ref,rms}\) is the same for both the data-aided +and decision-directed PEDs. It’s very important to observe that the gain of the ML-PED is scaled by the +received signal amplitude \(A_{rx,rms}\) and the reference signal amplitude \(A_{ref,rms}\). Because of this, +the ML-PED should only be used with automatic gain control (AGC).

    +
    In [6]: ped.gain
    +Out[6]: 15
    +
    +In [7]: A_rx * A_ref
    +Out[7]: 15
    +
    +
    +

    Also note that the unambiguous range of the data-aided ML-PED is \([-\pi, \pi)\) and the +decision-directed ML-PED is \([-\pi/M, \pi/M)\).

    +

    Constructors¶

    +
    +
    +MLPED(A_received: float = 1, A_reference: float = 1)
    +

    Initializes the ML-PED.

    +
    + +
    +
    +

    Special methods¶

    +
    +
    +__call__(received: ArrayLike, reference: ArrayLike) ndarray
    +

    Detects the phase error.

    +
    + +
    +
    +

    Methods¶

    +
    +
    +data_aided_error(...) tuple[NDArray[float_], NDArray[float_]]
    +

    Measures the average phase error of the data-aided PED using the specified modulation scheme.

    +
    + +
    +
    +decision_directed_error(...) tuple[NDArray[float_], NDArray[float_]]
    +

    Measures the average phase error of the decision-directed PED using the specified modulation scheme.

    +
    + +
    +
    +

    Properties¶

    +
    +
    +property gain : float
    +

    The gain of the phase error detector \(K_p\).

    +
    + +
    +
    +property A_received : float
    +

    (Settable) The received signal RMS amplitude \(A_{rx,rms}\).

    +
    + +
    +
    +property A_reference : float
    +

    (Settable) The reference signal RMS amplitude \(A_{ref,rms}\).

    +
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    Measure the RMS EVM, normalizing with the average power of the reference symbols. Either the symbol map or noiseless transmitted symbols may be passed.

    In [3]: sdr.evm(x_hat, psk.symbol_map)
    -Out[3]: 9.915481162490009
    +Out[3]: 9.90878176652984
     
     In [4]: sdr.evm(x_hat, x)
    -Out[4]: 9.915481162490009
    +Out[4]: 9.90878176652984
     

    Measure the RMS EVM, normalizing with the average power of the received symbols.

    In [5]: sdr.evm(x_hat, psk.symbol_map, norm="average-power")
    -Out[5]: 9.863809254031926
    +Out[5]: 9.875702609125584
     

    Measure the RMS EVM, normalizing with the peak power of the received symbols.

    In [6]: sdr.evm(x_hat, psk.symbol_map, norm="peak-power")
    -Out[6]: 8.10833271837992
    +Out[6]: 8.103383557967632
     

    Measure the 95th percentile EVM.

    In [7]: sdr.evm(x_hat, psk.symbol_map, output=95)
    -Out[7]: 16.73336373672585
    +Out[7]: 17.287420508363883
     

    Measure the instantaneous EVM for each symbol.

    diff --git a/v0.0.x/api/sdr.frequency_offset/index.html b/v0.0.x/api/sdr.frequency_offset/index.html index 2bd0c408a..44aab5126 100644 --- a/v0.0.x/api/sdr.frequency_offset/index.html +++ b/v0.0.x/api/sdr.frequency_offset/index.html @@ -6947,6 +6947,301 @@ + + + + + + +
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  • @@ -9873,6 +10282,12 @@

    Phase error detectors +
    +class sdr.MLPED(sdr.PED)
    +

    Implements a maximum-likelihood phase error detector (ML-PED).

    +
    +
    diff --git a/v0.0.x/development/documentation/index.html b/v0.0.x/development/documentation/index.html index 012852e42..2e3ec4dbc 100644 --- a/v0.0.x/development/documentation/index.html +++ b/v0.0.x/development/documentation/index.html @@ -6999,6 +6999,301 @@ + + + + + + +
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    Design a proporti
    -
    <sdr.LoopFilter object at 0x7f3e6865fa50>
    +
    <sdr.LoopFilter object at 0x7f5982f38210>
     
    @@ -9567,18 +9862,21 @@

    Implement a PLL in the time domainphase_error = np.zeros(x.size) freq_estimate = np.zeros(x.size) -# Create a proportional-plus-integrator (PPI) loop filter with a normalized -# noise bandwidth of 0.05 and a damping factor of 1 (critically damped) -loop_filter = sdr.LoopFilter(0.05, 1) - # Create a numerically controlled oscillator (NCO) with NCO gain of 1, # constant phase accumulation of theta_0 radians/sample, and initial phase # offset of theta_0 radians. nco = sdr.NCO(1, increment=theta_0, offset=theta_0) +# Create a heuristic phase error detector (PED). +ped = sdr.PED() + +# Create a proportional-plus-integrator (PPI) loop filter with a normalized +# noise bandwidth of 0.05 and a damping factor of 1 (critically damped) +loop_filter = sdr.LoopFilter(0.05, 1, K0=nco.K0, Kp=ped.gain) + for i in range(N): - # Phase error detector (PED) - phase_error[i] = np.angle(x[i] * y[i].conj()) + # Heuristic phase error detector (PED) + phase_error[i] = ped(x[i], y[i]) # Compute the frequency estimate freq_estimate[i] = loop_filter(phase_error[i]) @@ -9638,18 +9936,16 @@

    Implement a PLL in the time domainphase_error = np.zeros(a.size) freq_estimate = np.zeros(a.size) -# Create a proportional-plus-integrator (PPI) loop filter with a normalized -# noise bandwidth of 0.02 and a damping factor of 1/sqrt(2) -Kp = 2 # Phase error detector gain -loop_filter = sdr.LoopFilter(0.02, 1 / np.sqrt(2), Kp=Kp) -print(f"K1: {loop_filter.K1}") -print(f"K2: {loop_filter.K2}") - -# Create a numerically controlled oscillator (NCO) with NCO gain of 1, -# constant phase accumulation of theta_0 radians/sample, and initial phase -# offset of theta_0 radians. +# Create a numerically controlled oscillator (NCO) with NCO gain of 1. nco = sdr.NCO(1) +# Create a maximum-likelihood phase error detector (ML-PED). +ped = sdr.MLPED() + +# Create a proportional-plus-integrator (PPI) loop filter with a normalized +# noise bandwidth of 0.05 and a damping factor of 1 (critically damped) +loop_filter = sdr.LoopFilter(0.02, 1 / np.sqrt(2), K0=nco.K0, Kp=ped.gain) + for i in range(N): # De-rotate the input symbols a_tilde[i] = a[i] * lo[i].conj() @@ -9657,8 +9953,8 @@

    Implement a PLL in the time domain# Make a symbol decision s_hat, a_hat = qpsk.decide_symbols(a_tilde[i]) - # Phase error detector (PED) - phase_error[i] = Kp * np.angle(a_tilde[i] * a_hat.conj()) + # Maximum-likelihood phase error detector (ML-PED) + phase_error[i] = ped(a_tilde[i], a_hat) # Compute the frequency estimate freq_estimate[i] = loop_filter(phase_error[i]) @@ -9669,10 +9965,6 @@

    Implement a PLL in the time domain

    -
    K1: 0.02596503375454388
    -K2: 0.0006924009001211702
    -
    -
    -../../_images/8aac559f44b9a67914ffc93a8f94eb4e74be183360be92663548f372bd76895b.png +../../_images/c12607ae3632ed6fbfa086b0f2a87eeaf4aa012e88307232cd540d10824b253e.png

    Analyze PLL closed-loop performance¶

    @@ -9740,7 +10032,7 @@

    Compare step and freque
    plt.figure(figsize=(10, 5))
    -for zeta in [1 / 2, 1 / np.sqrt(2), 1, 2]:
    +for zeta in [1 / 2, 1 / np.sqrt(2), 1, np.sqrt(2), 2]:
         pll = sdr.ClosedLoopPLL(0.01, zeta)
         sdr.plot.step_response(pll.iir, N=500, label=rf"$\zeta = {zeta}$")
     plt.title("Step response of the closed-loop PLL across damping factor")
    @@ -9749,13 +10041,13 @@ 

    Compare step and freque

    -../../_images/6c64d1a7dfb8ef7caeae2091231c5810d60e3aa88fcd1815ebb780a647a9133c.png +../../_images/427e8f30274acbb196f8217e7f6856c4106fcb1f0c523cbd58a5f666411e07c4.png
    plt.figure(figsize=(10, 5))
    -for zeta in [1 / 2, 1 / np.sqrt(2), 1, 2]:
    +for zeta in [1 / 2, 1 / np.sqrt(2), 1, np.sqrt(2), 2]:
         pll = sdr.ClosedLoopPLL(0.01, zeta)
         sdr.plot.magnitude_response(pll.iir, sample_rate=2 * np.pi / pll.omega_n, x_axis="log", label=rf"$\zeta = {zeta}$")
     plt.xlim([10**-2, 10**2])
    @@ -9767,7 +10059,7 @@ 

    Compare step and freque

    -../../_images/10c0cc8ce7564a8b5d927cc6d0c92376c679846fead329173684d961aee9de59.png +../../_images/d1c32442510154d814c23299c170ee1151f0f64fe6f56a11f8966c22896d7d63.png

    Compare step and frequency response across \(B_n T\)¶

    diff --git a/v0.0.x/examples/psk/index.html b/v0.0.x/examples/psk/index.html index bb31fca60..b2f0c6289 100644 --- a/v0.0.x/examples/psk/index.html +++ b/v0.0.x/examples/psk/index.html @@ -7053,6 +7053,301 @@ + + + + + + +
  • + + + + + + + + + + +
  • + + + + + diff --git a/v0.0.x/examples/pulse-shapes/index.html b/v0.0.x/examples/pulse-shapes/index.html index 4f2660566..d433928db 100644 --- a/v0.0.x/examples/pulse-shapes/index.html +++ b/v0.0.x/examples/pulse-shapes/index.html @@ -6999,6 +6999,301 @@ + + + + + + +
  • + + + + + + + + + + +
  • + + + + + diff --git a/v0.0.x/genindex/index.html b/v0.0.x/genindex/index.html index a3153607c..f4de9377f 100644 --- a/v0.0.x/genindex/index.html +++ b/v0.0.x/genindex/index.html @@ -6940,6 +6940,301 @@ + + + + + + +
  • + + + + + + + + + + +
  • + + + + + diff --git a/v0.0.x/index.html b/v0.0.x/index.html index 0a03fdce0..e690f7753 100644 --- a/v0.0.x/index.html +++ b/v0.0.x/index.html @@ -6943,6 +6943,301 @@ + + + + + + +
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162, 184, 186, 187, 237, 259, 260, 261, 262, 269, 280, 283], "snr_to_esn0": [0, 121, 160, 260, 283], "pack": [1, 44, 46, 134, 144, 154, 162, 220, 224, 282, 283], "bpe": [1, 224, 263], "int_": [1, 5, 6, 107, 113, 114, 134, 144, 154, 162, 189, 191, 192, 202, 203, 204, 216, 219, 224, 263, 269], "binari": [1, 4, 6, 135, 145, 155, 161, 163, 188, 189, 190, 191, 192, 193, 204, 217, 224, 247, 263, 265, 269, 280, 282, 283], "arrai": [1, 33, 36, 44, 59, 84, 98, 103, 106, 108, 134, 135, 136, 144, 145, 154, 155, 161, 162, 163, 173, 179, 182, 185, 188, 189, 191, 192, 202, 203, 204, 208, 211, 216, 217, 219, 224, 225, 227, 248, 251, 263, 265, 277], "an": [1, 2, 3, 4, 26, 37, 39, 51, 59, 61, 76, 77, 79, 84, 86, 94, 95, 96, 97, 108, 135, 136, 145, 155, 158, 160, 163, 166, 171, 187, 198, 224, 230, 235, 244, 248, 263, 266, 273, 282, 283], "multipl": [1, 59, 84, 224, 263, 280, 283], "bit": [1, 5, 7, 44, 46, 49, 107, 111, 112, 134, 135, 144, 145, 154, 155, 158, 161, 162, 163, 187, 189, 190, 192, 193, 206, 207, 209, 220, 224, 230, 259, 263, 282, 283], "element": [1, 220, 224, 263], "unpack": [1, 44, 46, 220, 263, 280, 282, 283], "hexdump": [1, 44, 220, 282, 283], "byte": [1, 220], "width": [1, 198, 220], "16": [1, 158, 160, 161, 175, 198, 206, 207, 209, 212, 217, 220, 230, 244, 251, 254, 257, 259, 260, 265, 278, 283], "str": [1, 26, 29, 30, 37, 51, 55, 56, 76, 80, 81, 94, 96, 99, 100, 107, 109, 110, 134, 144, 146, 147, 154, 156, 157, 162, 171, 174, 175, 220, 232, 238, 241, 242, 245], "return": [1, 6, 9, 17, 19, 22, 23, 26, 27, 29, 30, 37, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 58, 59, 60, 61, 63, 66, 70, 76, 78, 80, 81, 84, 86, 91, 94, 96, 97, 99, 100, 107, 109, 110, 111, 113, 114, 115, 116, 121, 128, 134, 138, 143, 144, 146, 147, 149, 151, 152, 154, 156, 157, 158, 160, 162, 164, 165, 167, 168, 169, 170, 171, 174, 175, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 276, 277, 278, 280, 283], "specifi": [1, 44, 47, 48, 50, 148, 151, 152, 186, 187, 204, 220, 271, 276, 277, 283], "class": [2, 3, 5, 6, 9, 26, 37, 39, 44, 46, 47, 48, 49, 50, 51, 69, 76, 94, 96, 107, 125, 134, 136, 144, 148, 154, 162, 166, 171, 270, 276, 277, 280, 282, 283], "replicacorrel": [2, 166, 167, 168, 169, 170, 283], "implement": [2, 3, 6, 26, 37, 39, 51, 69, 76, 94, 96, 107, 125, 131, 134, 136, 144, 148, 154, 162, 166, 171, 184, 270, 275], "clairvoy": [2, 166], "replica": [2, 166], "correl": [2, 166, 188, 217, 265, 267], "energydetector": [2, 39, 40, 41, 42, 43, 283], "energi": [2, 39, 111, 121, 158, 160, 166, 167, 168, 169, 170, 187, 206, 207, 208, 209, 210, 215, 218, 230, 244, 254, 255, 257, 259, 260, 282, 283], "albersheim": [2, 184, 283], "p_d": [2, 7, 39, 40, 42, 166, 167, 169, 184, 237, 243, 283], "p_fa": [2, 7, 39, 40, 41, 42, 43, 166, 167, 168, 169, 170, 184, 243], "estim": [2, 9, 107, 113, 114, 134, 144, 154, 162, 184, 238, 245, 279], "minimum": [2, 6, 134, 184, 283], "requir": [2, 27, 52, 97, 184, 271, 272, 273, 274, 283], "singl": [2, 42, 59, 84, 158, 160, 184], "sampl": [2, 3, 9, 16, 24, 26, 27, 31, 37, 40, 41, 42, 43, 51, 52, 57, 59, 60, 61, 63, 66, 69, 73, 84, 86, 91, 96, 97, 98, 101, 107, 108, 114, 116, 122, 125, 129, 132, 134, 135, 136, 138, 139, 140, 142, 143, 144, 145, 154, 155, 162, 163, 171, 173, 176, 184, 186, 205, 207, 210, 213, 215, 218, 223, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 245, 246, 248, 254, 255, 257, 258, 259, 260, 261, 262, 264, 269, 275, 278, 279, 281, 282, 283], "given": [2, 39, 44, 46, 47, 48, 50, 69, 70, 166, 184, 212, 276, 277], "n_": [2, 40, 41, 42, 43, 184], "nc": [2, 40, 41, 42, 43, 184], "non": [2, 27, 40, 41, 42, 43, 52, 97, 184, 218, 248, 255], "coher": [2, 40, 41, 42, 43, 184], "combin": [2, 184], "achiev": [2, 184, 280, 281], "probabl": [2, 7, 39, 40, 41, 42, 43, 164, 165, 166, 167, 168, 169, 170, 184, 189, 190, 192, 193, 204, 237, 243, 269, 283], "fals": [2, 5, 26, 28, 29, 30, 37, 38, 39, 40, 41, 42, 43, 51, 53, 55, 56, 59, 69, 71, 76, 77, 79, 80, 81, 84, 94, 95, 96, 97, 98, 99, 100, 134, 144, 154, 158, 160, 162, 166, 167, 168, 169, 170, 171, 173, 174, 175, 184, 185, 189, 192, 204, 208, 223, 227, 228, 231, 238, 243, 245, 248, 256, 277, 281], "alarm": [2, 39, 40, 41, 42, 43, 166, 167, 168, 169, 170, 184, 243], "p_": [2, 7, 39, 40, 41, 42, 43, 158, 160, 166, 167, 168, 169, 170, 184, 185, 186, 195, 204, 212, 222, 225, 227, 230, 238, 243, 244], "fa": [2, 7, 39, 40, 41, 42, 43, 166, 167, 168, 169, 170, 184, 243], "thi": [2, 9, 26, 46, 47, 48, 50, 51, 76, 96, 98, 107, 108, 123, 134, 138, 144, 145, 154, 155, 161, 162, 163, 171, 173, 184, 186, 187, 189, 192, 204, 205, 212, 214, 217, 232, 238, 242, 245, 248, 264, 265, 271, 273, 274, 275, 277, 279, 280, 281], "function": [2, 7, 8, 9, 18, 37, 51, 76, 77, 94, 125, 164, 165, 184, 187, 205, 215, 217, 230, 237, 238, 243, 244, 245, 264, 265, 276, 277, 279, 281, 282, 283], "": [2, 3, 7, 9, 17, 19, 20, 21, 23, 24, 26, 37, 39, 46, 47, 48, 49, 50, 51, 59, 60, 63, 66, 76, 84, 91, 94, 96, 107, 108, 113, 114, 115, 116, 134, 144, 154, 162, 166, 168, 170, 171, 184, 186, 187, 207, 210, 212, 213, 221, 231, 232, 233, 234, 236, 238, 239, 240, 241, 242, 245, 246, 248, 249, 258, 259, 260, 261, 262, 274, 275, 278, 280, 282, 283], "equat": [2, 17, 19, 20, 21, 22, 23, 40, 41, 43, 76, 144, 154, 162, 167, 168, 170, 184, 214], "finit": [3, 51, 282, 283], "impuls": [3, 7, 26, 37, 51, 61, 76, 86, 94, 96, 171, 196, 197, 198, 199, 200, 201, 215, 233, 235, 281, 282, 283], "respons": [3, 7, 26, 37, 51, 59, 61, 66, 76, 84, 86, 91, 94, 96, 171, 196, 197, 198, 199, 200, 201, 215, 233, 234, 235, 236, 240, 246, 281, 282, 283], "differenti": [3, 6, 37, 38, 134, 158, 160, 202, 203, 248, 282, 283], "design_lowpass_fir": [3, 59, 200, 283], "order": [3, 9, 26, 27, 30, 37, 44, 49, 51, 52, 56, 62, 69, 72, 76, 81, 87, 94, 96, 97, 98, 100, 107, 108, 117, 125, 129, 134, 144, 154, 155, 162, 163, 171, 173, 175, 186, 196, 197, 199, 200, 206, 207, 209, 212, 213, 215, 231, 232, 241, 242, 254, 257, 258, 259, 270, 277, 278, 279, 280, 283], "design": [3, 26, 28, 32, 96, 98, 102, 108, 145, 155, 163, 171, 173, 178, 196, 197, 198, 199, 200, 201, 271, 282, 283], "lowpass": [3, 200], "h": [3, 7, 26, 37, 39, 51, 53, 55, 56, 59, 61, 76, 84, 86, 94, 96, 107, 108, 119, 120, 124, 125, 134, 144, 145, 154, 155, 162, 163, 166, 171, 196, 197, 198, 199, 200, 201, 215, 232, 233, 235, 236, 240, 251, 278, 279, 281], "n": [3, 5, 6, 7, 8, 9, 26, 27, 37, 39, 42, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 58, 60, 61, 62, 63, 65, 66, 68, 69, 70, 76, 78, 79, 82, 86, 87, 91, 94, 96, 97, 107, 108, 114, 116, 119, 120, 124, 125, 128, 134, 136, 138, 143, 144, 145, 154, 155, 162, 163, 164, 165, 166, 168, 170, 171, 172, 185, 186, 187, 188, 191, 194, 196, 197, 198, 199, 200, 201, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 216, 217, 219, 221, 223, 225, 227, 228, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 245, 246, 248, 256, 258, 259, 260, 261, 262, 264, 265, 267, 268, 269, 279, 281, 282], "us": [3, 7, 26, 28, 32, 35, 37, 38, 51, 53, 58, 59, 64, 69, 71, 76, 77, 79, 84, 89, 94, 95, 96, 97, 98, 102, 105, 107, 108, 113, 114, 125, 131, 134, 144, 145, 148, 151, 152, 154, 155, 162, 163, 171, 173, 178, 181, 187, 190, 193, 196, 197, 198, 199, 200, 201, 212, 217, 220, 224, 231, 232, 233, 235, 237, 238, 245, 246, 263, 265, 271, 272, 273, 274, 276, 277, 279, 280, 281, 282, 284], "window": [3, 26, 59, 96, 171, 196, 197, 198, 199, 200, 201, 238, 245, 283], "method": [3, 7, 30, 32, 98, 100, 102, 173, 175, 178, 196, 197, 198, 199, 200, 201, 238, 245, 276, 277, 283], "design_highpass_fir": [3, 199, 283], "highpass": [3, 199], "design_bandpass_fir": [3, 196, 283], "bandpass": [3, 196], "design_bandstop_fir": [3, 197, 283], "bandstop": [3, 197], "infinit": [3, 76, 282, 283], "integr": [3, 9, 14, 40, 41, 42, 43, 94, 95, 125, 127, 129, 184, 270, 274, 277, 282, 283], "interpol": [3, 26, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 124, 134, 144, 154, 162, 171, 173, 183, 201, 232, 264, 278, 280, 282, 283], "polyphas": [3, 26, 27, 28, 33, 36, 96, 97, 98, 103, 106, 171, 172, 173, 179, 182, 201, 205, 251, 264, 282, 283], "decim": [3, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 107, 108, 113, 114, 115, 116, 120, 123, 134, 135, 144, 145, 154, 155, 161, 162, 163, 171, 173, 177, 201, 205, 280, 282, 283], "ration": [3, 171, 173, 201, 283], "design_multirate_fir": [3, 28, 98, 173, 201, 283], "up": [3, 171, 173, 183, 201, 214, 272], "kaiser": [3, 26, 28, 29, 30, 32, 96, 97, 98, 99, 100, 102, 171, 173, 174, 175, 178, 196, 197, 198, 199, 200, 201], "polyphase_decompos": [3, 251, 283], "tap": [3, 26, 28, 33, 36, 37, 51, 56, 68, 69, 75, 76, 82, 83, 94, 96, 98, 103, 106, 171, 173, 179, 182, 251, 276, 277], "phase": [3, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 37, 51, 63, 96, 107, 108, 118, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 148, 149, 151, 152, 153, 154, 155, 158, 159, 160, 161, 162, 163, 171, 184, 213, 221, 223, 239, 240, 241, 251, 269, 282, 283], "decompos": [3, 26, 96, 171, 251], "h_i": [3, 26, 28, 33, 36, 37, 51, 53, 68, 96, 98, 103, 106, 171, 173, 179, 182, 251, 276], "matrix": [3, 204, 251, 269], "h_": [3, 9, 26, 33, 36, 96, 103, 106, 171, 179, 182, 251, 279], "i": [3, 9, 16, 25, 26, 27, 28, 33, 36, 37, 39, 41, 42, 43, 44, 49, 51, 52, 53, 59, 61, 66, 67, 68, 69, 74, 76, 79, 83, 84, 86, 91, 92, 94, 96, 97, 98, 103, 106, 107, 108, 125, 129, 130, 132, 134, 138, 142, 144, 145, 148, 154, 155, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 179, 182, 184, 185, 186, 187, 189, 190, 192, 193, 195, 196, 197, 198, 199, 200, 204, 206, 207, 208, 209, 210, 211, 213, 214, 215, 217, 218, 219, 220, 221, 222, 224, 225, 226, 227, 228, 231, 232, 233, 234, 235, 236, 238, 239, 240, 242, 245, 246, 248, 251, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 271, 272, 273, 274, 275, 276, 277, 278, 279, 280, 281, 282, 284], "j": [3, 26, 33, 36, 59, 76, 79, 82, 84, 94, 96, 103, 106, 134, 136, 144, 154, 162, 171, 179, 182, 186, 204, 221, 223, 251, 267, 276, 277], "b": [3, 76, 79, 184, 187, 215, 220, 233, 235, 246, 251, 271, 272, 281], "farrowresampl": [3, 69, 70, 71, 72, 73, 74, 75, 275, 283], "cubic": [3, 69], "farrow": [3, 69, 70, 71, 72, 73, 74, 75, 282, 283], "design_frac_delay_fir": [3, 198, 283], "length": [3, 6, 7, 26, 27, 37, 42, 51, 52, 54, 61, 66, 78, 96, 97, 98, 108, 114, 116, 135, 145, 155, 163, 171, 173, 188, 191, 196, 197, 198, 199, 200, 201, 215, 216, 217, 218, 233, 235, 238, 242, 245, 246, 254, 255, 257, 261, 265, 267, 268, 272, 275, 278, 281], "delai": [3, 7, 26, 27, 30, 31, 37, 51, 52, 56, 57, 60, 63, 69, 96, 97, 100, 101, 125, 136, 171, 175, 176, 198, 202, 203, 218, 234, 239, 255, 279, 282, 283], "fraction": [3, 69, 73, 198, 215, 275, 282, 283], "mix": [3, 223, 282, 283], "freq": [3, 4, 26, 37, 51, 59, 76, 84, 94, 96, 136, 138, 171, 213, 214, 223, 226, 266, 269, 275, 279], "float": [3, 5, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 37, 42, 44, 46, 47, 48, 50, 51, 59, 60, 63, 69, 70, 76, 77, 84, 85, 94, 96, 107, 108, 118, 125, 126, 127, 129, 130, 132, 134, 135, 136, 137, 139, 140, 141, 144, 145, 148, 153, 154, 155, 159, 162, 163, 169, 171, 180, 185, 186, 187, 189, 192, 194, 196, 197, 198, 199, 200, 201, 212, 213, 215, 221, 223, 225, 227, 228, 231, 232, 233, 234, 236, 238, 239, 240, 241, 242, 245, 247, 248, 254, 256, 257, 258, 269], "0": [3, 6, 8, 16, 26, 27, 33, 36, 37, 39, 42, 44, 51, 52, 53, 55, 56, 59, 60, 63, 68, 76, 77, 79, 80, 81, 82, 83, 84, 94, 96, 97, 98, 103, 106, 107, 108, 113, 114, 115, 116, 123, 129, 134, 135, 136, 139, 144, 145, 154, 155, 159, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 179, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 195, 196, 197, 198, 199, 200, 202, 203, 204, 205, 207, 208, 210, 211, 212, 213, 214, 215, 216, 217, 219, 221, 222, 223, 224, 226, 229, 231, 232, 233, 234, 235, 236, 239, 240, 241, 246, 247, 248, 249, 250, 251, 252, 253, 254, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 271, 272, 273, 275, 276, 277, 278, 279, 280, 281, 284], "time": [3, 5, 9, 16, 17, 19, 20, 21, 22, 23, 37, 51, 76, 94, 125, 129, 144, 148, 154, 162, 185, 186, 194, 196, 197, 199, 200, 204, 205, 208, 210, 211, 213, 215, 217, 219, 221, 223, 225, 227, 228, 232, 233, 238, 242, 245, 248, 254, 256, 257, 258, 260, 261, 262, 264, 265, 269, 275, 276, 277, 281, 282, 283], "domain": [3, 5, 185, 186, 194, 196, 197, 199, 200, 205, 208, 211, 213, 219, 221, 223, 225, 227, 228, 233, 238, 242, 245, 248, 256, 258, 261, 262, 264, 269, 282, 283], "complex": [3, 5, 7, 26, 37, 39, 40, 41, 42, 43, 51, 59, 76, 84, 94, 96, 107, 108, 113, 114, 115, 116, 123, 134, 135, 136, 138, 143, 144, 145, 148, 149, 154, 155, 161, 162, 163, 166, 167, 168, 169, 170, 171, 186, 187, 205, 212, 221, 223, 231, 232, 234, 236, 239, 240, 242, 247, 248, 261, 262, 264, 269, 275, 276, 277, 279, 280, 282, 283], "exponenti": [3, 138, 205, 223, 261, 262, 264, 275, 276, 277], "real": [3, 40, 41, 43, 134, 144, 164, 165, 167, 168, 170, 186, 223, 232, 234, 236, 239, 240, 242, 248, 261, 262, 275, 276, 277, 279, 282, 283], "sinusoid": [3, 154, 186, 223, 261, 262, 277, 283], "to_complex_bb": [3, 261, 283], "x_r": [3, 261, 262], "complex_": [3, 7, 107, 113, 114, 115, 116, 123, 134, 136, 143, 144, 148, 149, 154, 161, 162, 231, 247, 261, 262, 267, 268], "passband": [3, 196, 197, 198, 199, 200, 215, 218, 254, 255, 257, 261, 262, 278, 283], "center": [3, 196, 197, 198, 199, 200, 218, 248, 255, 261, 262, 283], "f_": [3, 9, 16, 24, 27, 59, 60, 63, 84, 97, 107, 108, 122, 134, 135, 144, 145, 154, 155, 162, 163, 196, 197, 199, 200, 205, 207, 210, 213, 215, 223, 232, 233, 234, 236, 238, 239, 240, 241, 242, 245, 248, 258, 259, 260, 261, 262, 264, 275, 276, 277, 279, 281], "r": [3, 26, 27, 28, 33, 34, 36, 69, 70, 96, 97, 98, 103, 104, 106, 187, 205, 206, 207, 209, 212, 215, 223, 254, 257, 259, 261, 262, 264, 271, 272, 273, 274, 277, 278, 279, 281], "4": [3, 7, 17, 19, 26, 33, 36, 37, 40, 42, 44, 59, 80, 81, 84, 94, 96, 97, 103, 106, 134, 135, 136, 144, 145, 148, 154, 158, 159, 160, 161, 162, 166, 167, 168, 169, 170, 171, 174, 175, 179, 182, 184, 186, 187, 188, 190, 191, 193, 196, 197, 198, 199, 200, 201, 204, 205, 206, 207, 209, 210, 212, 213, 214, 215, 216, 217, 218, 220, 221, 223, 224, 226, 230, 231, 232, 233, 234, 235, 236, 239, 240, 241, 244, 246, 247, 248, 249, 250, 251, 254, 255, 257, 258, 259, 260, 261, 262, 263, 264, 265, 267, 273, 275, 277, 278, 279, 280], "rate": [3, 5, 7, 9, 16, 24, 26, 27, 28, 30, 34, 44, 45, 46, 48, 49, 59, 60, 63, 69, 70, 84, 96, 97, 98, 100, 104, 107, 111, 121, 134, 144, 154, 158, 160, 162, 171, 172, 173, 175, 177, 180, 183, 201, 205, 206, 207, 209, 213, 223, 230, 232, 233, 234, 236, 238, 239, 240, 241, 242, 244, 245, 248, 258, 259, 261, 262, 264, 269, 282, 283], "baseband": [3, 7, 9, 134, 144, 154, 162, 223, 232, 241, 261, 262, 278, 279, 283], "x_c": [3, 261, 262], "c": [3, 9, 17, 19, 20, 21, 22, 23, 46, 47, 48, 49, 50, 107, 108, 123, 125, 134, 144, 154, 161, 162, 187, 190, 193, 214, 226, 247, 261, 262, 266, 279], "2": [3, 6, 7, 9, 17, 19, 22, 26, 29, 30, 33, 36, 37, 39, 40, 41, 42, 43, 44, 51, 55, 56, 57, 59, 60, 63, 80, 81, 84, 94, 96, 97, 99, 100, 103, 106, 107, 108, 117, 134, 136, 144, 145, 148, 154, 155, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 174, 175, 179, 182, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 223, 224, 226, 227, 229, 230, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 244, 245, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 267, 271, 274, 275, 276, 277, 278, 279, 280, 281], "to_real_pb": [3, 262, 278, 283], "2f_": [3, 262], "upsampl": [3, 96, 171, 264, 283], "factor": [3, 5, 9, 16, 25, 108, 125, 129, 130, 145, 155, 163, 194, 205, 264, 279], "downsampl": [3, 205, 283], "bsc_capac": [4, 193, 283], "p": [4, 8, 136, 138, 164, 165, 171, 173, 179, 180, 182, 183, 189, 190, 192, 193, 201, 204, 269], "calcul": [4, 5, 187, 190, 193, 212, 214, 226, 266, 283], "symmetr": [4, 192, 193, 204, 261, 262, 269, 282], "bsc": [4, 192, 193, 204, 269, 282, 283], "bec_capac": [4, 190, 283], "erasur": [4, 189, 190, 204, 269, 282], "bec": [4, 189, 190, 204, 269, 282, 283], "awgn_capac": [4, 187, 283], "addit": [4, 186, 187, 230, 231, 232, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 250, 264, 269, 282], "white": [4, 186, 187, 269, 282], "gaussian": [4, 6, 37, 94, 186, 187, 215, 269, 282, 283], "nois": [4, 9, 10, 11, 16, 22, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 111, 121, 125, 129, 132, 134, 144, 154, 158, 160, 162, 166, 167, 168, 169, 170, 186, 187, 206, 207, 209, 210, 230, 244, 259, 260, 269, 279, 282], "awgn": [4, 134, 144, 154, 158, 160, 162, 186, 187, 212, 230, 231, 244, 261, 262, 269, 280, 282, 283], "fspl": [4, 214], "distanc": [4, 211, 214, 219, 282, 283], "free": [4, 134, 144, 154, 162, 214, 282], "space": [4, 59, 84, 214, 282], "wavelength": [4, 266, 283], "lambda": [4, 214, 266], "electromagnet": [4, 266], "wave": [4, 134, 266], "frequenc": [4, 9, 17, 19, 21, 26, 37, 51, 59, 60, 63, 76, 84, 94, 96, 125, 134, 136, 138, 171, 196, 197, 198, 199, 200, 205, 213, 214, 223, 226, 233, 234, 236, 238, 239, 240, 245, 261, 262, 264, 266, 269, 281, 282, 283], "f": [4, 17, 19, 26, 42, 59, 60, 63, 84, 96, 136, 138, 171, 184, 186, 213, 214, 215, 223, 226, 258, 266, 267, 272, 275, 276, 277, 278, 279, 280, 281], "parabolic_antenna": [4, 226, 283], "tupl": [4, 26, 37, 39, 42, 44, 46, 49, 51, 59, 60, 63, 76, 84, 94, 96, 107, 113, 114, 134, 144, 148, 151, 152, 154, 162, 166, 169, 171, 185, 208, 211, 219, 225, 226, 227, 231, 233, 234, 235, 236, 239, 240, 246, 247, 250], "gain": [4, 9, 12, 13, 14, 15, 16, 76, 77, 85, 94, 125, 126, 127, 129, 136, 137, 139, 148, 153, 184, 196, 197, 198, 199, 200, 214, 215, 218, 226, 254, 255, 257, 279, 282], "g": [4, 49, 226, 273], "beamwidth": [4, 226], "theta": [4, 136, 139, 141, 142, 226], "parabol": [4, 226], "reflector": [4, 226], "signal": [5, 7, 9, 17, 19, 22, 23, 26, 27, 37, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 58, 69, 70, 76, 78, 94, 96, 97, 107, 108, 119, 125, 128, 134, 136, 138, 143, 144, 145, 154, 155, 162, 163, 166, 167, 168, 169, 170, 171, 172, 185, 186, 187, 194, 195, 196, 197, 199, 200, 201, 205, 206, 207, 208, 209, 210, 211, 213, 214, 215, 219, 221, 222, 223, 225, 226, 227, 228, 232, 233, 234, 236, 238, 239, 240, 241, 242, 245, 248, 251, 256, 258, 259, 260, 261, 262, 264, 266, 276, 277, 279, 281, 282, 283], "peak_pow": [5, 225, 227, 283], "peak": [5, 134, 144, 162, 194, 212, 225, 227, 228], "average_pow": [5, 185, 225, 283], "averag": [5, 44, 134, 144, 148, 151, 152, 162, 185, 186, 187, 212, 225, 238], "papr": [5, 134, 144, 162, 225, 278, 283], "ratio": [5, 22, 40, 42, 44, 46, 47, 48, 49, 50, 111, 121, 134, 144, 158, 160, 162, 167, 169, 186, 187, 206, 207, 209, 210, 225, 229, 230, 244, 252, 253, 259, 260], "peak_voltag": [5, 194, 228, 283], "bool": [5, 26, 28, 37, 38, 40, 41, 42, 43, 51, 53, 59, 67, 69, 71, 74, 76, 77, 79, 84, 92, 94, 95, 96, 98, 134, 144, 154, 158, 160, 162, 167, 168, 169, 170, 171, 173, 185, 208, 223, 227, 228, 231, 240, 242, 247, 248, 256], "rms_voltag": [5, 194, 256, 283], "root": [5, 6, 108, 145, 155, 163, 212, 232, 248, 256, 257, 267, 268, 276, 282], "mean": [5, 212, 238, 245, 256, 281], "squar": [5, 6, 108, 145, 155, 163, 212, 214, 226, 248, 256, 257, 276], "rm": [5, 194, 212, 256], "crest_factor": [5, 194, 225, 283], "crest": [5, 194], "euclidean": [5, 211, 282, 283], "y": [5, 6, 26, 27, 37, 51, 52, 58, 70, 76, 78, 94, 96, 97, 125, 128, 136, 138, 143, 171, 186, 189, 192, 202, 203, 204, 205, 211, 213, 219, 221, 223, 231, 236, 238, 245, 247, 258, 264, 279, 280], "between": [5, 26, 28, 38, 53, 67, 71, 74, 77, 79, 92, 95, 96, 98, 148, 171, 173, 211, 214, 219, 238, 242, 245, 279, 282], "two": [5, 196, 197, 211, 219, 232, 233, 234, 236, 238, 239, 240, 245, 267, 275, 276, 277], "ham": [5, 59, 196, 197, 199, 200, 219, 282, 283], "errorr": [5, 44, 45, 46, 47, 48, 49, 50, 280, 283], "A": [5, 9, 17, 19, 20, 21, 22, 23, 25, 27, 37, 44, 51, 52, 59, 84, 94, 97, 108, 125, 145, 148, 155, 163, 184, 191, 196, 197, 199, 200, 216, 220, 221, 226, 254, 257, 270, 272, 279], "error": [5, 7, 9, 15, 16, 22, 44, 45, 46, 48, 49, 50, 107, 111, 121, 125, 129, 134, 144, 148, 149, 151, 152, 153, 154, 158, 160, 162, 184, 193, 212, 230, 244, 279, 282, 283], "ber": [5, 7, 44, 107, 111, 134, 144, 154, 158, 162, 230, 280, 282, 283], "symbol": [5, 7, 44, 46, 49, 96, 107, 108, 112, 113, 114, 115, 116, 121, 122, 123, 134, 135, 144, 145, 148, 149, 154, 155, 158, 160, 161, 162, 163, 186, 206, 207, 209, 210, 212, 213, 215, 218, 231, 232, 241, 244, 247, 248, 254, 255, 257, 259, 260, 278, 279, 281, 282, 283], "ser": [5, 7, 44, 107, 121, 134, 144, 154, 160, 162, 244, 280, 282, 283], "evm": [5, 212, 282, 283], "x_hat": [5, 7, 44, 46, 212, 231, 280], "ref": [5, 184, 196, 197, 198, 199, 200, 201, 212, 215, 217, 265], "vector": [5, 44, 59, 73, 84, 196, 197, 199, 200, 212, 238, 245, 282, 283], "magnitud": [5, 7, 188, 198, 212, 217, 233, 236, 265, 267, 282, 283], "hat": [5, 7, 46, 107, 113, 114, 134, 144, 148, 149, 154, 162, 212, 231, 247], "k": [5, 6, 7, 46, 107, 108, 112, 113, 114, 115, 116, 117, 134, 144, 148, 149, 154, 155, 162, 163, 202, 203, 206, 207, 209, 212, 231, 247, 248, 259, 278, 281], "linearmodul": [6, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 151, 152, 154, 247, 283], "amplitud": [6, 107, 108, 221, 269, 275, 279], "arbitrari": [6, 69, 70, 71, 72, 73, 74, 75, 107, 282, 283], "psk": [6, 144, 148, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 186, 212, 213, 221, 230, 231, 232, 244, 247, 248, 258, 278, 279, 282, 283], "shift": [6, 134, 144, 154, 158, 159, 160, 161, 162, 267, 276, 277, 282, 283], "kei": [6, 134, 144, 154, 158, 159, 160, 161, 162, 282, 283], "demodul": [6, 107, 114, 134, 144, 154, 162, 283], "pimpsk": [6, 162, 163, 283], "pi": [6, 26, 80, 81, 84, 96, 97, 136, 144, 148, 154, 162, 163, 171, 186, 205, 214, 215, 221, 223, 226, 233, 234, 235, 236, 239, 240, 246, 250, 261, 262, 264, 267, 275, 276, 277, 279, 282, 283], "m": [6, 76, 79, 83, 94, 107, 108, 112, 113, 114, 115, 116, 117, 123, 134, 144, 148, 154, 155, 161, 162, 163, 204, 206, 207, 209, 214, 247, 259, 271, 272, 273, 274, 282, 283], "oqpsk": [6, 134, 144, 145, 146, 147, 283], "offset": [6, 17, 19, 26, 37, 96, 97, 107, 108, 118, 134, 135, 136, 138, 139, 141, 144, 145, 154, 155, 159, 162, 163, 171, 213, 223, 248, 258, 269, 279, 282, 283], "quadratur": [6, 134, 144, 221], "msk": [6, 134, 135, 241, 283], "rectangular": [6, 108, 145, 155, 163, 255, 278, 281, 282, 283], "span": [6, 7, 108, 145, 155, 163, 215, 218, 232, 241, 254, 255, 257, 278, 281], "half_sin": [6, 135, 218, 283], "half": [6, 134, 144, 201, 218, 226, 282, 283], "sine": [6, 134, 138, 218, 282, 283], "time_bandwidth": [6, 215], "raised_cosin": [6, 108, 145, 155, 163, 232, 254, 281, 283], "alpha": [6, 108, 145, 155, 163, 215, 249, 254, 257, 278, 281], "rais": [6, 37, 94, 108, 145, 155, 163, 232, 248, 254, 257, 276, 282], "cosin": [6, 37, 94, 108, 138, 145, 155, 163, 232, 248, 254, 257, 276, 282], "rc": [6, 108, 145, 155, 163, 254], "root_raised_cosin": [6, 37, 55, 56, 94, 108, 145, 155, 163, 232, 233, 234, 235, 236, 239, 240, 246, 250, 257, 276, 278, 280, 281, 283], "srrc": [6, 108, 144, 145, 154, 155, 162, 163, 232, 248, 257, 278, 280], "binary_cod": [6, 191, 283], "gener": [6, 134, 144, 154, 162, 186, 189, 191, 192, 204, 216, 243, 271, 280, 283], "code": [6, 26, 29, 37, 51, 55, 76, 80, 94, 96, 99, 107, 109, 134, 135, 144, 145, 146, 154, 155, 156, 161, 162, 163, 171, 174, 188, 191, 206, 207, 209, 216, 217, 231, 247, 259, 265, 268, 273, 280, 283], "gray_cod": [6, 216, 283], "grai": [6, 134, 135, 144, 145, 154, 155, 161, 162, 163, 216, 231, 247, 280, 282], "diff_encod": [6, 134, 144, 154, 158, 160, 162, 202, 203, 283], "y_prev": [6, 202, 203], "input": [6, 9, 17, 19, 22, 23, 26, 27, 28, 31, 37, 38, 51, 52, 53, 61, 65, 66, 69, 70, 71, 73, 76, 77, 78, 79, 86, 91, 94, 95, 96, 97, 98, 101, 125, 128, 136, 138, 144, 154, 158, 160, 162, 164, 171, 172, 173, 176, 186, 187, 189, 190, 192, 193, 195, 202, 203, 204, 205, 222, 224, 229, 235, 246, 252, 253, 263, 264, 269, 276, 277, 279], "data": [6, 148, 151, 202, 203, 220, 224, 248, 263, 282], "diff_decod": [6, 202, 203, 283], "decod": [6, 202], "use_styl": [7, 249], "appli": [7, 26, 96, 108, 171, 213, 221, 231, 232, 238, 245, 247, 248, 249, 258, 269], "default": [7, 61, 66, 135, 145, 155, 161, 163, 185, 208, 211, 219, 225, 227, 231, 234, 236, 239, 240, 242, 245, 247, 249, 280], "matplotlib": [7, 230, 231, 232, 234, 235, 236, 237, 238, 239, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 275, 276, 277, 278, 279, 280, 281, 282], "rcparam": [7, 249], "time_domain": [7, 26, 37, 94, 96, 97, 134, 136, 144, 154, 162, 171, 186, 205, 217, 223, 248, 261, 262, 264, 265, 278, 279, 280, 281, 283], "ani": [7, 26, 37, 51, 59, 76, 84, 94, 96, 136, 138, 171, 188, 195, 205, 217, 222, 248, 264, 265, 268, 274], "dtype": [7, 26, 37, 51, 59, 76, 84, 94, 96, 134, 136, 138, 144, 154, 162, 171, 188, 217, 224, 248, 263, 265, 268, 279], "_scalartype_co": [7, 248], "t": [7, 9, 11, 16, 39, 125, 129, 132, 166, 215, 220, 248, 271, 275], "raster": [7, 232, 241, 242, 282, 283], "none": [7, 26, 37, 42, 51, 59, 61, 66, 69, 73, 84, 96, 108, 125, 133, 138, 145, 155, 163, 169, 171, 185, 186, 187, 189, 192, 196, 197, 199, 200, 204, 208, 211, 219, 224, 225, 227, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 245, 246, 247, 248, 263, 269, 275, 278, 280], "periodogram": [7, 205, 238, 261, 262, 264, 278, 282, 283], "power": [7, 134, 144, 154, 162, 185, 186, 187, 195, 212, 215, 217, 218, 222, 225, 226, 227, 238, 254, 255, 257, 265, 281, 282], "densiti": [7, 22, 238, 278, 281], "xx": [7, 238], "welch": [7, 238, 245], "spectrogram": [7, 245, 282, 283], "constel": [7, 134, 144, 154, 159, 162, 186, 212, 213, 221, 231, 258, 267, 282, 283], "symbol_map": [7, 107, 108, 123, 134, 144, 154, 159, 161, 162, 212, 247, 280, 283], "map": [7, 107, 108, 115, 123, 134, 144, 154, 161, 162, 212, 247, 282, 283], "ey": [7, 134, 144, 154, 162, 232, 282, 283], "diagram": [7, 9, 26, 37, 94, 96, 125, 136, 171, 202, 203, 232, 282, 283], "phase_tre": [7, 134, 241, 283], "tree": [7, 241, 283], "continu": [7, 134, 241, 275, 283], "cpm": [7, 241, 283], "kwarg": [7, 230, 231, 232, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 250], "e_b": [7, 46, 47, 48, 49, 50, 107, 111, 134, 144, 154, 158, 162, 187, 206, 207, 209, 230, 259, 282], "n_0": [7, 22, 46, 47, 48, 49, 50, 107, 111, 121, 134, 144, 154, 158, 160, 162, 186, 187, 206, 207, 209, 210, 212, 230, 231, 244, 259, 260, 280, 282], "e_": [7, 46, 47, 48, 49, 50, 107, 121, 134, 144, 154, 160, 162, 186, 187, 206, 209, 210, 212, 231, 244, 260, 280, 282], "roc": [7, 39, 42, 166, 169, 243, 283], "receiv": [7, 39, 40, 42, 44, 46, 107, 113, 114, 120, 134, 144, 148, 149, 154, 158, 160, 162, 166, 167, 168, 169, 170, 212, 214, 232, 237, 243, 283], "oper": [7, 39, 42, 166, 169, 243, 283], "characterist": [7, 39, 42, 166, 169, 243, 283], "curv": [7, 39, 42, 158, 160, 166, 169, 230, 243, 244, 283], "enr": [7, 166, 167, 169, 237], "impulse_respons": [7, 26, 37, 51, 61, 76, 86, 94, 96, 171, 196, 197, 198, 199, 200, 201, 215, 218, 235, 254, 255, 257, 276, 277, 281, 283], "step_respons": [7, 26, 37, 51, 66, 76, 91, 94, 96, 171, 246, 276, 277, 279, 283], "step": [7, 26, 37, 51, 66, 76, 91, 94, 96, 136, 138, 143, 171, 233, 246, 282], "zeros_pol": [7, 250, 277, 283], "zero": [7, 26, 27, 37, 51, 58, 73, 76, 77, 80, 81, 84, 93, 94, 96, 97, 98, 125, 138, 171, 173, 198, 217, 218, 224, 233, 234, 235, 236, 239, 240, 246, 250, 255, 261, 265, 276, 278, 279, 281, 282, 283], "pole": [7, 76, 77, 80, 81, 84, 88, 94, 233, 234, 235, 236, 239, 240, 246, 250, 276, 282], "magnitude_respons": [7, 37, 59, 84, 94, 196, 197, 198, 199, 200, 201, 218, 236, 254, 255, 257, 276, 277, 279, 281, 283], "omega": [7, 26, 37, 51, 59, 60, 63, 76, 84, 94, 96, 136, 139, 140, 142, 171, 233, 234, 236, 239, 240, 279], "phase_respons": [7, 59, 84, 240, 283], "angl": [7, 148, 240, 279], "phase_delai": [7, 26, 37, 51, 63, 96, 171, 239, 283], "tau_": [7, 26, 37, 51, 63, 96, 171, 239], "phi": [7, 26, 37, 51, 63, 96, 107, 108, 118, 134, 135, 144, 145, 154, 155, 159, 162, 163, 171, 213, 221, 223, 239], "group_delai": [7, 26, 37, 51, 60, 96, 171, 198, 234, 276, 277, 283], "group": [7, 26, 37, 51, 60, 96, 171, 198, 234, 282], "tau_g": [7, 26, 37, 51, 60, 96, 171, 234], "iir": [7, 9, 18, 61, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 125, 131, 233, 234, 235, 236, 239, 240, 246, 250, 276, 279, 282, 283], "q": [8, 134, 144, 164, 165, 166, 167, 168, 170, 171, 173, 177, 180, 201, 267, 283], "comput": [8, 26, 39, 40, 41, 42, 43, 59, 84, 107, 111, 121, 134, 144, 148, 154, 158, 160, 162, 164, 165, 166, 167, 168, 169, 170, 185, 186, 208, 211, 214, 219, 225, 227, 276, 277, 279, 281, 283], "complementari": [8, 164, 165], "cumul": [8, 164, 165], "distribut": [8, 164, 165], "standard": [8, 164, 165], "normal": [8, 9, 11, 16, 125, 129, 132, 164, 165, 196, 197, 199, 200, 212, 215, 218, 233, 234, 236, 238, 239, 240, 245, 254, 255, 257, 279, 281], "mathcal": [8, 39, 164, 165, 166, 167, 168, 169, 170, 186, 204], "qinv": [8, 164, 165, 283], "invers": [8, 165], "closedlooppl": [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 270, 279, 283], "defin": [9, 51, 76, 186, 204, 215, 243, 267, 270, 277, 282], "perform": [9, 27, 52, 97, 158, 160, 198, 205, 264, 267, 270, 276, 277, 280, 282, 283], "close": [9, 16, 18, 270, 282, 283], "loop": [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 125, 126, 127, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143, 270, 282, 283], "pll": [9, 10, 11, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 270, 282, 283], "meant": 9, "analysi": [9, 16, 272, 279, 282, 283], "onli": [9, 27, 35, 52, 58, 59, 64, 69, 73, 84, 89, 97, 105, 108, 135, 145, 155, 161, 163, 181, 186, 196, 197, 199, 200, 214, 217, 218, 242, 255, 265, 274, 279, 280], "block": [9, 26, 37, 94, 96, 125, 136, 171, 202, 203], "bb": [9, 278, 279], "phase_err": [9, 279], "ped": [9, 15, 16, 129, 148, 149, 150, 151, 152, 153, 270, 279], "lf": [9, 279], "phase_est": [9, 279], "lo": [9, 279], "nco": [9, 12, 16, 129, 136, 137, 138, 139, 140, 141, 142, 143, 270, 279, 282, 283], "local": [9, 271, 279], "oscil": [9, 136, 139, 270, 279, 282, 283], "detector": [9, 15, 16, 39, 129, 148, 153, 166, 279, 283], "filter": [9, 13, 14, 16, 18, 26, 27, 28, 31, 32, 33, 35, 36, 37, 38, 51, 52, 53, 54, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 101, 102, 103, 105, 106, 107, 114, 120, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 144, 154, 162, 171, 172, 173, 176, 178, 179, 181, 182, 196, 197, 198, 199, 200, 201, 205, 215, 218, 232, 233, 234, 235, 236, 239, 240, 246, 250, 251, 254, 255, 257, 264, 270, 281, 282, 283], "numer": [9, 136, 139, 270, 277, 279, 282, 283], "control": [9, 136, 139, 254, 257, 270, 279, 282, 283], "The": [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 57, 58, 59, 60, 61, 62, 63, 65, 66, 68, 69, 70, 72, 73, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 101, 102, 103, 104, 106, 107, 108, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 148, 149, 151, 152, 153, 154, 155, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 176, 177, 178, 179, 180, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 271, 272, 273, 274, 276, 277, 279, 280, 281, 282, 284], "transfer": [9, 18, 37, 51, 76, 77, 94, 125, 215, 276, 277, 279], "2nd": [9, 125, 129, 270, 279, 283], "proport": [9, 13, 27, 97, 125, 126, 129, 214, 226, 270, 283], "plu": [9, 125, 129, 270, 283], "z": [9, 37, 51, 76, 94, 125, 136, 202, 203, 267, 276, 277, 279], "k_1": [9, 13, 125, 126, 279], "k_2": [9, 14, 125, 127, 279], "frac": [9, 17, 19, 22, 23, 37, 39, 40, 41, 43, 51, 57, 76, 94, 98, 125, 144, 154, 162, 166, 167, 168, 173, 184, 185, 186, 187, 194, 206, 207, 209, 210, 212, 214, 215, 221, 222, 223, 225, 226, 256, 259, 260, 266, 267, 279], "k_0": [9, 12, 16, 129, 136, 137, 139, 279], "k_p": [9, 15, 16, 129, 148, 153, 279], "refer": [9, 17, 19, 20, 21, 22, 23, 39, 40, 41, 43, 44, 69, 125, 148, 149, 158, 160, 166, 167, 168, 170, 184, 186, 194, 196, 197, 198, 199, 200, 201, 212, 213, 215, 217, 225, 251, 254, 257, 258, 265, 267, 277, 281, 282], "michael": [9, 17, 19, 20, 21, 22, 23, 125, 148, 254, 257], "rice": [9, 17, 19, 20, 21, 22, 23, 125, 148, 254, 257], "digit": [9, 17, 19, 20, 21, 22, 23, 125, 148, 158, 160, 254, 257, 279, 282, 283], "commun": [9, 17, 19, 20, 21, 22, 23, 125, 148, 158, 160, 201, 251, 254, 257, 279, 282], "discret": [9, 17, 19, 20, 21, 22, 23, 37, 94, 125, 148, 186, 204, 210, 254, 257, 260, 269, 275, 279, 282, 283], "approach": [9, 17, 19, 20, 21, 22, 23, 125, 148, 187, 190, 193, 254, 257, 279], "appendix": [9, 125, 254, 257], "lock": [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 125, 126, 127, 128, 129, 130, 131, 132, 133, 136, 137, 138, 139, 140, 141, 142, 143], "exampl": [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 33, 35, 36, 37, 38, 40, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 103, 105, 106, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 141, 142, 143, 144, 148, 154, 158, 159, 160, 161, 162, 164, 165, 167, 169, 171, 174, 175, 179, 181, 182, 184, 186, 187, 188, 189, 190, 191, 192, 193, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 209, 210, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 223, 224, 226, 229, 230, 231, 232, 233, 234, 235, 236, 239, 240, 241, 244, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 279], "see": [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 38, 47, 48, 49, 50, 51, 52, 53, 54, 57, 58, 62, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 85, 87, 88, 89, 90, 92, 93, 95, 105, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 136, 137, 138, 139, 140, 141, 142, 143, 144, 154, 159, 161, 162, 171, 181, 196, 197, 199, 200, 205, 215, 218, 233, 234, 235, 236, 239, 240, 246, 250, 254, 255, 257, 282], "noise_bandwidth": [9, 16, 125, 129, 132], "damping_factor": [9, 16, 125, 129, 130], "creat": [9, 16, 26, 28, 37, 38, 44, 45, 51, 53, 69, 71, 76, 77, 79, 94, 95, 96, 97, 98, 107, 108, 125, 129, 134, 135, 136, 139, 144, 145, 154, 155, 159, 162, 163, 171, 173, 186, 188, 212, 213, 217, 223, 258, 261, 262, 265, 267, 275, 279, 281], "object": [9, 16, 26, 29, 30, 37, 44, 45, 51, 55, 56, 76, 80, 81, 94, 96, 99, 100, 107, 108, 109, 110, 134, 135, 144, 145, 146, 147, 154, 155, 156, 157, 162, 163, 171, 174, 175, 217, 233, 234, 235, 236, 239, 240, 246, 250, 265, 279, 283], "phase_lock_tim": [9, 23], "frequency_lock_tim": [9, 17], "freq_offset": [9, 17, 19], "lock_tim": [9, 19, 279], "phase_error_vari": [9, 22], "cn0": [9, 22], "varianc": [9, 22, 39, 41, 43, 168, 170, 186], "steadi": [9, 22], "state": [9, 22, 26, 27, 35, 37, 51, 52, 58, 64, 65, 67, 69, 73, 74, 76, 89, 90, 92, 94, 96, 97, 105, 171, 181, 283], "sample_r": [9, 16, 24, 26, 59, 60, 63, 84, 96, 97, 134, 144, 154, 162, 171, 205, 213, 223, 232, 233, 234, 236, 238, 239, 240, 241, 242, 245, 248, 261, 262, 264, 275, 279, 281], "bnt": [9, 11, 279], "bandwidth": [9, 10, 11, 16, 20, 125, 129, 132, 187, 196, 197, 215, 254, 257, 279, 281], "b_n": [9, 10, 11, 16, 17, 19, 22, 23, 125, 129, 132], "bn": [9, 10], "hz": [9, 10, 16, 17, 19, 22, 59, 60, 63, 84, 125, 129, 132, 187, 195, 205, 213, 214, 215, 222, 223, 226, 261, 262, 266, 275], "zeta": [9, 16, 25, 125, 129, 130], "damp": [9, 16, 25, 125, 129, 130, 279], "k0": [9, 12, 16, 129, 136, 137, 139], "kp": [9, 15, 16, 129, 279], "k1": [9, 13, 125, 126, 279], "k2": [9, 14, 125, 127, 279], "repres": [9, 18, 189, 190], "omega_n": [9, 21, 279], "natur": [9, 21], "radian": [9, 20, 21, 22, 136, 138, 139, 140, 141, 142, 148, 149, 151, 152, 162, 279], "omega_3db": [9, 20], "3": [9, 17, 19, 20, 23, 26, 33, 36, 37, 39, 40, 44, 55, 56, 59, 80, 81, 84, 94, 96, 97, 103, 106, 134, 136, 144, 154, 158, 159, 160, 161, 162, 166, 167, 171, 174, 175, 179, 182, 184, 186, 187, 188, 189, 191, 192, 195, 196, 197, 198, 199, 200, 201, 204, 205, 206, 207, 209, 210, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 223, 224, 226, 231, 232, 233, 234, 235, 236, 239, 240, 246, 248, 250, 251, 254, 255, 257, 258, 259, 261, 262, 263, 264, 265, 266, 267, 271, 272, 277, 279, 281, 282], "omega_": [9, 20], "textrm": [9, 20], "properti": [10, 11, 12, 13, 14, 15, 18, 20, 21, 24, 25, 31, 32, 33, 34, 36, 57, 62, 65, 67, 68, 72, 74, 75, 82, 83, 85, 87, 88, 90, 92, 93, 101, 102, 103, 104, 106, 112, 117, 118, 119, 120, 122, 123, 124, 126, 127, 130, 131, 132, 137, 140, 141, 153, 159, 161, 176, 177, 178, 179, 180, 182, 183, 283], "paramet": [16, 17, 19, 22, 27, 28, 38, 40, 41, 42, 43, 46, 47, 48, 50, 52, 53, 59, 60, 61, 63, 66, 70, 71, 73, 77, 78, 79, 84, 86, 91, 95, 97, 98, 108, 111, 113, 114, 115, 116, 121, 128, 129, 135, 138, 139, 143, 145, 149, 151, 152, 155, 158, 160, 163, 164, 165, 167, 168, 169, 170, 173, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267], "where": [16, 27, 52, 97, 108, 125, 129, 132, 155, 163, 166, 186, 187, 204, 206, 207, 209, 215, 259, 267, 276, 277, 282], "period": [16, 125, 129, 132, 134, 267], "second": [16, 17, 19, 23, 44, 125, 129, 132, 215], "critic": [16, 25, 125, 129, 130, 279], "underdamp": [16, 25, 125, 129, 130], "overdamp": [16, 25, 125, 129, 130], "ted": [16, 129], "t_": [17, 19, 23, 70, 215, 281], "fl": [17, 19], "delta": [17, 19, 26, 37, 51, 61, 76, 86, 94, 96, 171, 198, 235, 276, 277], "take": [17, 19, 23, 271], "onto": [17, 19, 23], "39": 17, "pl": [19, 23], "38": 19, "34": [20, 248], "33": 21, "sigma_": [22, 39, 40, 42], "theta_": [22, 148, 149], "carrier": [22, 154], "43": 22, "40": [23, 96, 171, 205], "less": [25, 184], "than": [25, 134, 135, 145, 155, 161, 163, 184, 218, 221, 231, 247, 255], "greater": [25, 254, 257], "fir": [26, 27, 28, 29, 30, 31, 33, 35, 36, 37, 38, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 96, 97, 98, 99, 100, 101, 103, 105, 106, 171, 172, 173, 174, 175, 176, 179, 181, 182, 196, 197, 198, 199, 200, 201, 232, 233, 234, 235, 236, 239, 240, 246, 250, 251, 278, 282, 283], "note": [26, 33, 36, 37, 39, 40, 41, 43, 51, 76, 94, 96, 103, 106, 125, 136, 148, 166, 167, 168, 170, 171, 179, 182, 184, 186, 187, 190, 193, 198, 202, 203, 215, 221, 226, 232, 251, 267], "equival": [26, 96, 171, 186, 187, 196, 197, 198, 199, 200, 210, 217, 260, 265, 273, 275], "first": [26, 31, 44, 96, 98, 101, 134, 142, 144, 171, 173, 176, 224, 248, 263, 272, 274], "prototyp": [26, 33, 36, 96, 103, 106, 171, 179, 182], "feedforward": [26, 28, 33, 36, 37, 51, 53, 68, 76, 79, 83, 94, 96, 98, 103, 106, 171, 173, 179, 182, 233, 234, 235, 236, 239, 240, 246, 250, 276, 277], "coeffici": [26, 28, 51, 53, 76, 79, 96, 98, 107, 120, 124, 134, 144, 154, 162, 171, 173, 233, 234, 235, 236, 239, 240, 246, 250, 276, 277], "discard": [26, 171], "each": [26, 27, 52, 96, 97, 171, 212, 220, 238, 242, 245], "instead": [26, 96, 171, 231], "ar": [26, 27, 28, 33, 36, 38, 39, 44, 46, 47, 48, 50, 52, 53, 71, 77, 79, 95, 96, 97, 98, 103, 106, 107, 108, 120, 124, 134, 135, 138, 144, 145, 154, 155, 162, 163, 166, 171, 173, 179, 182, 187, 189, 190, 192, 193, 198, 214, 217, 218, 224, 231, 232, 233, 234, 236, 238, 239, 240, 241, 242, 245, 247, 248, 249, 251, 255, 261, 262, 265, 271, 273, 275, 277, 279, 281, 282, 284], "commut": [26, 96, 171], "parallel": [26, 96, 171], "output": [26, 27, 31, 37, 51, 52, 61, 66, 76, 77, 79, 86, 91, 94, 95, 96, 97, 98, 101, 114, 125, 128, 136, 138, 142, 143, 171, 173, 176, 186, 187, 188, 189, 190, 192, 193, 203, 204, 212, 217, 222, 224, 235, 246, 263, 265, 268, 271, 275, 276, 277, 279], "sum": [26, 39, 51, 76, 166, 281], "prevent": [26, 96, 144, 162, 171], "need": [26, 96, 171, 271, 272, 274], "done": [26, 271], "case": [26, 96, 162, 166, 171], "3x": [26, 96], "6": [26, 33, 36, 37, 44, 55, 56, 80, 81, 84, 94, 96, 97, 103, 106, 134, 136, 144, 154, 161, 162, 167, 168, 170, 171, 179, 182, 184, 191, 195, 198, 204, 205, 206, 207, 212, 214, 216, 217, 220, 222, 226, 231, 232, 233, 234, 235, 236, 239, 240, 246, 247, 248, 250, 251, 254, 257, 261, 262, 264, 265, 267, 271, 272, 273, 274, 276, 277, 279, 280], "9": [26, 33, 36, 59, 84, 96, 97, 103, 106, 134, 144, 154, 162, 167, 171, 179, 182, 184, 191, 204, 212, 216, 217, 220, 251, 254, 257, 265, 271, 277, 278, 280, 281], "v": [26, 136, 195, 222, 271], "5": [26, 33, 36, 37, 39, 40, 41, 42, 43, 44, 55, 56, 59, 94, 96, 97, 103, 106, 134, 136, 144, 154, 162, 167, 169, 171, 179, 182, 184, 186, 189, 191, 192, 193, 196, 197, 198, 199, 200, 204, 205, 206, 207, 209, 210, 212, 213, 214, 215, 216, 217, 220, 221, 226, 229, 232, 233, 234, 235, 236, 239, 240, 246, 248, 250, 251, 254, 257, 258, 259, 260, 261, 262, 264, 265, 267, 271, 275, 276, 277, 278, 279, 280, 281], "7": [26, 29, 30, 33, 36, 96, 97, 99, 100, 103, 106, 134, 144, 148, 154, 161, 162, 167, 171, 179, 182, 184, 191, 198, 199, 201, 204, 212, 216, 217, 220, 251, 265, 267, 271, 277, 279], "8": [26, 33, 36, 37, 40, 42, 59, 80, 81, 84, 94, 96, 97, 103, 106, 108, 134, 135, 136, 144, 145, 148, 154, 155, 158, 159, 160, 161, 162, 163, 167, 169, 171, 179, 182, 184, 186, 187, 188, 190, 191, 193, 196, 197, 198, 199, 200, 201, 204, 205, 212, 214, 215, 216, 217, 218, 220, 223, 226, 230, 231, 232, 233, 234, 235, 236, 239, 240, 241, 244, 246, 247, 248, 249, 250, 251, 254, 255, 257, 261, 262, 264, 265, 267, 276, 277, 278, 279, 281], "summat": 26, "bottom": [26, 96, 171], "top": [26, 96, 171], "adder": [26, 125, 136, 202, 203, 279], "relat": [26, 33, 36, 96, 103, 106, 171, 179, 182, 187, 215], "In": [26, 27, 28, 29, 30, 33, 36, 37, 38, 40, 42, 44, 52, 53, 55, 56, 59, 67, 71, 74, 77, 79, 80, 81, 84, 92, 94, 95, 96, 97, 98, 99, 100, 103, 106, 134, 136, 144, 148, 154, 158, 159, 160, 161, 162, 164, 165, 167, 169, 171, 173, 174, 175, 179, 182, 184, 186, 187, 188, 189, 190, 191, 192, 193, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 209, 210, 212, 213, 214, 215, 216, 217, 218, 220, 221, 222, 223, 224, 226, 229, 230, 231, 232, 233, 234, 235, 236, 239, 240, 241, 244, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 275, 280], "np": [26, 33, 36, 40, 42, 59, 80, 81, 84, 96, 97, 103, 106, 107, 119, 123, 134, 136, 144, 154, 158, 160, 161, 162, 167, 169, 171, 179, 182, 184, 186, 187, 188, 189, 190, 192, 193, 204, 205, 212, 213, 214, 217, 221, 223, 230, 231, 232, 233, 234, 235, 236, 239, 240, 241, 244, 246, 248, 250, 251, 258, 261, 262, 264, 265, 267, 275, 276, 277, 278, 279, 280, 281], "co": [26, 96, 97, 171, 223], "64": [26, 198, 220, 277], "arang": [26, 33, 36, 96, 97, 103, 106, 171, 179, 182, 186, 188, 205, 217, 223, 251, 261, 262, 264, 265, 267, 275, 279], "280": 26, "out": [26, 29, 33, 36, 44, 55, 59, 80, 84, 96, 97, 99, 103, 106, 134, 144, 154, 159, 161, 162, 164, 165, 171, 174, 179, 182, 188, 189, 191, 192, 195, 202, 203, 204, 206, 207, 209, 210, 212, 214, 216, 217, 222, 224, 226, 229, 249, 251, 252, 253, 259, 260, 263, 265, 266], "plt": [26, 37, 40, 42, 94, 96, 97, 134, 136, 144, 148, 154, 158, 159, 160, 161, 162, 167, 169, 171, 184, 186, 187, 188, 190, 193, 196, 197, 198, 199, 200, 201, 205, 212, 213, 214, 215, 217, 218, 221, 223, 230, 231, 232, 233, 234, 235, 236, 239, 240, 241, 244, 246, 247, 248, 250, 254, 255, 257, 258, 261, 262, 264, 265, 267, 275, 276, 277, 278, 279, 280, 281], "figur": [26, 37, 40, 42, 94, 96, 97, 134, 136, 144, 148, 154, 158, 159, 160, 161, 162, 167, 169, 171, 184, 186, 187, 188, 190, 193, 196, 197, 198, 199, 200, 201, 205, 212, 213, 214, 215, 217, 218, 221, 223, 230, 231, 232, 233, 234, 235, 236, 239, 240, 241, 244, 246, 247, 248, 249, 250, 254, 255, 257, 258, 261, 262, 264, 265, 267, 275, 276, 277, 278, 279, 280, 281], "figsiz": [26, 37, 40, 42, 94, 96, 97, 134, 136, 144, 148, 154, 158, 159, 160, 161, 162, 167, 169, 171, 184, 186, 187, 188, 190, 193, 196, 197, 198, 199, 200, 201, 205, 212, 213, 214, 215, 217, 218, 221, 223, 230, 231, 232, 233, 234, 235, 236, 239, 240, 241, 244, 246, 247, 248, 249, 250, 254, 255, 257, 258, 261, 262, 264, 265, 267, 275, 276, 277, 278, 279, 280, 281], "plot": [26, 37, 40, 42, 59, 60, 61, 63, 66, 84, 86, 91, 94, 96, 97, 134, 136, 144, 148, 154, 158, 159, 160, 161, 162, 167, 169, 171, 186, 187, 188, 190, 193, 196, 197, 198, 199, 200, 201, 205, 212, 213, 214, 215, 217, 218, 221, 223, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 254, 255, 257, 258, 261, 262, 264, 265, 267, 275, 276, 277, 279, 280, 281, 282, 283], "marker": [26, 96, 97, 136, 171, 231, 247, 248, 275, 276, 277, 280], "label": [26, 37, 40, 42, 94, 96, 97, 135, 145, 148, 155, 158, 160, 163, 167, 169, 171, 184, 186, 196, 197, 198, 199, 200, 212, 213, 215, 217, 221, 230, 232, 233, 234, 236, 237, 238, 239, 240, 241, 242, 244, 245, 248, 254, 257, 258, 265, 275, 278, 279, 280, 281], "o": [26, 96, 97, 171, 275], "titl": [26, 37, 94, 96, 134, 136, 144, 148, 158, 160, 171, 184, 186, 187, 188, 190, 193, 205, 212, 213, 217, 221, 223, 230, 244, 248, 258, 261, 262, 264, 265, 267, 275, 278, 279, 280, 281], "tight_layout": [26, 37, 94, 96, 134, 136, 144, 148, 158, 160, 171, 184, 186, 187, 188, 190, 193, 205, 212, 213, 214, 217, 223, 230, 244, 248, 258, 261, 262, 264, 265, 267, 278, 279, 280, 281], "preserv": [26, 28, 38, 53, 67, 71, 74, 77, 79, 92, 95, 96, 98, 171, 173, 232, 242], "call": [26, 27, 28, 38, 52, 53, 67, 71, 74, 77, 79, 92, 95, 96, 97, 98, 171, 173], "true": [26, 40, 41, 42, 43, 59, 84, 96, 97, 134, 144, 148, 151, 152, 154, 158, 160, 162, 167, 168, 169, 170, 171, 184, 185, 187, 189, 190, 192, 193, 204, 208, 214, 217, 223, 227, 228, 231, 240, 242, 247, 248, 249, 256, 265, 278, 279, 280], "y1": [26, 96, 97, 171, 221], "70": [26, 220], "y2": [26, 96, 97, 171, 221], "140": [26, 205], "y3": [26, 96, 97, 171], "210": 26, "y4": [26, 96, 171], "y5": [26, 96, 171], "flush": [26, 27, 37, 51, 52, 58, 96, 97, 171, 283], "y_1": [26, 96, 171, 221], "y_2": [26, 96, 171, 221], "y_3": [26, 96, 171], "y_4": [26, 96, 171], "y_5": [26, 96, 171], "__call__": [26, 27, 28, 37, 38, 51, 52, 53, 67, 69, 70, 71, 74, 76, 77, 78, 79, 92, 94, 95, 96, 97, 98, 125, 128, 136, 138, 148, 149, 171, 172, 173, 283], "full": [26, 27, 52, 96, 97, 171, 172, 188, 217, 265], "__len__": [26, 37, 51, 54, 96, 171], "__repr__": [26, 29, 37, 51, 55, 76, 80, 94, 96, 99, 107, 109, 134, 144, 146, 154, 156, 162, 171, 174], "style": [26, 29, 37, 51, 55, 76, 80, 94, 96, 99, 107, 109, 134, 144, 146, 154, 156, 162, 171, 174, 249], "__str__": [26, 30, 37, 51, 56, 76, 81, 94, 96, 100, 107, 110, 134, 144, 147, 154, 157, 162, 171, 175], "human": [26, 30, 37, 51, 56, 76, 81, 94, 96, 100, 107, 110, 134, 144, 147, 154, 157, 162, 171, 175], "readabl": [26, 30, 37, 51, 56, 76, 81, 94, 96, 100, 107, 110, 134, 144, 147, 154, 157, 162, 171, 175], "reset": [26, 35, 37, 51, 64, 69, 73, 76, 89, 94, 96, 105, 125, 133, 136, 142, 171, 181], "when": [26, 35, 37, 51, 58, 61, 64, 66, 76, 86, 89, 91, 94, 96, 105, 171, 181, 186, 187, 189, 190, 192, 193, 210, 217, 233, 234, 235, 236, 239, 240, 246, 260, 265, 267, 275, 276, 277], "pass": [26, 37, 51, 58, 96, 171, 186, 189, 192, 204, 212, 230, 231, 232, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 250, 269, 271, 273, 276, 277, 283], "through": [26, 37, 51, 58, 96, 144, 162, 171, 189, 192, 204, 269, 276, 277, 279], "indic": [26, 28, 31, 37, 38, 41, 42, 43, 51, 53, 67, 69, 71, 74, 76, 77, 79, 92, 94, 95, 96, 98, 101, 107, 108, 134, 135, 144, 145, 154, 155, 158, 160, 162, 163, 167, 168, 169, 170, 171, 173, 176, 185, 208, 215, 218, 221, 223, 227, 228, 232, 240, 241, 242, 248, 254, 255, 256, 257, 265], "whether": [26, 28, 37, 38, 41, 42, 43, 51, 53, 67, 69, 71, 74, 76, 77, 79, 92, 94, 95, 96, 98, 158, 160, 167, 168, 169, 170, 171, 173, 185, 208, 223, 227, 228, 240, 242, 248, 256], "consist": [26, 37, 46, 47, 48, 49, 50, 51, 65, 96, 171], "previou": [26, 28, 37, 38, 51, 53, 65, 71, 73, 77, 79, 95, 96, 98, 171, 173, 202, 203], "u": [26, 37, 51, 66, 76, 91, 94, 96, 171, 184, 246, 267, 268, 276, 277], "frequency_respons": [26, 37, 51, 59, 76, 84, 94, 96, 171, 283], "numpi": [26, 37, 51, 59, 76, 84, 94, 96, 138, 171, 186, 189, 192, 204, 263, 275, 276, 277, 278, 279, 280, 281, 282], "float64": [26, 37, 51, 59, 76, 84, 94, 96, 136, 138, 171, 188, 217, 265, 268], "complex128": [26, 37, 51, 59, 76, 84, 94, 96, 136, 138, 171], "custom": [26, 32, 96, 102, 108, 145, 155, 163, 171, 178, 196, 197, 199, 200, 283], "multir": [26, 27, 28, 32, 96, 97, 98, 102, 171, 173, 178, 201, 251, 283], "polyphase_tap": [26, 30, 33, 36, 96, 97, 100, 103, 106, 171, 175, 179, 182], "index": [26, 31, 69, 73, 96, 101, 107, 134, 144, 154, 162, 171, 176, 217, 232, 241, 242, 247, 265, 268, 271], "correspond": [26, 31, 44, 49, 96, 101, 171, 176, 242], "mode": [27, 28, 35, 38, 52, 53, 58, 64, 67, 69, 71, 73, 74, 77, 79, 89, 92, 95, 97, 98, 105, 172, 173, 181, 188, 217, 265, 267], "l": [27, 52, 78, 97, 198], "stream": [27, 28, 29, 30, 35, 38, 52, 53, 55, 56, 58, 64, 67, 69, 71, 73, 74, 77, 79, 80, 81, 89, 92, 95, 97, 98, 99, 100, 105, 134, 144, 154, 162, 173, 174, 175, 181, 277], "convolut": [27, 52, 96, 97], "ha": [27, 52, 96, 97, 134, 144, 154, 186, 196, 197, 198, 199, 200, 205, 214, 215, 226, 264, 267, 279, 280, 281], "align": [27, 52, 97, 98, 144, 173, 217, 265, 275], "howev": [27, 46, 47, 48, 50, 52, 97, 125, 190, 193, 217, 265, 275], "produc": [27, 52, 96, 97, 171, 215, 281], "final": [27, 52, 97], "dictat": [27, 52, 97], "argument": [27, 28, 52, 97, 98, 173, 230, 231, 232, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 250, 276, 277], "specif": [28, 49, 59, 84, 98, 173, 274, 281], "npt": [28, 59, 84, 98, 108, 135, 145, 155, 163, 173, 196, 197, 199, 200, 233, 234, 235, 236, 239, 240, 246, 250], "string": [29, 30, 55, 56, 80, 81, 99, 100, 108, 109, 110, 145, 146, 147, 155, 156, 157, 163, 174, 175, 220, 238, 245, 283], "represent": [29, 30, 55, 56, 80, 81, 99, 100, 109, 110, 146, 147, 156, 157, 174, 175, 247, 283], "print": [30, 56, 81, 100, 175, 220, 275, 276, 277, 279], "167": [30, 100], "24": [30, 100, 175], "shape": [30, 56, 81, 97, 100, 107, 108, 114, 116, 119, 120, 124, 134, 144, 145, 154, 155, 162, 163, 175, 215, 218, 232, 248, 254, 255, 257, 277, 282, 283], "12": [30, 96, 134, 144, 154, 162, 168, 170, 184, 191, 201, 216, 251, 276, 280, 283], "befor": [33, 36, 103, 106, 179, 182, 284], "decomposit": [33, 36, 103, 106, 179, 182, 283], "after": [33, 36, 103, 106, 179, 182], "10": [33, 36, 37, 40, 42, 44, 94, 96, 97, 103, 106, 108, 134, 144, 145, 154, 155, 158, 160, 162, 163, 167, 169, 171, 179, 182, 184, 185, 186, 191, 195, 196, 197, 199, 200, 204, 206, 207, 208, 209, 210, 213, 214, 215, 216, 217, 218, 220, 221, 222, 223, 225, 226, 227, 228, 230, 231, 233, 234, 235, 236, 239, 240, 244, 246, 248, 250, 251, 254, 255, 256, 257, 258, 259, 260, 265, 275, 276, 277, 278, 279, 280, 281], "puls": [37, 94, 107, 108, 114, 116, 119, 120, 124, 134, 144, 145, 154, 155, 162, 163, 215, 218, 232, 248, 254, 255, 257, 282, 283], "deriv": 37, "d": [37, 51, 57, 211, 214, 219, 226, 271, 273, 282], "lfloor": [37, 51, 57], "rfloor": [37, 51, 57], "null": [39, 166, 281], "altern": [39, 166, 277], "hypothes": [39, 166], "follow": [39, 44, 107, 134, 144, 154, 162, 221, 231, 242, 245, 247, 249, 251, 279], "assum": [39, 166, 186, 204, 224, 248, 263], "valu": [39, 107, 108, 111, 121, 134, 135, 144, 145, 154, 155, 158, 160, 162, 163, 164, 165, 188, 195, 202, 203, 215, 217, 221, 222, 231, 234, 236, 239, 240, 247, 265, 277, 283], "random": [39, 134, 144, 154, 162, 186, 189, 192, 204, 212, 213, 221, 231, 232, 241, 248, 258, 278, 279, 280], "process": [39, 40, 41, 43, 166, 167, 168, 170, 201, 251, 277, 279, 282], "w": [39, 166, 186, 275, 276, 277, 278, 279, 280, 281], "sigma": [39, 40, 41, 42, 43, 166, 167, 168, 169, 170, 186, 187], "_0": [39, 166], "_1": [39, 166], "test": [39, 166, 273, 282], "statist": [39, 40, 41, 43, 166, 167, 168, 170], "limits_": [39, 51, 76, 166], "left": [39, 40, 41, 76, 144, 148, 154, 162, 166, 167, 168, 170, 184, 185, 186, 187, 208, 211, 212, 214, 215, 221, 223, 226, 227, 228, 256, 267], "right": [39, 40, 41, 76, 144, 148, 154, 162, 166, 167, 168, 170, 184, 185, 186, 187, 208, 211, 212, 214, 215, 221, 223, 226, 227, 228, 256, 267], "gamma": [39, 41, 43, 166, 168, 170, 184], "sim": [39, 166, 186, 272], "chi_": [39, 40, 41], "2n": [39, 40, 41], "text": [39, 162, 166, 184, 185, 186, 187, 190, 193, 194, 195, 201, 212, 213, 214, 222, 225, 227, 228, 256, 258], "under": [39, 166], "detect": [39, 40, 41, 42, 43, 148, 149, 151, 152, 166, 167, 168, 169, 170, 184, 237, 243, 283], "threshold": [39, 41, 43, 166, 168, 170], "q_": [39, 40, 41, 43], "chi_n": [39, 40, 41, 43], "steven": [39, 40, 41, 43, 166, 167, 168, 170], "kai": [39, 40, 41, 43, 166, 167, 168, 170], "fundament": [39, 40, 41, 43, 166, 167, 168, 170], "theori": [39, 40, 41, 43, 166, 167, 168, 170], "section": [39, 46, 47, 48, 49, 50, 148, 166, 277, 279], "static": [39, 40, 41, 42, 43, 166, 167, 168, 169, 170, 272], "n_nc": [39, 40, 41, 42, 43, 184], "number": [40, 41, 42, 43, 44, 46, 47, 50, 59, 60, 61, 63, 66, 84, 86, 91, 107, 108, 112, 122, 134, 135, 143, 144, 145, 151, 152, 154, 155, 162, 163, 184, 186, 189, 192, 204, 206, 207, 209, 215, 218, 220, 224, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 245, 246, 251, 254, 255, 257, 259, 263], "For": [40, 41, 43, 167, 168, 170, 186, 205, 214, 264, 271, 276], "linspac": [40, 59, 84, 158, 160, 167, 187, 190, 193, 214, 230, 244, 277, 278, 279, 280], "20": [40, 42, 96, 97, 134, 136, 144, 154, 162, 167, 171, 184, 187, 189, 192, 195, 204, 212, 213, 220, 221, 222, 228, 251, 256, 264, 278, 280, 283], "101": [40, 42, 167, 169, 196, 197, 199, 200], "25": [40, 189, 192, 198, 204, 229, 232, 252, 253, 275, 278, 279, 281], "1e": [40, 167, 213, 280], "sigma2": [41, 43, 168, 170], "If": [42, 73, 108, 138, 145, 155, 163, 169, 171, 185, 186, 187, 204, 208, 224, 227, 228, 231, 232, 233, 234, 235, 236, 238, 239, 240, 241, 242, 245, 246, 247, 248, 256, 261, 263, 282], "logspac": [42, 59, 84, 169, 184], "theoret": [42, 158, 160, 230, 244, 280, 283], "variou": [42, 272, 281], "100": [42, 59, 76, 84, 86, 91, 94, 136, 158, 160, 184, 186, 187, 190, 193, 195, 196, 197, 199, 200, 212, 222, 223, 230, 232, 233, 235, 241, 244, 246, 258, 261, 262, 264, 275, 279], "1_000": [42, 186, 213, 214, 221, 258, 278], "000": [42, 213], "5_000": 42, "measur": [44, 46, 148, 151, 152, 185, 186, 194, 195, 208, 211, 212, 219, 222, 225, 227, 228, 256, 279, 282, 283], "new": [44, 45, 69, 71, 107, 108, 134, 135, 144, 145, 154, 155, 162, 163, 258], "accumul": [44, 136, 138, 139, 140, 142, 279], "from": [44, 60, 63, 76, 77, 94, 98, 107, 123, 134, 144, 154, 161, 162, 173, 195, 206, 207, 209, 210, 222, 229, 238, 245, 252, 253, 259, 260, 271, 276, 277, 279, 282], "contain": [44, 186, 220], "add": [44, 46, 49, 134, 144, 154, 162, 186, 213, 218, 242, 255, 258, 269, 280, 284], "total": [44, 215, 218, 254, 255, 257, 281], "count": [44, 47, 212], "error_r": [44, 48, 49, 280], "everi": [44, 275], "can": [44, 46, 47, 48, 50, 125, 134, 186, 212, 215, 217, 224, 232, 238, 245, 265, 273, 276, 277, 280, 282, 284], "obtain": 44, "tabul": [44, 45], "all": [44, 49, 138, 212, 232, 241, 242, 272, 274, 282], "ascend": [44, 49], "other": [46, 47, 48, 50, 275, 284], "quantiti": [46, 47, 48, 49, 50], "user": [46, 47, 48, 50, 276, 277], "caution": [46, 47, 48, 50], "instanc": [46, 47, 48, 50, 134], "transmit": [46, 107, 124, 134, 144, 148, 149, 154, 162, 212, 232], "e": [49, 136, 148, 166, 167, 168, 169, 170, 185, 189, 190, 208, 267, 272, 273, 276, 277, 280], "whatev": 49, "wa": [49, 187], "provid": [49, 107, 111, 121, 134, 144, 154, 158, 160, 162, 242, 272, 282], "wrapper": [51, 76], "scipi": [51, 76, 196, 197, 199, 200, 238, 245, 281, 282], "convolv": 51, "It": [51, 76, 96, 108, 125, 145, 155, 163, 186, 232], "support": [51, 76, 283], "one": [51, 76, 135, 144, 145, 155, 161, 163, 215, 220, 232, 233, 234, 236, 238, 239, 240, 245, 261, 276, 277, 278, 281], "its": [51, 76, 77, 94, 186, 276, 277, 281], "sum_": [51, 76, 168, 170, 185, 186, 187, 208, 211, 212, 219, 256], "valid": [52, 214, 232, 241, 242, 267], "same": [52, 97, 148, 248, 276], "0013559842808217807": [55, 56], "005995136544658217": [55, 56], "008698817681933214": [55, 56], "0024103767414047302": [55, 56], "010205586837665018": [55, 56], "018983779931504997": [55, 56], "011950905288150394": [55, 56], "01518393864077397": [55, 56], "051622191325047306": [55, 56], "07210389837804473": [55, 56], "04745944982876247": [55, 56], "039173517569276436": [55, 56], "17918683372907862": [55, 56], "3367363220550604": [55, 56], "4611457574513795": [55, 56], "5084040873607553": [55, 56], "30": [56, 96, 171, 205, 233, 235, 246, 261, 262, 277, 283], "31": [56, 276], "15": [56, 134, 169, 191, 216, 217, 251, 264, 265], "remain": [58, 205, 224], "1024": [59, 60, 63, 84, 233, 234, 236, 239, 240, 278, 281], "whole": [59, 84, 281], "decad": [59, 84, 233, 234, 236, 239, 240, 276, 279], "point": [59, 84, 151, 152, 238, 245], "endpoint": [59, 84, 277], "includ": [59, 84, 272, 273, 274, 282], "integ": [59, 84, 224], "maximum": [59, 84, 107, 113, 114, 134, 144, 154, 162, 215, 218, 231, 247, 254, 255, 257], "max_f": [59, 84], "log10": [59, 84], "evenli": [59, 84], "00000000e": [59, 84, 161, 162, 277], "00": [59, 84, 161, 162, 277], "76562500e": [59, 84], "04": [59, 84, 220, 277], "95312500e": [59, 84], "03": [59, 84, 220, 277], "97070312e": [59, 84], "01": [59, 84, 161, 162, 220, 277, 279], "98046875e": [59, 84], "99023438e": [59, 84], "95337172": 59, "30202676j": 59, "8178049": 59, "5759632j": 59, "6058636": 59, "79630028j": 59, "rad": [59, 84], "0000000000000002": 59, "0j": [59, 84, 135, 145, 155, 163], "sever": [59, 84], "200": [59, 84, 205, 275, 280], "300": [59, 84, 261, 262], "400": [59, 84, 205, 275], "1000": [59, 84, 134, 144, 151, 152, 154, 162, 212, 214, 261, 262, 280], "00391660e": 59, "14686183e": 59, "17j": 59, "53081763e": 59, "88127210e": 59, "62720131e": 59, "03715849e": 59, "83622458e": 59, "27280811e": 59, "resampl": [69, 70, 71, 72, 73, 74, 75, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 201, 251, 282, 283], "http": [69, 184, 194, 196, 197, 198, 199, 200, 201, 215, 217, 225, 265, 267, 271, 272, 273], "wirelesspi": 69, "com": [69, 184, 196, 197, 198, 199, 200, 201, 215, 217, 265, 272, 273], "structur": 69, "should": [73, 134, 232, 273], "equal": [73, 134], "three": [73, 275, 281], "lfilter": 76, "b_i": [76, 79, 83, 94, 233, 234, 235, 236, 239, 240, 246, 250, 277], "feedback": [76, 79, 82, 94, 233, 234, 235, 236, 239, 240, 246, 250, 277], "a_j": [76, 79, 82, 94, 233, 234, 235, 236, 239, 240, 246, 250, 277], "These": [76, 144, 154, 162, 249, 273, 279], "differ": [76, 135, 145, 155, 161, 163, 196, 197, 198, 199, 200, 217, 248, 265, 267, 281], "a_0": 76, "classmethod": [76, 77, 94], "zerospol": [76, 77, 80, 81, 84, 94, 233, 234, 235, 236, 239, 240, 246, 250, 277], "self": [76, 77, 94], "b_tap": [76, 81, 83, 94, 277], "a_tap": [76, 81, 82, 94, 277], "exp": [80, 81, 84, 138, 144, 154, 162, 205, 215, 221, 223, 233, 234, 235, 236, 239, 240, 246, 250, 262, 264, 267, 275, 277, 279], "1j": [80, 81, 84, 205, 223, 233, 234, 235, 236, 239, 240, 246, 250, 262, 264, 275, 277, 279], "conj": [80, 81, 84, 233, 234, 235, 236, 239, 240, 246, 250, 277, 279], "478207252018059": [80, 81, 277], "6400000000000001": [80, 81, 277], "7391036260090295": [81, 277], "3061467458920719j": [81, 277], "4722987": 84, "47271105": 84, "0041658j": 84, "47394825": 84, "00830241j": 84, "47601067": 84, "01238051j": 84, "472298696877605": 84, "36961426": 84, "9678537j": 84, "57338213": 84, "77694738j": 84, "52496713": 84, "3885743j": 84, "51520024": 84, "1706839j": 84, "insert": [96, 171], "multipli": [96, 171], "hold": [96, 98, 171, 173, 224, 283], "recommend": 96, "wai": [96, 273], "11": [96, 134, 144, 154, 162, 191, 201, 216, 217, 251, 265, 271], "zoh": [96, 98, 102, 171, 173, 178], "13": [96, 134, 144, 154, 162, 166, 167, 168, 170, 188, 191, 216, 248, 251, 283], "matlab": [96, 98, 102, 171, 173, 178, 282], "iter": 97, "concaten": [97, 277], "linearli": [98, 173], "2r": 98, "ramp": [98, 125, 173], "advanc": [98, 173], "ones": [98, 173, 196, 197, 199, 200, 279], "84": 100, "modul": [107, 108, 116, 117, 119, 134, 136, 144, 145, 148, 151, 152, 154, 155, 158, 160, 162, 163, 206, 207, 209, 212, 230, 232, 241, 244, 247, 248, 259, 271, 274, 280, 282, 283], "nomenclatur": [107, 134, 144, 154, 162], "variabl": [107, 134, 136, 138, 144, 154, 162, 220, 279], "name": [107, 134, 144, 154, 162], "decis": [107, 113, 114, 134, 144, 148, 149, 152, 154, 162, 232, 279], "tild": [107, 113, 114, 134, 144, 148, 149, 154, 162], "map_symbol": [107, 115, 134, 144, 154, 162, 186, 212, 213, 221, 231, 232, 258, 278, 279, 280, 283], "decide_symbol": [107, 113, 134, 144, 154, 162, 279, 280, 283], "a_tild": [107, 113, 134, 144, 154, 162, 279, 280], "likelihood": [107, 113, 114, 134, 144, 154, 162], "mle": [107, 113, 134, 144, 154, 162], "match": [107, 108, 114, 120, 134, 144, 145, 154, 155, 162, 163, 283], "abstract": [107, 111, 121], "log_2": [107, 112, 134, 144, 154, 162, 187, 206, 207, 209, 259], "phase_offset": [107, 108, 118, 134, 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283, "move": 283, "model": 283, "replac": 283, "pylint": 283, "black": 283, "improv": 283, "septemb": 283, "sensibl": 283, "august": 283, "27": 283, "without": 283, "superflu": 283, "translat": 283, "fix": [283, 284], "juli": 283, "firinterpol": 283, "impair": 283, "fpsl": 283, "helper": 283, "synthes": 283, "semant": 284, "major": 284, "minor": 284, "patch": 284, "introduc": 284, "featur": 284, "backward": 284, "compat": 284, "bug": 284, "There": 284, "guarante": 284, "them": 284}, "objects": {"": [[3, 0, 0, 1, "sdr", ""]], "sdr": [[9, 1, 1, "", "ClosedLoopPLL", "A class that defines the performance of a closed-loop PLL."], [26, 1, 1, "", "Decimator", "Implements a polyphase decimating FIR filter."], [37, 1, 1, "", "Differentiator", "Implements a differentiator FIR filter."], [39, 1, 1, "", "EnergyDetector", "Implements an energy detector."], [44, 1, 1, "", "ErrorRate", "A class for measuring bit error rates (BER) or symbol error rates (SER)."], [51, 1, 1, "", "FIR", "Implements a finite impulse response (FIR) filter."], [69, 1, 1, "", "FarrowResampler", "Implements a cubic Farrow arbitrary resampler."], [76, 1, 1, "", "IIR", "Implements an infinite impulse response (IIR) filter."], [94, 1, 1, "", "Integrator", "Implements an integrator IIR filter."], [96, 1, 1, "", "Interpolator", "Implements a polyphase interpolating FIR filter."], [107, 1, 1, "", "LinearModulation", "Implements linear phase/amplitude modulation with arbitrary symbol mapping."], [125, 1, 1, "", "LoopFilter", "Implements a 2nd order, proportional-plus-integrator (PPI) loop filter."], [134, 1, 1, "", "MSK", "Implements minimum-shift keying (MSK) modulation and demodulation."], [136, 1, 1, "", "NCO", "Implements a numerically-controlled oscillator (NCO)."], [144, 1, 1, "", "OQPSK", "Implements offset quadrature phase-shift keying (OQPSK) modulation and demodulation."], [148, 1, 1, "", "PED", "Implements a heuristic phase error detector (PED)."], [154, 1, 1, "", "PSK", "Implements phase-shift keying (PSK) modulation and demodulation."], [162, 1, 1, "", "PiMPSK", "Implements $pi/M$ phase-shift keying ($pi/M$ PSK) modulation and demodulation."], [164, 5, 1, "", "Q", "Computes the complementary cumulative distribution function $Q(x)$ of the standard normal distribution $mathcal{N}(0, 1)$."], [165, 5, 1, "", "Qinv", "Computes the inverse complementary cumulative distribution function $Q^{-1}(p)$ of the standard normal distribution $mathcal{N}(0, 1)$."], [166, 1, 1, "", "ReplicaCorrelator", "Implements an clairvoyant replica-correlator detector."], [171, 1, 1, "", "Resampler", "Implements a polyphase rational resampling FIR filter."], [184, 5, 1, "", "albersheim", "Estimates the minimum required single-sample SNR, given $N_{NC}$ non-coherent combinations, to achieve a probability of detection $P_D$ and probability of false alarm $P_{FA}$. This function implements Albersheim's equation."], [185, 5, 1, "", "average_power", "Measures the average power of a time-domain signal $x[n]$."], [186, 5, 1, "", "awgn", "Adds additive white Gaussian noise (AWGN) to the time-domain signal $x[n]$."], [187, 5, 1, "", "awgn_capacity", "Calculates the capacity of an additive white Gaussian noise (AWGN) channel."], [188, 5, 1, "", "barker", "Returns the Barker code/sequence of length $N$."], [189, 5, 1, "", "bec", "Passes the binary input sequence $x$ through a binary erasure channel (BEC) with erasure probability $p$."], [190, 5, 1, "", "bec_capacity", "Calculates the capacity of a binary erasure channel (BEC)."], [191, 5, 1, "", "binary_code", "Generates a binary code of length $2^n$."], [192, 5, 1, "", "bsc", "Passes the binary input sequence $x$ through a binary symmetric channel (BSC) with transition probability $p$."], [193, 5, 1, "", "bsc_capacity", "Calculates the capacity of a binary symmetric channel (BSC)."], [194, 5, 1, "", "crest_factor", "Measures the crest factor of a time-domain signal $x[n]$."], [195, 5, 1, "", "db", "Converts from linear units to decibels."], [196, 5, 1, "", "design_bandpass_fir", "Designs a bandpass FIR filter impulse response $h[n]$ using the window method."], [197, 5, 1, "", "design_bandstop_fir", "Designs a bandstop FIR filter impulse response $h[n]$ using the window method."], [198, 5, 1, "", "design_frac_delay_fir", "Designs a fractional delay FIR filter impulse response $h[n]$ using the Kaiser window method."], [199, 5, 1, "", "design_highpass_fir", "Designs a highpass FIR filter impulse response $h[n]$ using the window method."], [200, 5, 1, "", "design_lowpass_fir", "Designs a lowpass FIR filter impulse response $h[n]$ using the window method."], [201, 5, 1, "", "design_multirate_fir", "Designs a multirate FIR filter impulse response $h[n]$ using the Kaiser window method."], [202, 5, 1, "", "diff_decode", "Differentially decodes the input data $y[k]$."], [203, 5, 1, "", "diff_encode", "Differentially encodes the input data $x[k]$."], [204, 5, 1, "", "dmc", "Passes the input sequence $x$ through a discrete memoryless channel (DMC) with transition probability matrix $P$."], [205, 5, 1, "", "downsample", "Downsamples the time-domain signal $x[n]$ by the factor $r$."], [206, 5, 1, "", "ebn0_to_esn0", "Converts from $E_b/N_0$ to $E_s/N_0$."], [207, 5, 1, "", "ebn0_to_snr", "Converts from $E_b/N_0$ to $S/N$."], [208, 5, 1, "", "energy", "Measures the energy of a time-domain signal $x[n]$."], [209, 5, 1, "", "esn0_to_ebn0", "Converts from $E_s/N_0$ to $E_b/N_0$."], [210, 5, 1, "", "esn0_to_snr", "Converts from $E_s/N_0$ to $S/N$."], [211, 5, 1, "", "euclidean", "Measures the Euclidean distance between two signals $x[n]$ and $y[n]$."], [212, 5, 1, "", "evm", "Calculates the error-vector magnitude (EVM) of the complex symbols $hat{x}[k]$."], [213, 5, 1, "", "frequency_offset", "Applies a frequency and phase offset to the time-domain signal $x[n]$."], [214, 5, 1, "", "fspl", "Calculates the free-space path loss (FSPL) in dB."], [215, 5, 1, "", "gaussian", "Returns a Gaussian pulse shape."], [216, 5, 1, "", "gray_code", "Generates a Gray code of length $2^n$."], [217, 5, 1, "", "hadamard", "Returns the Hadamard code/sequence of length $N$."], [218, 5, 1, "", "half_sine", "Returns a half-sine pulse shape."], [219, 5, 1, "", "hamming", "Measures the Hamming distance between two signals $x[n]$ and $y[n]$."], [220, 5, 1, "", "hexdump", "Returns a hexdump of the specified data."], [221, 5, 1, "", "iq_imbalance", "Applies IQ imbalance to the complex time-domain signal $x[n]$."], [222, 5, 1, "", "linear", "Converts from decibels to linear units."], [223, 5, 1, "", "mix", "Mixes the time-domain signal $x[n]$ with a complex exponential or real sinusoid."], [224, 5, 1, "", "pack", "Packs a binary array into an array with multiple bits per element."], [225, 5, 1, "", "papr", "Measures the peak-to-average power ratio (PAPR) of a time-domain signal $x[n]$."], [226, 5, 1, "", "parabolic_antenna", "Calculates the gain $G$ and beamwidth $theta$ of a parabolic reflector."], [227, 5, 1, "", "peak_power", "Measures the peak power of a time-domain signal $x[n]$."], [228, 5, 1, "", "peak_voltage", "Measures the peak voltage of a time-domain signal $x[n]$."], [229, 5, 1, "", "percent", "Converts from a ratio to a percentage."], [251, 5, 1, "", "polyphase_decompose", "Decomposes the FIR filter taps $h_i$ into the polyphase matrix $H_{i, j}$ with $B$ phases."], [252, 5, 1, "", "ppb", "Converts from a ratio to parts per billion (ppb)."], [253, 5, 1, "", "ppm", "Converts from a ratio to parts per million (ppm)."], [254, 5, 1, "", "raised_cosine", "Returns a raised cosine (RC) pulse shape."], [255, 5, 1, "", "rectangular", "Returns a rectangular pulse shape."], [256, 5, 1, "", "rms_voltage", "Measures the root-mean-square (RMS) voltage of a time-domain signal $x[n]$."], [257, 5, 1, "", "root_raised_cosine", "Returns a square root raised cosine (SRRC) pulse shape."], [258, 5, 1, "", "sample_rate_offset", "Applies a sample rate offset to the time-domain signal $x[n]$."], [259, 5, 1, "", "snr_to_ebn0", "Converts from $S/N$ to $E_b/N_0$."], [260, 5, 1, "", "snr_to_esn0", "Converts from $S/N$ to $E_s/N_0$."], [261, 5, 1, "", "to_complex_bb", "Converts the real passband signal $x_r[n]$ centered at $f_{s,r}/4$ with sample rate $f_{s,r}$ to a complex baseband signal $x_c[n]$ centered at $0$ with sample rate $f_{s,c} = f_{s,r}/2$."], [262, 5, 1, "", "to_real_pb", "Converts the complex baseband signal $x_c[n]$ centered at $0$ with sample rate $f_{s,c}$ to a real passband signal $x_r[n]$ centered at $f_{s,r}/4$ with sample rate $f_{s,r} = 2f_{s,c}$."], [263, 5, 1, "", "unpack", "Unpacks an array with multiple bits per element into a binary array."], [264, 5, 1, "", "upsample", "Upsamples the time-domain signal $x[n]$ by the factor $r$."], [265, 5, 1, "", "walsh", "Returns the Walsh code/sequence of length $N$."], [266, 5, 1, "", "wavelength", "Calculates the wavelength $lambda$ of an electromagnetic wave with frequency $f$."], [267, 5, 1, "", "zadoff_chu", "Returns the root-$u$ Zadoff-Chu sequence of length $N$."]], "sdr.ClosedLoopPLL": [[10, 2, 1, "", "Bn", "The noise bandwidth $B_n$ of the PLL in Hz."], [11, 2, 1, "", "BnT", "The normalized noise bandwidth $B_n T$ of the PLL."], [12, 2, 1, "", "K0", "The NCO gain $K_0$."], [13, 2, 1, "", "K1", "The proportional gain $K_1$ of the loop filter."], [14, 2, 1, "", "K2", "The integral gain $K_2$ of the loop filter."], [15, 2, 1, "", "Kp", "The phase error detector (PED) gain $K_p$."], [16, 3, 1, "", "__init__", "Creates a closed-loop PLL analysis object."], [17, 3, 1, "", "frequency_lock_time", "Returns the frequency lock time of the PLL."], [18, 2, 1, "", "iir", "The IIR filter that represents the closed-loop transfer function of the PLL."], [19, 3, 1, "", "lock_time", "Returns the lock time of the PLL."], [20, 2, 1, "", "omega_3dB", "The 3-dB bandwidth $omega_{3textrm{dB}}$ of the PLL in radians/s."], [21, 2, 1, "", "omega_n", "The natural frequency $omega_n$ of the PLL in radians/s."], [22, 3, 1, "", "phase_error_variance", "Returns the variance of the phase error of the PLL in steady state."], [23, 3, 1, "", "phase_lock_time", "Returns the phase lock time of the PLL."], [24, 2, 1, "", "sample_rate", "The sample rate $f_s$ of the PLL in samples/s."], [25, 2, 1, "", "zeta", "The damping factor $zeta$ of the PLL."]], "sdr.ClosedLoopPLL.__init__": [[16, 4, 2, "p-K0", "K0", "The NCO gain $K_0$."], [16, 4, 2, "p-Kp", "Kp", "The gain $K_p$ of the phase error detector (PED) or time error detector (TED)."], [16, 4, 2, "p-damping_factor", "damping_factor", "The damping factor $zeta$ of the loop filter. $zeta = 1$ is critically damped, $zeta < 1$ is underdamped, and $zeta > 1$ is overdamped."], [16, 4, 2, "p-noise_bandwidth", "noise_bandwidth", "The normalized noise bandwidth $B_n T$ of the loop filter, where $B_n$ is the noise bandwidth in Hz and $T$ is the sampling period in seconds."], [16, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the PLL in Hz."]], "sdr.ClosedLoopPLL.frequency_lock_time": [[17, 4, 2, "p-freq_offset", "freq_offset", "The frequency offset $Delta f$ of the input signal in Hz."]], "sdr.ClosedLoopPLL.lock_time": [[19, 4, 2, "p-freq_offset", "freq_offset", "The frequency offset $Delta f$ of the input signal in Hz."]], "sdr.ClosedLoopPLL.phase_error_variance": [[22, 4, 2, "p-cn0", "cn0", "The carrier-to-noise density ratio $C/N_0$ of the input signal in dB-Hz."]], "sdr.Decimator": [[27, 3, 1, "", "__call__", "Filters and decimates the input signal $x[n]$ with the polyphase FIR filter."], [28, 3, 1, "", "__init__", "Creates a polyphase FIR decimating filter."], [29, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [30, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [31, 2, 1, "", "delay", "The delay of FIR filter in samples. The delay indicates the output sample index that corresponds to the first input sample."], [32, 2, 1, "", "method", "The method used to design the multirate filter."], [33, 2, 1, "", "polyphase_taps", "The polyphase feedforward taps $h_{i, j}$."], [34, 2, 1, "", "rate", "The decimation rate $r$."], [35, 3, 1, "", "reset", "Resets the filter state. Only useful when using streaming mode."], [36, 2, 1, "", "taps", "The prototype feedforward taps $h_i$."]], "sdr.Decimator.__call__": [[27, 4, 2, "p-mode", "mode", "The non-streaming convolution mode."], [27, 4, 2, "p-x", "x", "The input signal $x[n]$ with sample rate $f_s$ and length $L$."]], "sdr.Decimator.__init__": [[28, 4, 2, "p-rate", "rate", "The decimation rate $r$."], [28, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs are preserved between calls to __call__()."], [28, 4, 2, "p-taps", "taps", "The multirate filter design specification."]], "sdr.Differentiator": [[38, 3, 1, "", "__init__", "Creates a differentiator FIR filter."]], "sdr.Differentiator.__init__": [[38, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs are preserved between calls to __call__()."]], "sdr.EnergyDetector": [[40, 3, 1, "", "p_d", "Computes the probability of detection $P_D$."], [41, 3, 1, "", "p_fa", "Computes the probability of false alarm $P_{FA}$."], [42, 3, 1, "", "roc", "Computes the receiver operating characteristic (ROC) curve."], [43, 3, 1, "", "threshold", "Computes the threshold $gamma'$."]], "sdr.EnergyDetector.p_d": [[40, 4, 2, "p-N_nc", "N_nc", "The number of samples $N_{NC}$ to non-coherently integrate."], [40, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$."], [40, 4, 2, "p-snr", "snr", "The received signal-to-noise ratio $sigma_s^2 / sigma^2$ in dB."]], "sdr.EnergyDetector.p_fa": [[41, 4, 2, "p-N_nc", "N_nc", "The number of samples $N_{NC}$ to non-coherently integrate."], [41, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [41, 4, 2, "p-sigma2", "sigma2", "The noise variance $sigma^2$."], [41, 4, 2, "p-threshold", "threshold", "The threshold $gamma'$."]], "sdr.EnergyDetector.roc": [[42, 4, 2, "p-N_nc", "N_nc", "The number of samples $N_{NC}$ to non-coherently integrate."], [42, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [42, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$. If None, the ROC curve is computed for p_fa = np.logspace(-10, 0, 101)."], [42, 4, 2, "p-snr", "snr", "The received signal-to-noise ratio $sigma_s^2 / sigma^2$ in dB."]], "sdr.EnergyDetector.threshold": [[43, 4, 2, "p-N_nc", "N_nc", "The number of samples $N_{NC}$ to non-coherently integrate."], [43, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [43, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$."], [43, 4, 2, "p-sigma2", "sigma2", "The noise variance $sigma^2$."]], "sdr.ErrorRate": [[45, 3, 1, "", "__init__", "Creates a new error rate tabulation object."], [46, 3, 1, "", "add", "Measures the number of bit or symbol errors at the given signal-to-noise ratio (SNR)."], [47, 3, 1, "", "counts", "Returns the number of counts at the specified signal-to-noise ratio (SNR)."], [48, 3, 1, "", "error_rate", "Returns the error rate at the specified signal-to-noise ratio (SNR)."], [49, 3, 1, "", "error_rates", "Returns all signal-to-noise ratios (SNRs) in ascending order and their corresponding error rates."], [50, 3, 1, "", "errors", "Returns the number of errors at the specified signal-to-noise ratio (SNR)."]], "sdr.ErrorRate.add": [[46, 4, 2, "p-snr", "snr", "The signal-to-noise ratio (SNR) in dB. This can be $E_b/N_0$, $E_s/N_0$, $S/N$, $C/N_0$, or other SNR quantities. However, users are cautioned to be consistent for a given class instance."], [46, 4, 2, "p-x", "x", "The transmitted bits or symbols $x[k]$."], [46, 4, 2, "p-x_hat", "x_hat", "The received bits or symbols $hat{x}[k]$."]], "sdr.ErrorRate.counts": [[47, 4, 2, "p-snr", "snr", "The signal-to-noise ratio (SNR) in dB. This can be $E_b/N_0$, $E_s/N_0$, $S/N$, $C/N_0$, or other SNR quantities. However, users are cautioned to be consistent for a given class instance."]], "sdr.ErrorRate.error_rate": [[48, 4, 2, "p-snr", "snr", "The signal-to-noise ratio (SNR) in dB. This can be $E_b/N_0$, $E_s/N_0$, $S/N$, $C/N_0$, or other SNR quantities. However, users are cautioned to be consistent for a given class instance."]], "sdr.ErrorRate.errors": [[50, 4, 2, "p-snr", "snr", "The signal-to-noise ratio (SNR) in dB. This can be $E_b/N_0$, $E_s/N_0$, $S/N$, $C/N_0$, or other SNR quantities. However, users are cautioned to be consistent for a given class instance."]], "sdr.FIR": [[52, 3, 1, "", "__call__", "Filters the input signal $x[n]$ with the FIR filter."], [53, 3, 1, "", "__init__", "Creates a FIR filter with feedforward coefficients $h_i$."], [54, 3, 1, "", "__len__", "Returns the filter length $N + 1$."], [55, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [56, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [57, 2, 1, "", "delay", "The delay of the FIR filter $d = lfloor frac{N + 1}{2} rfloor$ in samples."], [58, 3, 1, "", "flush", "Flushes the filter state by passing zeros through the filter. Only useful when using streaming mode."], [59, 3, 1, "", "frequency_response", "Returns the frequency response $H(omega)$ of the FIR filter."], [60, 3, 1, "", "group_delay", "Returns the group delay $tau_g(omega)$ of the FIR filter."], [61, 3, 1, "", "impulse_response", "Returns the impulse response $h[n]$ of the FIR filter. The impulse response $h[n]$ is the filter output when the input is an impulse $delta[n]$."], [62, 2, 1, "", "order", "The order of the FIR filter $N$."], [63, 3, 1, "", "phase_delay", "Returns the phase delay $tau_{phi}(omega)$ of the FIR filter."], [64, 3, 1, "", "reset", "Resets the filter state. Only useful when using streaming mode."], [65, 2, 1, "", "state", "The filter state consisting of the previous $N$ inputs."], [66, 3, 1, "", "step_response", "Returns the step response $s[n]$ of the FIR filter. The step response $s[n]$ is the filter output when the input is a unit step $u[n]$."], [67, 2, 1, "", "streaming", "Indicates whether the filter is in streaming mode."], [68, 2, 1, "", "taps", "The feedforward taps $h_i$ for $i = 0,...,N$."]], "sdr.FIR.__call__": [[52, 4, 2, "p-mode", "mode", "The non-streaming convolution mode."], [52, 4, 2, "p-x", "x", "The input signal $x[n]$ with length $L$."]], "sdr.FIR.__init__": [[53, 4, 2, "p-h", "h", "The feedforward coefficients $h_i$ for $i = 0,...N$."], [53, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs are preserved between calls to __call__()."]], "sdr.FIR.frequency_response": [[59, 4, 2, "p-decades", "decades", "Only used if freqs is an integer."], [59, 4, 2, "p-freqs", "freqs", "The frequency specification."], [59, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the filter in samples/s."], [59, 4, 2, "p-whole", "whole", "Only used if freqs is an integer."]], "sdr.FIR.group_delay": [[60, 4, 2, "p-N", "N", "The number of samples in the group delay."], [60, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the filter in samples/s."]], "sdr.FIR.impulse_response": [[61, 4, 2, "p-N", "N", "The number of samples to return. The default is the filter length."]], "sdr.FIR.phase_delay": [[63, 4, 2, "p-N", "N", "The number of samples in the phase delay."], [63, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the filter in samples/s."]], "sdr.FIR.step_response": [[66, 4, 2, "p-N", "N", "The number of samples to return. The default is the filter length."]], "sdr.FarrowResampler": [[70, 3, 1, "", "__call__", "Resamples the input signal $x[n]$ by the given arbitrary rate $r$."], [71, 3, 1, "", "__init__", "Creates a new Farrow arbitrary resampler."], [72, 2, 1, "", "order", "The order of the filter."], [73, 3, 1, "", "reset", "Streaming-mode only: Resets the filter state and fractional sample index."], [74, 2, 1, "", "streaming", "Indicates whether the filter is in streaming mode."], [75, 2, 1, "", "taps", "The Farrow filter taps."]], "sdr.FarrowResampler.__call__": [[70, 4, 2, "p-rate", "rate", "The resampling rate $r$."], [70, 4, 2, "p-x", "x", "The input signal $x[n] = x(n T_s)$."]], "sdr.FarrowResampler.__init__": [[71, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs are preserved between calls to __call__()."]], "sdr.FarrowResampler.reset": [[73, 4, 2, "p-state", "state", "The filter state to reset to. The state vector should equal the previous three inputs. If None, the filter state will be reset to zero."]], "sdr.IIR": [[77, 3, 1, "", "ZerosPoles", "Creates an IIR filter from its zeros, poles, and gain."], [78, 3, 1, "", "__call__", "Filters the input signal $x[n]$ with the IIR filter."], [79, 3, 1, "", "__init__", "Creates an IIR filter with feedforward coefficients $b_i$ and feedback coefficients $a_j$."], [80, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [81, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [82, 2, 1, "", "a_taps", "The feedback taps $a_j$ for $j = 0,...,N$."], [83, 2, 1, "", "b_taps", "The feedforward taps $b_i$ for $i = 0,...,M$."], [84, 3, 1, "", "frequency_response", "Returns the frequency response $H(omega)$ of the IIR filter."], [85, 2, 1, "", "gain", "The gain of the IIR filter."], [86, 3, 1, "", "impulse_response", "Returns the impulse response $h[n]$ of the IIR filter. The impulse response $h[n]$ is the filter output when the input is an impulse $delta[n]$."], [87, 2, 1, "", "order", "The order of the IIR filter $N$."], [88, 2, 1, "", "poles", "The poles of the IIR filter."], [89, 3, 1, "", "reset", "Resets the filter state. Only useful when using streaming mode."], [90, 2, 1, "", "state", "The filter state."], [91, 3, 1, "", "step_response", "Returns the step response $s[n]$ of the IIR filter. The step response $s[n]$ is the filter output when the input is a unit step $u[n]$."], [92, 2, 1, "", "streaming", "Indicates whether the filter is in streaming mode."], [93, 2, 1, "", "zeros", "The zeros of the IIR filter."]], "sdr.IIR.ZerosPoles": [[77, 4, 2, "p-gain", "gain", "The gain of the transfer function."], [77, 4, 2, "p-poles", "poles", "The poles of the transfer function."], [77, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs and outputs are preserved between calls to __call__()."], [77, 4, 2, "p-zeros", "zeros", "The zeros of the transfer function."]], "sdr.IIR.__call__": [[78, 4, 2, "p-x", "x", "The input signal $x[n]$ with length $L$."]], "sdr.IIR.__init__": [[79, 4, 2, "p-a", "a", "The feedback coefficients $a_j$ for $j = 0,...,N$."], [79, 4, 2, "p-b", "b", "The feedforward coefficients $b_i$ for $i = 0,...,M$."], [79, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs and outputs are preserved between calls to __call__()."]], "sdr.IIR.frequency_response": [[84, 4, 2, "p-decades", "decades", "Only used if freqs is an integer."], [84, 4, 2, "p-freqs", "freqs", "The frequency specification."], [84, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the filter in samples/s."], [84, 4, 2, "p-whole", "whole", "Only used if freqs is an integer."]], "sdr.IIR.impulse_response": [[86, 4, 2, "p-N", "N", "The number of samples to return."]], "sdr.IIR.step_response": [[91, 4, 2, "p-N", "N", "The number of samples to return."]], "sdr.Integrator": [[95, 3, 1, "", "__init__", "Creates an integrating IIR filter."]], "sdr.Integrator.__init__": [[95, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs and outputs are preserved between calls to __call__()."]], "sdr.Interpolator": [[97, 3, 1, "", "__call__", "Interpolates and filters the input signal $x[n]$ with the polyphase FIR filter."], [98, 3, 1, "", "__init__", "Creates a polyphase FIR interpolating filter."], [99, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [100, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [101, 2, 1, "", "delay", "The delay of FIR filter in samples. The delay indicates the output sample index that corresponds to the first input sample."], [102, 2, 1, "", "method", "The method used to design the multirate filter."], [103, 2, 1, "", "polyphase_taps", "The polyphase feedforward taps $h_{i, j}$."], [104, 2, 1, "", "rate", "The interpolation rate $r$."], [105, 3, 1, "", "reset", "Resets the filter state. Only useful when using streaming mode."], [106, 2, 1, "", "taps", "The prototype feedforward taps $h_i$."]], "sdr.Interpolator.__call__": [[97, 4, 2, "p-mode", "mode", "The non-streaming convolution mode."], [97, 4, 2, "p-x", "x", "The input signal $x[n]$ with sample rate $f_s$ and length $L$."]], "sdr.Interpolator.__init__": [[98, 4, 2, "p-rate", "rate", "The interpolation rate $r$."], [98, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs are preserved between calls to __call__()."], [98, 4, 2, "p-taps", "taps", "The multirate filter design specification."]], "sdr.LinearModulation": [[108, 3, 1, "", "__init__", "Creates a new linear phase/amplitude modulation object."], [109, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [110, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [111, 3, 1, "", "ber", "Computes the bit error rate (BER) at the provided $E_b/N_0$ values."], [112, 2, 1, "", "bps", "The number of bits per symbol $k = log_2 M$."], [113, 3, 1, "", "decide_symbols", "Converts the received complex symbols $tilde{a}[k]$ into decimal symbol decisions $hat{s}[k]$ and complex symbol decisions $hat{a}[k]$ using maximum-likelihood estimation (MLE)."], [114, 3, 1, "", "demodulate", "Demodulates the pulse-shaped complex samples $tilde{x}[n]$ into decimal symbol decisions $hat{s}[k]$ using matched filtering and maximum-likelihood estimation."], [115, 3, 1, "", "map_symbols", "Converts the decimal symbols $s[k]$ to complex symbols $a[k]$."], [116, 3, 1, "", "modulate", "Modulates the decimal symbols $s[k]$ into pulse-shaped complex samples $x[n]$."], [117, 2, 1, "", "order", "The modulation order $M = 2^k$."], [118, 2, 1, "", "phase_offset", "The phase offset $phi$ in degrees."], [119, 2, 1, "", "pulse_shape", "The pulse shape $h[n]$ of the modulated signal."], [120, 2, 1, "", "rx_filter", "The receive decimating matched filter. The filter coefficients are matched to the pulse shape $h[-n]^*$."], [121, 3, 1, "", "ser", "Computes the symbol error rate (SER) at the provided $E_s/N_0$ values."], [122, 2, 1, "", "sps", "The number of samples per symbol $f_s / f_{sym}$."], [123, 2, 1, "", "symbol_map", "The symbol map ${0, dots, M-1} mapsto mathbb{C}$. This maps decimal symbols from $0$ to $M-1$ to complex symbols."], [124, 2, 1, "", "tx_filter", "The transmit interpolating pulse shaping filter. The filter coefficients are the pulse shape $h[n]$."]], "sdr.LinearModulation.__init__": [[108, 4, 2, "p-alpha", "alpha", "The roll-off factor of the pulse shape. If None, 0.2 is used for \"rc\" and \"srrc\"."], [108, 4, 2, "p-phase_offset", "phase_offset", "A phase offset $phi$ in degrees to apply to symbol_map."], [108, 4, 2, "p-pulse_shape", "pulse_shape", "The pulse shape $h[n]$ of the modulated signal."], [108, 4, 2, "p-span", "span", "The span of the pulse shape in symbols. This is only used if pulse_shape is a string. If None, 1 is used for \"rect\" and 10 is used for \"rc\" and \"srrc\"."], [108, 4, 2, "p-sps", "sps", "The number of samples per symbol $f_s / f_{sym}$."], [108, 4, 2, "p-symbol_map", "symbol_map", "The symbol mapping ${0, dots, M-1} mapsto mathbb{C}$. An $M$-length array whose indices are decimal symbols $s[k]$ and whose values are complex symbols $a[k]$, where $M$ is the modulation order."]], "sdr.LinearModulation.ber": [[111, 4, 2, "p-ebn0", "ebn0", "Bit energy $E_b$ to noise PSD $N_0$ ratio in dB."]], "sdr.LinearModulation.decide_symbols": [[113, 4, 2, "p-a_tilde", "a_tilde", "The received complex symbols $tilde{a}[k]$."]], "sdr.LinearModulation.demodulate": [[114, 4, 2, "p-x_tilde", "x_tilde", "The received pulse-shaped complex samples $tilde{x}[n]$ to demodulate, with sps samples per symbol and length sps * s_hat.size + pulse_shape.size - 1."]], "sdr.LinearModulation.map_symbols": [[115, 4, 2, "p-s", "s", "The decimal symbols $s[k]$ to map, $0$ to $M-1$."]], "sdr.LinearModulation.modulate": [[116, 4, 2, "p-s", "s", "The decimal symbols $s[k]$ to modulate, $0$ to $M-1$."]], "sdr.LinearModulation.ser": [[121, 4, 2, "p-esn0", "esn0", "Symbol energy $E_s$ to noise PSD $N_0$ ratio in dB."]], "sdr.LoopFilter": [[126, 2, 1, "", "K1", "The proportional gain $K_1$ of the loop filter."], [127, 2, 1, "", "K2", "The integral gain $K_2$ of the loop filter."], [128, 3, 1, "", "__call__", "Filters the input signal $x[n]$."], [129, 3, 1, "", "__init__", "Creates a 2nd order, proportional-plus-integrator (PPI) loop filter."], [130, 2, 1, "", "damping_factor", "The damping factor $zeta$ of the loop filter. $zeta = 1$ is critically damped, $zeta < 1$ is underdamped, and $zeta > 1$ is overdamped."], [131, 2, 1, "", "iir", "The underlying IIR filter used to implement the loop filter."], [132, 2, 1, "", "noise_bandwidth", "The normalized noise bandwidth $B_n T$ of the loop filter, where $B_n$ is the noise bandwidth in Hz and $T$ is the sampling period in seconds."], [133, 3, 1, "", "reset", "Resets the loop filter."]], "sdr.LoopFilter.__call__": [[128, 4, 2, "p-x", "x", "The input signal $x[n]$."]], "sdr.LoopFilter.__init__": [[129, 4, 2, "p-K0", "K0", "The NCO gain $K_0$."], [129, 4, 2, "p-Kp", "Kp", "The gain $K_p$ of the phase error detector (PED) or time error detector (TED)."], [129, 4, 2, "p-damping_factor", "damping_factor", "The damping factor $zeta$ of the loop filter. $zeta = 1$ is critically damped, $zeta < 1$ is underdamped, and $zeta > 1$ is overdamped."], [129, 4, 2, "p-noise_bandwidth", "noise_bandwidth", "The normalized noise bandwidth $B_n T$ of the loop filter, where $B_n$ is the noise bandwidth in Hz and $T$ is the sampling period in seconds."]], "sdr.MSK": [[135, 3, 1, "", "__init__", "Creates a new MSK object."]], "sdr.MSK.__init__": [[135, 4, 2, "p-phase_offset", "phase_offset", "The absolute phase offset $phi$ in degrees."], [135, 4, 2, "p-sps", "sps", "The number of samples per symbol $f_s / f_{sym}$."], [135, 4, 2, "p-symbol_labels", "symbol_labels", "The decimal symbol labels of consecutive complex symbols."]], "sdr.NCO": [[137, 2, 1, "", "K0", "(Settable) The NCO gain $K_0$."], [138, 3, 1, "", "__call__", "Steps the NCO with variable frequency and/or phase signals."], [139, 3, 1, "", "__init__", "Creates a numerically-controlled oscillator (NCO)."], [140, 2, 1, "", "increment", "(Settable) The constant phase accumulation $omega$ of the NCO in radians/sample."], [141, 2, 1, "", "offset", "(Settable) The absolute phase offset $theta$ of the NCO in radians."], [142, 3, 1, "", "reset", "Resets the NCO."], [143, 3, 1, "", "step", "Steps the NCO forward by $N$ samples."]], "sdr.NCO.__call__": [[138, 4, 2, "p-freq", "freq", "The variable frequency signal $f[n]$ in radians/sample. This input signal varies the per-sample phase increment of the NCO. If None, the signal is all zeros."], [138, 4, 2, "p-output", "output", "The format of the output signal $y[n]$. Options are the accumulated phase, sine, cosine, or complex exponential."], [138, 4, 2, "p-phase", "phase", "The variable phase signal $p[n]$ in radians. This input signal varies the per-sample phase offset of the NCO. If None, the signal is all zeros."]], "sdr.NCO.__init__": [[139, 4, 2, "p-K0", "K0", "The NCO gain $K_0$."], [139, 4, 2, "p-increment", "increment", "The constant accumulation $omega$ of the NCO in radians/sample."], [139, 4, 2, "p-offset", "offset", "The absolute offset $theta$ of the NCO in radians."]], "sdr.NCO.step": [[143, 4, 2, "p-N", "N", "The number of samples $N$ to step the NCO forward."]], "sdr.OQPSK": [[145, 3, 1, "", "__init__", "Creates a new OQPSK object."], [146, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [147, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."]], "sdr.OQPSK.__init__": [[145, 4, 2, "p-alpha", "alpha", "The roll-off factor of the pulse shape. If None, 0.2 is used for \"rc\" and \"srrc\"."], [145, 4, 2, "p-phase_offset", "phase_offset", "The absolute phase offset $phi$ in degrees."], [145, 4, 2, "p-pulse_shape", "pulse_shape", "The pulse shape $h[n]$ of the modulated signal."], [145, 4, 2, "p-span", "span", "The span of the pulse shape in symbols. This is only used if pulse_shape is a string. If None, 1 is used for \"rect\" and 10 is used for \"rc\" and \"srrc\"."], [145, 4, 2, "p-sps", "sps", "The number of samples per symbol $f_s / f_{sym}$."], [145, 4, 2, "p-symbol_labels", "symbol_labels", "The decimal symbol labels of consecutive complex symbols."]], "sdr.PED": [[149, 3, 1, "", "__call__", "Detects the phase error."], [150, 3, 1, "", "__init__", "Initializes the PED."], [151, 3, 1, "", "data_aided_error", "Measures the average phase error of the data-aided PED using the specified modulation scheme."], [152, 3, 1, "", "decision_directed_error", "Measures the average phase error of the decision-directed PED using the specified modulation scheme."], [153, 2, 1, "", "gain", "The gain of the phase error detector $K_p$."]], "sdr.PED.__call__": [[149, 4, 2, "p-received", "received", "The received complex symbols $tilde{a}[k]$."], [149, 4, 2, "p-reference", "reference", "The reference complex symbols, either the known transmitted complex symbols $a[k]$ or the complex symbols decisions $hat{a}[k]$."]], "sdr.PED.data_aided_error": [[151, 4, 2, "p-modem", "modem", "The linear modulation scheme."], [151, 4, 2, "p-n_points", "n_points", "The number of points to use to measure the phase error."]], "sdr.PED.decision_directed_error": [[152, 4, 2, "p-modem", "modem", "The linear modulation scheme."], [152, 4, 2, "p-n_points", "n_points", "The number of points to use to measure the phase error."]], "sdr.PSK": [[155, 3, 1, "", "__init__", "Creates a new PSK object."], [156, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [157, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [158, 3, 1, "", "ber", "Computes the bit error rate (BER) at the provided $E_b/N_0$ values."], [159, 2, 1, "", "phase_offset", "The phase offset $phi$ in degrees."], [160, 3, 1, "", "ser", "Computes the symbol error rate (SER) at the provided $E_s/N_0$ values."], [161, 2, 1, "", "symbol_map", "The symbol map ${0, dots, M-1} mapsto mathbb{C}$. This maps decimal symbols from $0$ to $M-1$ to complex symbols."]], "sdr.PSK.__init__": [[155, 4, 2, "p-alpha", "alpha", "The roll-off factor of the pulse shape. If None, 0.2 is used for \"rc\" and \"srrc\"."], [155, 4, 2, "p-order", "order", "The modulation order $M = 2^k$, where $k ge 1$ is the bits per symbol."], [155, 4, 2, "p-phase_offset", "phase_offset", "The phase offset $phi$ in degrees."], [155, 4, 2, "p-pulse_shape", "pulse_shape", "The pulse shape $h[n]$ of the modulated signal."], [155, 4, 2, "p-span", "span", "The span of the pulse shape in symbols. This is only used if pulse_shape is a string. If None, 1 is used for \"rect\" and 10 is used for \"rc\" and \"srrc\"."], [155, 4, 2, "p-sps", "sps", "The number of samples per symbol $f_s / f_{sym}$."], [155, 4, 2, "p-symbol_labels", "symbol_labels", "The decimal symbol labels of consecutive complex symbols."]], "sdr.PSK.ber": [[158, 4, 2, "p-diff_encoded", "diff_encoded", "Indicates whether the input symbols were differentially encoded."], [158, 4, 2, "p-ebn0", "ebn0", "Bit energy $E_b$ to noise PSD $N_0$ ratio in dB."]], "sdr.PSK.ser": [[160, 4, 2, "p-diff_encoded", "diff_encoded", "Indicates whether the input symbols were differentially encoded."], [160, 4, 2, "p-esn0", "esn0", "Symbol energy $E_s$ to noise PSD $N_0$ ratio in dB."]], "sdr.PiMPSK": [[163, 3, 1, "", "__init__", "Creates a new $pi/M$ PSK object."]], "sdr.PiMPSK.__init__": [[163, 4, 2, "p-alpha", "alpha", "The roll-off factor of the pulse shape. If None, 0.2 is used for \"rc\" and \"srrc\"."], [163, 4, 2, "p-order", "order", "The modulation order $M = 2^k$, where $k ge 1$ is the bits per symbol."], [163, 4, 2, "p-phase_offset", "phase_offset", "The absolute phase offset $phi$ in degrees."], [163, 4, 2, "p-pulse_shape", "pulse_shape", "The pulse shape $h[n]$ of the modulated signal."], [163, 4, 2, "p-span", "span", "The span of the pulse shape in symbols. This is only used if pulse_shape is a string. If None, 1 is used for \"rect\" and 10 is used for \"rc\" and \"srrc\"."], [163, 4, 2, "p-sps", "sps", "The number of samples per symbol $f_s / f_{sym}$."], [163, 4, 2, "p-symbol_labels", "symbol_labels", "The decimal symbol labels of consecutive complex symbols."]], "sdr.Q": [[164, 4, 2, "p-x", "x", "The real-valued input $x$."]], "sdr.Qinv": [[165, 4, 2, "p-p", "p", "The probability $p$ of exceeding the returned value $x$."]], "sdr.ReplicaCorrelator": [[167, 3, 1, "", "p_d", "Computes the probability of detection $P_D$."], [168, 3, 1, "", "p_fa", "Computes the probability of false alarm $P_{FA}$."], [169, 3, 1, "", "roc", "Computes the receiver operating characteristic (ROC) curve."], [170, 3, 1, "", "threshold", "Computes the threshold $gamma'$."]], "sdr.ReplicaCorrelator.p_d": [[167, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [167, 4, 2, "p-enr", "enr", "The received energy-to-noise ratio $mathcal{E}/sigma^2$ in dB."], [167, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$."]], "sdr.ReplicaCorrelator.p_fa": [[168, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [168, 4, 2, "p-energy", "energy", "The received energy $mathcal{E} = sum_{i=0}^{N-1} left| s[n] right|^2$."], [168, 4, 2, "p-sigma2", "sigma2", "The noise variance $sigma^2$."], [168, 4, 2, "p-threshold", "threshold", "The threshold $gamma'$."]], "sdr.ReplicaCorrelator.roc": [[169, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [169, 4, 2, "p-enr", "enr", "The received energy-to-noise ratio $mathcal{E}/sigma^2$ in dB."], [169, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$. If None, the ROC curve is computed for p_fa = np.logspace(-10, 0, 101)."]], "sdr.ReplicaCorrelator.threshold": [[170, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [170, 4, 2, "p-energy", "energy", "The received energy $mathcal{E} = sum_{i=0}^{N-1} left| s[n] right|^2$."], [170, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$."], [170, 4, 2, "p-sigma2", "sigma2", "The noise variance $sigma^2$."]], "sdr.Resampler": [[172, 3, 1, "", "__call__", "Resamples and filters the input signal $x[n]$ with the polyphase FIR filter."], [173, 3, 1, "", "__init__", "Creates a polyphase FIR rational resampling filter."], [174, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [175, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [176, 2, 1, "", "delay", "The delay of FIR filter in samples. The delay indicates the output sample index that corresponds to the first input sample."], [177, 2, 1, "", "down", "The decimation rate $Q$."], [178, 2, 1, "", "method", "The method used to design the multirate filter."], [179, 2, 1, "", "polyphase_taps", "The polyphase feedforward taps $h_{i, j}$."], [180, 2, 1, "", "rate", "The resampling rate $P/Q$."], [181, 3, 1, "", "reset", "Resets the filter state. Only useful when using streaming mode."], [182, 2, 1, "", "taps", "The prototype feedforward taps $h_i$."], [183, 2, 1, "", "up", "The interpolation rate $P$."]], "sdr.Resampler.__init__": [[173, 4, 2, "p-down", "down", "The decimation rate $Q$."], [173, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs are preserved between calls to __call__()."], [173, 4, 2, "p-taps", "taps", "The multirate filter design specification."], [173, 4, 2, "p-up", "up", "The interpolation rate $P$."]], "sdr.albersheim": [[184, 4, 2, "p-N_nc", "N_nc", "The number of non-coherent combinations $N_{NC} ge 1$."], [184, 4, 2, "p-p_d", "p_d", "The desired probability of detection $P_D$ in $(0, 1)$."], [184, 4, 2, "p-p_fa", "p_fa", "The desired probability of false alarm $P_{FA}$ in $(0, 1)$."]], "sdr.average_power": [[185, 4, 2, "p-axis", "axis", "Axis or axes along which to compute the average power. The default is None, which computes the average power of the entire array."], [185, 4, 2, "p-db", "db", "Indicates whether to return the result in decibels (dB)."], [185, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.awgn": [[186, 4, 2, "p-noise", "noise", "The noise power (variance) in linear units. If noise is None, snr must be specified."], [186, 4, 2, "p-seed", "seed", "The seed for the random number generator. This is passed to numpy.random.default_rng()."], [186, 4, 2, "p-snr", "snr", "The desired signal-to-noise ratio (SNR) in dB. If specified, the average signal power is measured explicitly. It is assumed that $x[n]$ contains signal only. If the signal power is known, the desired noise variance can be computed and passed in noise. If snr is None, noise must be specified."], [186, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to which AWGN is added."]], "sdr.awgn_capacity": [[187, 4, 2, "p-bandwidth", "bandwidth", "The bandwidth $B$ of the channel in Hz. If specified, the capacity is calculated in bits/s. If None, the capacity is calculated in bits/2D."], [187, 4, 2, "p-snr", "snr", "The signal-to-noise ratio $S / N$ in dB of the channel."]], "sdr.barker": [[188, 4, 2, "p-length", "length", "The length $N$ of the Barker code/sequence."], [188, 4, 2, "p-output", "output", "The output format of the Barker code/sequence."]], "sdr.bec": [[189, 4, 2, "p-p", "p", "The probability $p$ of a bit erasure."], [189, 4, 2, "p-seed", "seed", "The seed for the random number generator. This is passed to numpy.random.default_rng()."], [189, 4, 2, "p-x", "x", "The input sequence $x$ with $x_i in {0, 1}$."]], "sdr.bec_capacity": [[190, 4, 2, "p-p", "p", "The erasure probability $p$ of the BEC channel."]], "sdr.binary_code": [[191, 4, 2, "p-n", "n", "The length of the binary code."]], "sdr.bsc": [[192, 4, 2, "p-p", "p", "The probability $p$ of a bit flip."], [192, 4, 2, "p-seed", "seed", "The seed for the random number generator. This is passed to numpy.random.default_rng()."], [192, 4, 2, "p-x", "x", "The input sequence $x$ with $x_i in {0, 1}$."]], "sdr.bsc_capacity": [[193, 4, 2, "p-p", "p", "The transition probability $p$ of the BSC channel."]], "sdr.crest_factor": [[194, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.db": [[195, 4, 2, "p-type", "type", "The type of input value or signal."], [195, 4, 2, "p-x", "x", "The input value or signal."]], "sdr.design_bandpass_fir": [[196, 4, 2, "p-atten", "atten", "The sidelobe attenuation in dB. Only used if window is \"chebyshev\" or \"kaiser\"."], [196, 4, 2, "p-bandwidth", "bandwidth", "The two-sided bandwidth about $f_{center}$, normalized to the Nyquist frequency $f_s / 2$."], [196, 4, 2, "p-center_freq", "center_freq", "The center frequency $f_{center}$, normalized to the Nyquist frequency $f_s / 2$."], [196, 4, 2, "p-order", "order", "The filter order $N$. Must be even."], [196, 4, 2, "p-window", "window", "The time-domain window to use."]], "sdr.design_bandstop_fir": [[197, 4, 2, "p-atten", "atten", "The sidelobe attenuation in dB. Only used if window is \"chebyshev\" or \"kaiser\"."], [197, 4, 2, "p-bandwidth", "bandwidth", "The two-sided bandwidth about $f_{center}$, normalized to the Nyquist frequency $f_s / 2$."], [197, 4, 2, "p-center_freq", "center_freq", "The center frequency $f_{center}$, normalized to the Nyquist frequency $f_s / 2$."], [197, 4, 2, "p-order", "order", "The filter order $N$. Must be even."], [197, 4, 2, "p-window", "window", "The time-domain window to use."]], "sdr.design_frac_delay_fir": [[198, 4, 2, "p-delay", "delay", "The fractional delay $0 le Delta n le 1$."], [198, 4, 2, "p-length", "length", "The filter length $L$. Filters with even length have best performance. Filters with odd length are equivalent to an even-length filter with an appended zero."]], "sdr.design_highpass_fir": [[199, 4, 2, "p-atten", "atten", "The sidelobe attenuation in dB. Only used if window is \"chebyshev\" or \"kaiser\"."], [199, 4, 2, "p-cutoff_freq", "cutoff_freq", "The cutoff frequency $f_c$, normalized to the Nyquist frequency $f_s / 2$."], [199, 4, 2, "p-order", "order", "The filter order $N$. Must be even."], [199, 4, 2, "p-window", "window", "The time-domain window to use."]], "sdr.design_lowpass_fir": [[200, 4, 2, "p-atten", "atten", "The sidelobe attenuation in dB. Only used if window is \"chebyshev\" or \"kaiser\"."], [200, 4, 2, "p-cutoff_freq", "cutoff_freq", "The cutoff frequency $f_c$, normalized to the Nyquist frequency $f_s / 2$."], [200, 4, 2, "p-order", "order", "The filter order $N$. Must be even."], [200, 4, 2, "p-window", "window", "The time-domain window to use."]], "sdr.design_multirate_fir": [[201, 4, 2, "p-A_stop", "A_stop", "The stopband attenuation $A_{text{stop}}$ in dB."], [201, 4, 2, "p-down", "down", "The decimation rate $Q$."], [201, 4, 2, "p-half_length", "half_length", "The half-length of the polyphase filters."], [201, 4, 2, "p-up", "up", "The interpolation rate $P$."]], "sdr.diff_decode": [[202, 4, 2, "p-y", "y", "The input encoded data $y[k]$."], [202, 4, 2, "p-y_prev", "y_prev", "The previous value of the encoded data $y[k-1]$."]], "sdr.diff_encode": [[203, 4, 2, "p-x", "x", "The input uncoded data $x[k]$."], [203, 4, 2, "p-y_prev", "y_prev", "The previous value of the output encoded data $y[k-1]$."]], "sdr.dmc": [[204, 4, 2, "p-P", "P", "The $m times n$ transition probability matrix $P$, where $P_{i,j} = Pr(Y = y_j | X = x_i)$."], [204, 4, 2, "p-X", "X", "The input alphabet $mathcal{X}$ of size $m$. If None, it is assumed that $mathcal{X} = {0, 1, ldots, m-1}$."], [204, 4, 2, "p-Y", "Y", "The output alphabet $mathcal{Y}$ of size $n$. If None, it is assumed that $mathcal{Y} = {0, 1, ldots, n-1}$."], [204, 4, 2, "p-seed", "seed", "The seed for the random number generator. This is passed to numpy.random.default_rng()."], [204, 4, 2, "p-x", "x", "The input sequence $x$ with $x_i in mathcal{X}$."]], "sdr.downsample": [[205, 4, 2, "p-rate", "rate", "The downsampling factor $r$."], [205, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ with sample rate $f_s$."]], "sdr.ebn0_to_esn0": [[206, 4, 2, "p-bps", "bps", "Bits per symbol $log_2 M$, where $M$ is the modulation order."], [206, 4, 2, "p-ebn0", "ebn0", "Bit energy $E_b$ to noise PSD $N_0$ ratio in dB."], [206, 4, 2, "p-rate", "rate", "Code rate $r = k/n$, where $k$ is the number of information bits and $n$ is the number of coded bits."]], "sdr.ebn0_to_snr": [[207, 4, 2, "p-bps", "bps", "Bits per symbol $log_2 M$, where $M$ is the modulation order."], [207, 4, 2, "p-ebn0", "ebn0", "Bit energy $E_b$ to noise PSD $N_0$ ratio in dB."], [207, 4, 2, "p-rate", "rate", "Code rate $r = k/n$, where $k$ is the number of information bits and $n$ is the number of coded bits."], [207, 4, 2, "p-sps", "sps", "Samples per symbol $f_s / f_{sym}$."]], "sdr.energy": [[208, 4, 2, "p-axis", "axis", "Axis or axes along which to compute the energy. The default is None, which computes the energy of the entire array."], [208, 4, 2, "p-db", "db", "Indicates whether to return the result in decibels (dB)."], [208, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.esn0_to_ebn0": [[209, 4, 2, "p-bps", "bps", "Bits per symbol $log_2 M$, where $M$ is the modulation order."], [209, 4, 2, "p-esn0", "esn0", "Symbol energy $E_s$ to noise PSD $N_0$ ratio in dB."], [209, 4, 2, "p-rate", "rate", "Code rate $r = k/n$, where $k$ is the number of information bits and $n$ is the number of coded bits."]], "sdr.esn0_to_snr": [[210, 4, 2, "p-esn0", "esn0", "Symbol energy $E_s$ to noise PSD $N_0$ ratio in dB."], [210, 4, 2, "p-sps", "sps", "Samples per symbol $f_s / f_{sym}$."]], "sdr.euclidean": [[211, 4, 2, "p-axis", "axis", "Axis or axes along which to compute the distance. The default is None, which computes the distance across the entire array."], [211, 4, 2, "p-x", "x", "The time-domain signal $x[n]$."], [211, 4, 2, "p-y", "y", "The time-domain signal $y[n]$."]], "sdr.evm": [[212, 4, 2, "p-norm", "norm", "The normalization source used in the EVM calculation."], [212, 4, 2, "p-output", "output", "The output type of the EVM calculation."], [212, 4, 2, "p-ref", "ref", "The complex reference symbols $x[k]$. This can be the noiseless transmitted symbols or the modulation's symbol map."], [212, 4, 2, "p-x_hat", "x_hat", "The complex symbols $hat{x}[k]$ to be measured."]], "sdr.frequency_offset": [[213, 4, 2, "p-freq", "freq", "The frequency offset $f$ in Hz (or in cycles/sample if sample_rate=1)."], [213, 4, 2, "p-freq_rate", "freq_rate", "The frequency offset rate $f_{text{rate}}$ in Hz/s (or in cycles/sample^2 if sample_rate=1)."], [213, 4, 2, "p-phase", "phase", "The phase offset $phi$ in degrees."], [213, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ in samples/s."], [213, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to which the frequency offset is applied."]], "sdr.fspl": [[214, 4, 2, "p-distance", "distance", "The distance $d$ in meters between the transmitter and receiver."], [214, 4, 2, "p-freq", "freq", "The frequency $f$ in Hz of the signal."]], "sdr.gaussian": [[215, 4, 2, "p-norm", "norm", "Indicates how to normalize the pulse shape."], [215, 4, 2, "p-span", "span", "The length of the filter in symbols. The length of the filter is span * sps + 1 samples. The filter order span * sps must be even."], [215, 4, 2, "p-sps", "sps", "The number of samples per symbol."], [215, 4, 2, "p-time_bandwidth", "time_bandwidth", "The time-bandwidth product $B T_{sym}$ of the filter, where $B$ is the one-sided 3-dB bandwidth in Hz and $T_{sym}$ is the symbol time in seconds. The time-bandwidth product can also be thought of as the fractional bandwidth $B / f_{sym}$. Smaller values produce wider pulses."]], "sdr.gray_code": [[216, 4, 2, "p-n", "n", "The length of the Gray code."]], "sdr.hadamard": [[217, 4, 2, "p-index", "index", "The index $i$ of the Hadamard code."], [217, 4, 2, "p-length", "length", "The length $N$ of the Hadamard code/sequence. Must be a power of 2."], [217, 4, 2, "p-output", "output", "The output format of the Hadamard code/sequence."]], "sdr.half_sine": [[218, 4, 2, "p-norm", "norm", "Indicates how to normalize the pulse shape."], [218, 4, 2, "p-span", "span", "The length of the filter in symbols. The length of the filter is span * sps samples, but only the center sps samples are non-zero. The only reason for span to be larger than 1 is to add delay to the filter."], [218, 4, 2, "p-sps", "sps", "The number of samples per symbol."]], "sdr.hamming": [[219, 4, 2, "p-axis", "axis", "Axis or axes along which to compute the distance. The default is None, which computes the distance across the entire array."], [219, 4, 2, "p-x", "x", "The time-domain signal $x[n]$."], [219, 4, 2, "p-y", "y", "The time-domain signal $y[n]$."]], "sdr.hexdump": [[220, 4, 2, "p-data", "data", "The data to display. Each element is considered one byte. Use sdr.pack() or sdr.unpack() to convert data with variable bits per element."], [220, 4, 2, "p-width", "width", "The number of bytes per line."]], "sdr.iq_imbalance": [[221, 4, 2, "p-amplitude", "amplitude", "The amplitude imbalance $A$ in dB. A positive value indicates that the in-phase component is larger than the quadrature component."], [221, 4, 2, "p-phase", "phase", "The phase imbalance $phi$ in degrees. A positive value indicates that the quadrature component leads the in-phase component."], [221, 4, 2, "p-x", "x", "The complex time-domain signal $x[n]$ to which IQ imbalance is applied."]], "sdr.linear": [[222, 4, 2, "p-type", "type", "The type of output value or signal."], [222, 4, 2, "p-x", "x", "The input value or signal in dB."]], "sdr.mix": [[223, 4, 2, "p-complex", "complex", "Indicates whether to mix by a complex exponential or real sinusoid."], [223, 4, 2, "p-freq", "freq", "The frequency $f$ of the sinusoid in Hz (or 1/samples if sample_rate=1). The frequency must satisfy $-f_s/2 le f le f_s/2$."], [223, 4, 2, "p-phase", "phase", "The phase $phi$ of the sinusoid in degrees."], [223, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal."], [223, 4, 2, "p-x", "x", "The time-domain signal $x[n]$."]], "sdr.pack": [[224, 4, 2, "p-bpe", "bpe", "The number of bits per element in the output array."], [224, 4, 2, "p-dtype", "dtype", "The data type of the output array. If None, the smallest unsigned integer dtype that can hold bpe bits is used."], [224, 4, 2, "p-x", "x", "The input binary array with 1 bit per element."]], "sdr.papr": [[225, 4, 2, "p-axis", "axis", "Axis or axes along which to compute the PAPR. The default is None, which computes the PAPR of the entire array."], [225, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.parabolic_antenna": [[226, 4, 2, "p-diameter", "diameter", "The diameter $d$ in meters of the parabolic reflector."], [226, 4, 2, "p-efficiency", "efficiency", "The efficiency $0 le eta le 1$ of the parabolic reflector."], [226, 4, 2, "p-freq", "freq", "The frequency $f$ in Hz of the signal."]], "sdr.peak_power": [[227, 4, 2, "p-axis", "axis", "Axis or axes along which to compute the peak power. The default is None, which computes the peak power of the entire array."], [227, 4, 2, "p-db", "db", "Indicates whether to return the result in decibels (dB)."], [227, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.peak_voltage": [[228, 4, 2, "p-db", "db", "Indicates whether to return the result in decibels (dB)."], [228, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.percent": [[229, 4, 2, "p-x", "x", "The input ratio."]], "sdr.plot": [[230, 5, 1, "", "ber", "Plots the bit error rate (BER) as a function of $E_b/N_0$."], [231, 5, 1, "", "constellation", "Plots the constellation of the complex symbols $hat{x}[k]$."], [232, 5, 1, "", "eye", "Plots the eye diagram of the baseband modulated signal $x[n]$."], [233, 5, 1, "", "filter", "Plots the magnitude response $|H(omega)|^2$, impulse response $h[n]$, step response $s[n]$, and zeros and poles of the filter."], [234, 5, 1, "", "group_delay", "Plots the group delay $tau_g(omega)$ of the IIR filter."], [235, 5, 1, "", "impulse_response", "Plots the impulse response $h[n]$ of a filter."], [236, 5, 1, "", "magnitude_response", "Plots the magnitude response $|H(omega)|^2$ of the filter."], [237, 5, 1, "", "p_d", "Plots the probability of detection $P_D$ as a function of received SNR or ENR."], [238, 5, 1, "", "periodogram", "Plots the estimated power spectral density $P_{xx}$ of a time-domain signal $x[n]$ using Welch's method."], [239, 5, 1, "", "phase_delay", "Plots the phase delay $tau_{phi}(omega)$ of the filter."], [240, 5, 1, "", "phase_response", "Plots the phase response $angle H(omega)$ of the filter."], [241, 5, 1, "", "phase_tree", "Plots the phase tree of a continuous-phase modulated (CPM) signal signal $x[n]$."], [242, 5, 1, "", "raster", "Plots a raster of the time-domain signal $x[n]$."], [243, 5, 1, "", "roc", "Plots the receiver operating characteristic (ROC) curve as a function of $P_{FA}$."], [244, 5, 1, "", "ser", "Plots the symbol error rate (SER) as a function of $E_s/N_0$."], [245, 5, 1, "", "spectrogram", "Plots the spectrogram of a time-domain signal $x[n]$ using Welch's method."], [246, 5, 1, "", "step_response", "Plots the step response $s[n]$ of a filter."], [247, 5, 1, "", "symbol_map", "Plots the symbol map of the complex symbols $hat{x}[k]$."], [248, 5, 1, "", "time_domain", "Plots a time-domain signal $x[n]$."], [249, 5, 1, "", "use_style", "Applies sdr's default matplotlib rcParams."], [250, 5, 1, "", "zeros_poles", "Plots the zeros and poles of the filter."]], "sdr.plot.ber": [[230, 4, 2, "p-ber", "ber", "The bit error rate $P_{be}$."], [230, 4, 2, "p-ebn0", "ebn0", "The bit energy $E_b$ to noise PSD $N_0$ ratio (dB)."], [230, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.semilogy()."]], "sdr.plot.constellation": [[231, 4, 2, "p-heatmap", "heatmap", "If True, a heatmap is plotted instead of a scatter plot."], [231, 4, 2, "p-kwargs", "kwargs", "If heatmap=False, additional keyword arguments to pass to matplotlib.pyplot.scatter(). The following keyword arguments are set by default. The defaults may be overwritten."], [231, 4, 2, "p-limits", "limits", "The axis limits, which apply to both the x- and y-axis. If None, the axis limits are set to 10% larger than the maximum value."], [231, 4, 2, "p-x_hat", "x_hat", "The complex symbols $hat{x}[k]$."]], "sdr.plot.eye": [[232, 4, 2, "p-color", "color", "Indicates how to color the rasters. If \"index\", the rasters are colored based on their index. If a valid Matplotlib color, the rasters are all colored with that color."], [232, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to sdr.plot.raster()."], [232, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Samples\"."], [232, 4, 2, "p-span", "span", "The number of symbols per raster."], [232, 4, 2, "p-sps", "sps", "The number of samples per symbol."], [232, 4, 2, "p-x", "x", "The baseband modulated signal $x[n]$. If x is complex, the real and imaginary rasters are interleaved. Time order is preserved."]], "sdr.plot.filter": [[233, 4, 2, "p-N_freq", "N_freq", "The number of samples $N_f$ in the frequency response."], [233, 4, 2, "p-N_time", "N_time", "The number of samples $N_t$ in the time domain. If None, the length of b is used for FIR filters and 100 for IIR filters."], [233, 4, 2, "p-decades", "decades", "The number of decades to plot when x_axis=\"log\"."], [233, 4, 2, "p-filter", "filter", "The filter definition."], [233, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Normalized Frequency\"."], [233, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum, a two-sided spectrum, or one-sided spectrum with a logarithmic frequency axis."]], "sdr.plot.group_delay": [[234, 4, 2, "p-N", "N", "The number of samples $N$ in the frequency response."], [234, 4, 2, "p-decades", "decades", "The number of decades to plot when x_axis=\"log\"."], [234, 4, 2, "p-filter", "filter", "The filter definition."], [234, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [234, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Normalized Frequency\"."], [234, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum, a two-sided spectrum, or one-sided spectrum with a logarithmic frequency axis. The default is \"auto\" which selects \"one-sided\" for real-valued filters and \"two-sided\" for complex-valued filters."]], "sdr.plot.impulse_response": [[235, 4, 2, "p-N", "N", "The number of samples $N$ to plot. If None, the length of b is used for FIR filters and 100 for IIR filters."], [235, 4, 2, "p-filter", "filter", "The filter definition."], [235, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."]], "sdr.plot.magnitude_response": [[236, 4, 2, "p-N", "N", "The number of samples $N$ in the frequency response."], [236, 4, 2, "p-decades", "decades", "The number of decades to plot when x_axis=\"log\"."], [236, 4, 2, "p-filter", "filter", "The filter definition."], [236, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [236, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Normalized Frequency\"."], [236, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum, a two-sided spectrum, or one-sided spectrum with a logarithmic frequency axis. The default is \"auto\" which selects \"one-sided\" for real-valued filters and \"two-sided\" for complex-valued filters."], [236, 4, 2, "p-y_axis", "y_axis", "The y-axis scaling. Options are to display a linear or logarithmic magnitude response."]], "sdr.plot.p_d": [[237, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [237, 4, 2, "p-p_d", "p_d", "The probability of detection $P_D$."], [237, 4, 2, "p-x", "x", "The SNR or ENR in dB."], [237, 4, 2, "p-x_label", "x_label", "The x-axis label to use."]], "sdr.plot.periodogram": [[238, 4, 2, "p-average", "average", "The type of averaging to use. Options are to average the periodograms using the mean or median."], [238, 4, 2, "p-detrend", "detrend", "The type of detrending to apply. Options are to remove the mean or a linear trend from each segment."], [238, 4, 2, "p-fft", "fft", "The number of points to use in the FFT. If None, the FFT length is set to length."], [238, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [238, 4, 2, "p-length", "length", "The length of each segment in samples. If None, the length is set to 256."], [238, 4, 2, "p-overlap", "overlap", "The number of samples to overlap between segments. If None, the overlap is set to length // 2."], [238, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Normalized Frequency\"."], [238, 4, 2, "p-window", "window", "The windowing function to use. This can be a string or a vector of length length."], [238, 4, 2, "p-x", "x", "The time-domain signal $x[n]$."], [238, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum, a two-sided spectrum, or one-sided spectrum with a logarithmic frequency axis."], [238, 4, 2, "p-y_axis", "y_axis", "The y-axis scaling. Options are to display a linear or logarithmic power spectral density."]], "sdr.plot.phase_delay": [[239, 4, 2, "p-N", "N", "The number of samples $N$ in the phase delay."], [239, 4, 2, "p-decades", "decades", "The number of decades to plot when x_axis=\"log\"."], [239, 4, 2, "p-filter", "filter", "The filter definition."], [239, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [239, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Normalized Frequency\"."], [239, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum, a two-sided spectrum, or one-sided spectrum with a logarithmic frequency axis. The default is \"auto\" which selects \"one-sided\" for real-valued filters and \"two-sided\" for complex-valued filters."]], "sdr.plot.phase_response": [[240, 4, 2, "p-N", "N", "The number of samples $N$ in the phase response."], [240, 4, 2, "p-decades", "decades", "The number of decades to plot when x_axis=\"log\"."], [240, 4, 2, "p-filter", "filter", "The filter definition."], [240, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [240, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Normalized Frequency\"."], [240, 4, 2, "p-unwrap", "unwrap", "Indicates whether to unwrap the phase response."], [240, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum, a two-sided spectrum, or one-sided spectrum with a logarithmic frequency axis. The default is \"auto\" which selects \"one-sided\" for real-valued filters and \"two-sided\" for complex-valued filters."]], "sdr.plot.phase_tree": [[241, 4, 2, "p-color", "color", "Indicates how to color the rasters. If \"index\", the rasters are colored based on their index. If a valid Matplotlib color, the rasters are all colored with that color."], [241, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to sdr.plot.raster()."], [241, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Samples\"."], [241, 4, 2, "p-span", "span", "The number of symbols per raster."], [241, 4, 2, "p-sps", "sps", "The number of samples per symbol."], [241, 4, 2, "p-x", "x", "The baseband CPM signal $x[n]$."]], "sdr.plot.raster": [[242, 4, 2, "p-color", "color", "Indicates how to color the rasters. If \"index\", the rasters are colored based on their index. If a valid Matplotlib color, the rasters are all colored with that color."], [242, 4, 2, "p-colorbar", "colorbar", "Indicates whether to add a colorbar to the plot. This is only added if color=\"index\"."], [242, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.collections.LineCollection. The following keyword arguments are set by default. The defaults may be overwritten."], [242, 4, 2, "p-length", "length", "The length of each raster in samples. This must be provided if x is 1D."], [242, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Samples\"."], [242, 4, 2, "p-stride", "stride", "The stride between each raster in samples. If None, the stride is set to length."], [242, 4, 2, "p-x", "x", "The time-domain signal $x[n]$. If x is complex, the real and imaginary rasters are interleaved. Time order is preserved. If x is 1D, the rastering is determined by length and stride. If x is 2D, the rows correspond to each raster."]], "sdr.plot.roc": [[243, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to the plotting function defined by type."], [243, 4, 2, "p-p_d", "p_d", "The probability of detection $P_D$."], [243, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$."], [243, 4, 2, "p-type", "type", "The type of plot to generate."]], "sdr.plot.ser": [[244, 4, 2, "p-esn0", "esn0", "The symbol energy $E_s$ to noise PSD $N_0$ ratio (dB)."], [244, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.semilogy()."], [244, 4, 2, "p-ser", "ser", "The symbol error rate $P_{se}$."]], "sdr.plot.spectrogram": [[245, 4, 2, "p-detrend", "detrend", "The type of detrending to apply. Options are to remove the mean or a linear trend from each segment."], [245, 4, 2, "p-fft", "fft", "The number of points to use in the FFT. If None, the FFT length is set to length."], [245, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.pcolormesh(). The following keyword arguments are set by default. The defaults may be overwritten."], [245, 4, 2, "p-length", "length", "The length of each segment in samples. If None, the length is set to 256."], [245, 4, 2, "p-overlap", "overlap", "The number of samples to overlap between segments. If None, the overlap is set to length // 2."], [245, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be label as \"Samples\" and the y-axis as \"Normalized Frequency\"."], [245, 4, 2, "p-window", "window", "The windowing function to use. This can be a string or a vector of length length."], [245, 4, 2, "p-x", "x", "The time-domain signal $x[n]$."], [245, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum or two-sided spectrum."]], "sdr.plot.step_response": [[246, 4, 2, "p-N", "N", "The number of samples $N$ to plot. If None, the length of b is used for FIR filters and 100 for IIR filters."], [246, 4, 2, "p-filter", "filter", "The filter definition."], [246, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."]], "sdr.plot.symbol_map": [[247, 4, 2, "p-annotate", "annotate", "If True, the symbols are annotated with their index. If \"bin\", the symbols are annotated with their binary representation."], [247, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot(). The following keyword arguments are set by default. The defaults may be overwritten."], [247, 4, 2, "p-limits", "limits", "The axis limits, which apply to both the x- and y-axis. If None, the axis limits are set to 50% larger than the maximum value."], [247, 4, 2, "p-modulation", "modulation", "The linear modulation or symbol map ${0, dots, M-1} mapsto mathbb{C}$."]], "sdr.plot.time_domain": [[248, 4, 2, "p-centered", "centered", "Indicates whether to center the x-axis about 0. This argument is mutually exclusive with offset."], [248, 4, 2, "p-diff", "diff", "Indicates how to differentiate the real and imaginary parts of a complex signal. If \"color\", the real and imaginary parts will have different colors based on the current Matplotlib color cycle. If \"line\", the real part will have a solid line and the imaginary part will have a dashed line, and both lines will share the same color."], [248, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [248, 4, 2, "p-offset", "offset", "The x-axis offset to apply to the first sample. The units of the offset are $1/f_s$. This argument is mutually exclusive with centered."], [248, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Samples\"."], [248, 4, 2, "p-t", "t", "The time signal $t[n]$. The units are assumed to be $1/f_s$."], [248, 4, 2, "p-x", "x", "The time-domain signal $x[n]$."]], "sdr.plot.zeros_poles": [[250, 4, 2, "p-filter", "filter", "The filter definition."], [250, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."]], "sdr.polyphase_decompose": [[251, 4, 2, "p-phases", "phases", "The number of phases $B$."], [251, 4, 2, "p-taps", "taps", "The multirate FIR filter taps $h_i$."]], "sdr.ppb": [[252, 4, 2, "p-x", "x", "The input ratio."]], "sdr.ppm": [[253, 4, 2, "p-x", "x", "The input ratio."]], "sdr.raised_cosine": [[254, 4, 2, "p-alpha", "alpha", "The excess bandwidth $0 le alpha le 1$ of the filter."], [254, 4, 2, "p-norm", "norm", "Indicates how to normalize the pulse shape."], [254, 4, 2, "p-span", "span", "The length of the filter in symbols. The length of the filter is span * sps + 1 samples. The filter order span * sps must be even."], [254, 4, 2, "p-sps", "sps", "The number of samples per symbol."]], "sdr.rectangular": [[255, 4, 2, "p-norm", "norm", "Indicates how to normalize the pulse shape."], [255, 4, 2, "p-span", "span", "The length of the filter in symbols. The length of the filter is span * sps samples, but only the center sps samples are non-zero. The only reason for span to be larger than 1 is to add delay to the filter."], [255, 4, 2, "p-sps", "sps", "The number of samples per symbol."]], "sdr.rms_voltage": [[256, 4, 2, "p-db", "db", "Indicates whether to return the result in decibels (dB)."], [256, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.root_raised_cosine": [[257, 4, 2, "p-alpha", "alpha", "The excess bandwidth $0 le alpha le 1$ of the filter."], [257, 4, 2, "p-norm", "norm", "Indicates how to normalize the pulse shape."], [257, 4, 2, "p-span", "span", "The length of the filter in symbols. The length of the filter is span * sps + 1 samples. The filter order span * sps must be even."], [257, 4, 2, "p-sps", "sps", "The number of samples per symbol."]], "sdr.sample_rate_offset": [[258, 4, 2, "p-ppm", "ppm", "The sample rate offset $f_{s,text{new}} / f_s$ in parts per million (ppm)."], [258, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to which the sample rate offset is applied."]], "sdr.snr_to_ebn0": [[259, 4, 2, "p-bps", "bps", "Bits per symbol $log_2 M$, where $M$ is the modulation order."], [259, 4, 2, "p-rate", "rate", "Code rate $r = k/n$, where $k$ is the number of information bits and $n$ is the number of coded bits."], [259, 4, 2, "p-snr", "snr", "Signal-to-noise ratio $S/N$ in dB."], [259, 4, 2, "p-sps", "sps", "Samples per symbol $f_s / f_{sym}$."]], "sdr.snr_to_esn0": [[260, 4, 2, "p-snr", "snr", "Signal-to-noise ratio $S/N$ in dB."], [260, 4, 2, "p-sps", "sps", "Samples per symbol $f_s / f_{sym}$."]], "sdr.to_complex_bb": [[261, 4, 2, "p-x_r", "x_r", "The real passband signal $x_r[n]$ centered at $f_{s,r}/4$ with sample rate $f_{s,r}$. If the length is odd, one zero is appended to the end."]], "sdr.to_real_pb": [[262, 4, 2, "p-x_c", "x_c", "The complex baseband signal $x_c[n]$ centered at $0$ with sample rate $f_{s,c}$."]], "sdr.unpack": [[263, 4, 2, "p-bpe", "bpe", "The number of bits per element in the input array."], [263, 4, 2, "p-dtype", "dtype", "The data type of the output array. If None, numpy.uint8 is used."], [263, 4, 2, "p-x", "x", "The input array with bpe bits per element."]], "sdr.upsample": [[264, 4, 2, "p-rate", "rate", "The upsampling factor $r$."], [264, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ with sample rate $f_s$."]], "sdr.walsh": [[265, 4, 2, "p-index", "index", "The index $i$ of the Walsh code. Indicates how many transitions there are in the code."], [265, 4, 2, "p-length", "length", "The length $N$ of the Walsh code/sequence. Must be a power of 2."], [265, 4, 2, "p-output", "output", "The output format of the Walsh code/sequence."]], "sdr.wavelength": [[266, 4, 2, "p-freq", "freq", "The frequency $f$ in Hz of the signal."]], "sdr.zadoff_chu": [[267, 4, 2, "p-length", "length", "The length $N$ of the Zadoff-Chu sequence."], [267, 4, 2, "p-root", "root", "The root $0 < u < N$ of the Zadoff-Chu sequence. The root must be relatively prime to the length, i.e., $gcd(u, N) = 1$."], [267, 4, 2, "p-shift", "shift", "The shift $q in mathbb{Z}$ of the Zadoff-Chu sequence. When $q ne 0$, the returned sequence is a cyclic shift of the root-$u$ Zadoff-Chu sequence."]]}, "objtypes": {"0": "py:module", "1": "py:class", "2": "py:property", "3": "py:method", "4": "py:parameter", "5": "py:function"}, "objnames": {"0": ["py", "module", "Python module"], "1": ["py", "class", "Python class"], "2": ["py", "property", "Python property"], "3": ["py", "method", "Python method"], "4": ["py", "parameter", "Python parameter"], "5": ["py", "function", "Python function"]}, "titleterms": {"convers": 0, "decibel": 0, "ratio": 0, "from": [0, 272, 273, 274], "e_b": 0, "n_0": 0, "e_": 0, "": [0, 276, 277], "n": [0, 275, 276, 277], "data": 1, "manipul": [1, 3], "detect": [2, 7], "detector": [2, 270], "theoret": 2, "limit": 2, "digit": [3, 277], "signal": [3, 269, 275, 278], "process": 3, "fir": [3, 276], "filter": [3, 7, 276, 277, 279], "iir": [3, 277], "multir": 3, "arbitrari": [3, 275], "resampl": [3, 275], "correl": 3, "link": 4, "budget": 4, "channel": [4, 269], "capac": 4, 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"examples/peak-to-average-power/", "examples/phase-locked-loop/", "examples/psk/", "examples/pulse-shapes/", "", "release-notes/v0.0/", "release-notes/versioning/"]}) \ No newline at end of file +Search.setIndex({"titles": ["Conversions", "Data manipulation", "Detection", "Digital signal processing", "Link budgets", "Measurement", "Modulation", "Plotting", "Probability", "sdr.ClosedLoopPLL", "sdr.ClosedLoopPLL.Bn", "sdr.ClosedLoopPLL.BnT", "sdr.ClosedLoopPLL.K0", "sdr.ClosedLoopPLL.K1", "sdr.ClosedLoopPLL.K2", "sdr.ClosedLoopPLL.Kp", "sdr.ClosedLoopPLL.__init__", "sdr.ClosedLoopPLL.frequency_lock_time", "sdr.ClosedLoopPLL.iir", "sdr.ClosedLoopPLL.lock_time", "sdr.ClosedLoopPLL.omega_3dB", "sdr.ClosedLoopPLL.omega_n", "sdr.ClosedLoopPLL.phase_error_variance", "sdr.ClosedLoopPLL.phase_lock_time", "sdr.ClosedLoopPLL.sample_rate", "sdr.ClosedLoopPLL.zeta", "sdr.Decimator", "sdr.Decimator.__call__", "sdr.Decimator.__init__", "sdr.Decimator.__repr__", "sdr.Decimator.__str__", 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2, 3, 4, 26, 37, 39, 51, 59, 61, 76, 77, 79, 84, 86, 94, 95, 96, 97, 108, 143, 144, 153, 163, 166, 168, 171, 174, 179, 195, 206, 232, 238, 243, 252, 256, 271, 274, 281, 290, 291], "multipl": [1, 59, 84, 232, 271, 288, 291], "bit": [1, 5, 7, 44, 46, 49, 107, 111, 112, 142, 143, 152, 153, 162, 163, 166, 169, 170, 171, 195, 197, 198, 200, 201, 214, 215, 217, 228, 232, 238, 267, 271, 290, 291], "element": [1, 228, 232, 271], "unpack": [1, 44, 46, 228, 271, 288, 290, 291], "hexdump": [1, 44, 228, 290, 291], "byte": [1, 228], "width": [1, 206, 228], "16": [1, 166, 168, 169, 183, 206, 214, 215, 217, 225, 228, 238, 252, 259, 262, 265, 267, 268, 273, 286, 291], "str": [1, 26, 29, 30, 37, 51, 55, 56, 76, 80, 81, 94, 96, 99, 100, 107, 109, 110, 142, 152, 154, 155, 162, 164, 165, 170, 179, 182, 183, 228, 240, 246, 249, 250, 253], "return": [1, 6, 9, 17, 19, 22, 23, 26, 27, 29, 30, 37, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 54, 55, 56, 58, 59, 60, 61, 63, 66, 70, 76, 78, 80, 81, 84, 86, 91, 94, 96, 97, 99, 100, 107, 109, 110, 111, 113, 114, 115, 116, 121, 128, 137, 139, 140, 142, 146, 151, 152, 154, 155, 157, 159, 160, 162, 164, 165, 166, 168, 170, 172, 173, 175, 176, 177, 178, 179, 182, 183, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 276, 284, 285, 286, 288, 291], "specifi": [1, 44, 47, 48, 50, 134, 139, 140, 156, 159, 160, 194, 195, 212, 228, 279, 284, 285, 291], "class": [2, 3, 5, 6, 9, 26, 37, 39, 44, 46, 47, 48, 49, 50, 51, 69, 76, 94, 96, 107, 125, 134, 142, 144, 152, 156, 162, 170, 174, 179, 278, 284, 285, 288, 290, 291], "replicacorrel": [2, 174, 175, 176, 177, 178, 291], "implement": [2, 3, 6, 26, 37, 39, 51, 69, 76, 94, 96, 107, 125, 131, 134, 142, 144, 152, 156, 162, 170, 174, 179, 192, 278, 283], "clairvoy": [2, 174], "replica": [2, 174], "correl": [2, 174, 196, 225, 273, 275], "energydetector": [2, 39, 40, 41, 42, 43, 291], "energi": [2, 39, 111, 121, 166, 168, 174, 175, 176, 177, 178, 195, 214, 215, 216, 217, 218, 223, 226, 238, 252, 262, 263, 265, 267, 268, 290, 291], "albersheim": [2, 192, 291], "p_d": [2, 7, 39, 40, 42, 174, 175, 177, 192, 245, 251, 291], "p_fa": [2, 7, 39, 40, 41, 42, 43, 174, 175, 176, 177, 178, 192, 251], "estim": [2, 9, 107, 113, 114, 142, 152, 162, 170, 192, 246, 253, 287], "minimum": [2, 6, 142, 192, 291], "requir": [2, 27, 52, 97, 192, 279, 280, 281, 282, 291], "singl": [2, 42, 59, 84, 166, 168, 192], "sampl": [2, 3, 9, 16, 24, 26, 27, 31, 37, 40, 41, 42, 43, 51, 52, 57, 59, 60, 61, 63, 66, 69, 73, 84, 86, 91, 96, 97, 98, 101, 107, 108, 114, 116, 122, 125, 129, 132, 142, 143, 144, 146, 147, 148, 150, 151, 152, 153, 162, 163, 170, 171, 179, 181, 184, 192, 194, 213, 215, 218, 221, 223, 226, 231, 240, 241, 242, 243, 244, 246, 247, 248, 249, 250, 253, 254, 256, 262, 263, 265, 266, 267, 268, 269, 270, 272, 277, 283, 286, 287, 289, 290, 291], "given": [2, 39, 44, 46, 47, 48, 50, 69, 70, 174, 192, 220, 284, 285], "n_": [2, 40, 41, 42, 43, 192], "nc": [2, 40, 41, 42, 43, 192], "non": [2, 27, 40, 41, 42, 43, 52, 97, 192, 226, 256, 263], "coher": [2, 40, 41, 42, 43, 192], "combin": [2, 192], "achiev": [2, 192, 288, 289], "probabl": [2, 7, 39, 40, 41, 42, 43, 172, 173, 174, 175, 176, 177, 178, 192, 197, 198, 200, 201, 212, 245, 251, 277, 291], "fals": [2, 5, 26, 28, 29, 30, 37, 38, 39, 40, 41, 42, 43, 51, 53, 55, 56, 59, 69, 71, 76, 77, 79, 80, 81, 84, 94, 95, 96, 97, 98, 99, 100, 142, 152, 162, 166, 168, 170, 174, 175, 176, 177, 178, 179, 181, 182, 183, 192, 193, 197, 200, 212, 216, 231, 235, 236, 239, 246, 251, 253, 256, 264, 285, 289], "alarm": [2, 39, 40, 41, 42, 43, 174, 175, 176, 177, 178, 192, 251], "p_": [2, 7, 39, 40, 41, 42, 43, 166, 168, 174, 175, 176, 177, 178, 192, 193, 194, 203, 212, 220, 230, 233, 235, 238, 246, 251, 252], "fa": [2, 7, 39, 40, 41, 42, 43, 174, 175, 176, 177, 178, 192, 251], "thi": [2, 9, 26, 46, 47, 48, 50, 51, 76, 96, 98, 107, 108, 123, 134, 142, 146, 152, 153, 162, 163, 169, 170, 171, 179, 181, 192, 194, 195, 197, 200, 212, 213, 220, 222, 225, 240, 246, 250, 253, 256, 272, 273, 279, 281, 282, 283, 285, 287, 288, 289], "function": [2, 7, 8, 9, 18, 37, 51, 76, 77, 94, 125, 172, 173, 192, 195, 213, 223, 225, 238, 245, 246, 251, 252, 253, 272, 273, 284, 285, 287, 289, 290, 291], "": [2, 3, 7, 9, 17, 19, 20, 21, 23, 24, 26, 37, 39, 46, 47, 48, 49, 50, 51, 59, 60, 63, 66, 76, 84, 91, 94, 96, 107, 108, 113, 114, 115, 116, 134, 142, 152, 162, 170, 174, 176, 178, 179, 192, 194, 195, 215, 218, 220, 221, 229, 239, 240, 241, 242, 244, 246, 247, 248, 249, 250, 253, 254, 256, 257, 266, 267, 268, 269, 270, 282, 283, 286, 288, 290, 291], "equat": [2, 17, 19, 20, 21, 22, 23, 40, 41, 43, 76, 152, 162, 170, 175, 176, 178, 192, 222], "finit": [3, 51, 290, 291], "impuls": [3, 7, 26, 37, 51, 61, 76, 86, 94, 96, 179, 204, 205, 206, 207, 208, 209, 223, 241, 243, 289, 290, 291], "respons": [3, 7, 26, 37, 51, 59, 61, 66, 76, 84, 86, 91, 94, 96, 179, 204, 205, 206, 207, 208, 209, 223, 241, 242, 243, 244, 248, 254, 289, 290, 291], "differenti": [3, 6, 37, 38, 142, 166, 168, 210, 211, 256, 290, 291], "design_lowpass_fir": [3, 59, 208, 291], "order": [3, 9, 26, 27, 30, 37, 44, 49, 51, 52, 56, 62, 69, 72, 76, 81, 87, 94, 96, 97, 98, 100, 107, 108, 117, 125, 129, 142, 152, 162, 163, 170, 171, 179, 181, 183, 194, 204, 205, 207, 208, 214, 215, 217, 220, 221, 223, 239, 240, 249, 250, 262, 265, 266, 267, 278, 285, 286, 287, 288, 291], "design": [3, 26, 28, 32, 96, 98, 102, 108, 153, 163, 171, 179, 181, 186, 204, 205, 206, 207, 208, 209, 279, 290, 291], "lowpass": [3, 208], "h": [3, 7, 26, 37, 39, 51, 53, 55, 56, 59, 61, 76, 84, 86, 94, 96, 107, 108, 119, 120, 124, 125, 142, 152, 153, 162, 163, 170, 171, 174, 179, 204, 205, 206, 207, 208, 209, 223, 240, 241, 243, 244, 248, 259, 286, 287, 289], "n": [3, 5, 6, 7, 8, 9, 26, 27, 37, 39, 42, 46, 47, 48, 49, 50, 51, 52, 53, 54, 57, 58, 60, 61, 62, 63, 65, 66, 68, 69, 70, 76, 78, 79, 82, 86, 87, 91, 94, 96, 97, 107, 108, 114, 116, 119, 120, 124, 125, 128, 142, 144, 146, 151, 152, 153, 162, 163, 170, 171, 172, 173, 174, 176, 178, 179, 180, 193, 194, 195, 196, 199, 202, 204, 205, 206, 207, 208, 209, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 224, 225, 227, 229, 231, 233, 235, 236, 240, 241, 242, 243, 244, 246, 247, 248, 249, 250, 253, 254, 256, 264, 266, 267, 268, 269, 270, 272, 273, 275, 276, 277, 287, 289, 290], "us": [3, 7, 26, 28, 32, 35, 37, 38, 51, 53, 58, 59, 64, 69, 71, 76, 77, 79, 84, 89, 94, 95, 96, 97, 98, 102, 105, 107, 108, 113, 114, 125, 131, 134, 139, 140, 142, 152, 153, 156, 159, 160, 162, 163, 170, 171, 179, 181, 186, 189, 195, 198, 201, 204, 205, 206, 207, 208, 209, 220, 225, 228, 232, 239, 240, 241, 243, 245, 246, 253, 254, 271, 273, 279, 280, 281, 282, 284, 285, 287, 288, 289, 290, 292], "window": [3, 26, 59, 96, 179, 204, 205, 206, 207, 208, 209, 246, 253, 291], "method": [3, 7, 30, 32, 98, 100, 102, 181, 183, 186, 204, 205, 206, 207, 208, 209, 246, 253, 284, 285, 291], "design_highpass_fir": [3, 207, 291], "highpass": [3, 207], "design_bandpass_fir": [3, 204, 291], "bandpass": [3, 204], "design_bandstop_fir": [3, 205, 291], "bandstop": [3, 205], "infinit": [3, 76, 290, 291], "integr": [3, 9, 14, 40, 41, 42, 43, 94, 95, 125, 127, 129, 192, 278, 282, 285, 290, 291], "interpol": [3, 26, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 124, 142, 152, 162, 170, 179, 181, 191, 209, 240, 272, 286, 288, 290, 291], "polyphas": [3, 26, 27, 28, 33, 36, 96, 97, 98, 103, 106, 179, 180, 181, 187, 190, 209, 213, 259, 272, 290, 291], "decim": [3, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 107, 108, 113, 114, 115, 116, 120, 123, 142, 143, 152, 153, 162, 163, 169, 170, 171, 179, 181, 185, 209, 213, 288, 290, 291], "ration": [3, 179, 181, 209, 291], "design_multirate_fir": [3, 28, 98, 181, 209, 291], "up": [3, 179, 181, 191, 209, 222, 280], "kaiser": [3, 26, 28, 29, 30, 32, 96, 97, 98, 99, 100, 102, 179, 181, 182, 183, 186, 204, 205, 206, 207, 208, 209], "polyphase_decompos": [3, 259, 291], "tap": [3, 26, 28, 33, 36, 37, 51, 56, 68, 69, 75, 76, 82, 83, 94, 96, 98, 103, 106, 179, 181, 187, 190, 259, 284, 285], "phase": [3, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 37, 51, 63, 96, 107, 108, 118, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 137, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 156, 157, 159, 160, 161, 162, 163, 166, 167, 168, 169, 170, 171, 179, 192, 221, 229, 231, 247, 248, 249, 259, 277, 290, 291], "decompos": [3, 26, 96, 179, 259], "h_i": [3, 26, 28, 33, 36, 37, 51, 53, 68, 96, 98, 103, 106, 179, 181, 187, 190, 259, 284], "matrix": [3, 212, 259, 277], "h_": [3, 9, 26, 33, 36, 96, 103, 106, 179, 187, 190, 259, 287], "i": [3, 9, 16, 25, 26, 27, 28, 33, 36, 37, 39, 41, 42, 43, 44, 49, 51, 52, 53, 59, 61, 66, 67, 68, 69, 74, 76, 79, 83, 84, 86, 91, 92, 94, 96, 97, 98, 103, 106, 107, 108, 125, 129, 130, 132, 134, 142, 146, 150, 152, 153, 156, 162, 163, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 181, 187, 190, 192, 193, 194, 195, 197, 198, 200, 201, 203, 204, 205, 206, 207, 208, 212, 214, 215, 216, 217, 218, 219, 221, 222, 223, 225, 226, 227, 228, 229, 230, 232, 233, 234, 235, 236, 239, 240, 241, 242, 243, 244, 246, 247, 248, 250, 253, 254, 256, 259, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 273, 274, 275, 279, 280, 281, 282, 283, 284, 285, 286, 287, 288, 289, 290, 292], "j": [3, 26, 33, 36, 59, 76, 79, 82, 84, 94, 96, 103, 106, 142, 144, 152, 162, 170, 179, 187, 190, 194, 212, 229, 231, 259, 275, 284, 285], "b": [3, 76, 79, 192, 195, 223, 228, 241, 243, 254, 259, 279, 280, 289], "farrowresampl": [3, 69, 70, 71, 72, 73, 74, 75, 283, 291], "cubic": [3, 69], "farrow": [3, 69, 70, 71, 72, 73, 74, 75, 290, 291], "design_frac_delay_fir": [3, 206, 291], "length": [3, 6, 7, 26, 27, 37, 42, 51, 52, 54, 61, 66, 78, 96, 97, 98, 108, 114, 116, 143, 153, 163, 171, 179, 181, 196, 199, 204, 205, 206, 207, 208, 209, 223, 224, 225, 226, 241, 243, 246, 250, 253, 254, 262, 263, 265, 269, 273, 275, 276, 280, 283, 286, 289], "delai": [3, 7, 26, 27, 30, 31, 37, 51, 52, 56, 57, 60, 63, 69, 96, 97, 100, 101, 125, 144, 179, 183, 184, 206, 210, 211, 226, 242, 247, 263, 287, 290, 291], "fraction": [3, 69, 73, 206, 223, 283, 290, 291], "mix": [3, 231, 290, 291], "freq": [3, 4, 26, 37, 51, 59, 76, 84, 94, 96, 144, 146, 179, 221, 222, 231, 234, 274, 277, 283, 287], "float": [3, 5, 6, 9, 10, 11, 12, 13, 14, 15, 16, 17, 19, 20, 21, 22, 23, 24, 25, 26, 37, 42, 44, 46, 47, 48, 50, 51, 59, 60, 63, 69, 70, 76, 77, 84, 85, 94, 96, 107, 108, 118, 125, 126, 127, 129, 130, 132, 134, 135, 136, 138, 141, 142, 143, 144, 145, 147, 148, 149, 152, 153, 156, 161, 162, 163, 167, 170, 171, 177, 179, 188, 193, 194, 195, 197, 200, 202, 204, 205, 206, 207, 208, 209, 220, 221, 223, 229, 231, 233, 235, 236, 239, 240, 241, 242, 244, 246, 247, 248, 249, 250, 253, 255, 256, 262, 264, 265, 266, 277], "0": [3, 6, 8, 16, 26, 27, 33, 36, 37, 39, 42, 44, 51, 52, 53, 55, 56, 59, 60, 63, 68, 76, 77, 79, 80, 81, 82, 83, 84, 94, 96, 97, 98, 103, 106, 107, 108, 113, 114, 115, 116, 123, 129, 142, 143, 144, 147, 152, 153, 162, 163, 167, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 181, 187, 190, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 203, 204, 205, 206, 207, 208, 210, 211, 212, 213, 215, 216, 218, 219, 220, 221, 222, 223, 224, 225, 227, 229, 230, 231, 232, 234, 237, 239, 240, 241, 242, 243, 244, 247, 248, 249, 254, 255, 256, 257, 258, 259, 260, 261, 262, 264, 265, 266, 267, 268, 269, 270, 271, 273, 274, 275, 279, 280, 281, 283, 284, 285, 286, 287, 288, 289, 292], "time": [3, 5, 9, 16, 17, 19, 20, 21, 22, 23, 37, 51, 76, 94, 125, 129, 134, 152, 156, 162, 170, 193, 194, 202, 204, 205, 207, 208, 212, 213, 216, 218, 219, 221, 223, 225, 227, 229, 231, 233, 235, 236, 240, 241, 246, 250, 253, 256, 262, 264, 265, 266, 268, 269, 270, 272, 273, 277, 283, 284, 285, 289, 290, 291], "domain": [3, 5, 193, 194, 202, 204, 205, 207, 208, 213, 216, 219, 221, 227, 229, 231, 233, 235, 236, 241, 246, 250, 253, 256, 264, 266, 269, 270, 272, 277, 290, 291], "complex": [3, 5, 7, 26, 37, 39, 40, 41, 42, 43, 51, 59, 76, 84, 94, 96, 107, 108, 113, 114, 115, 116, 123, 134, 137, 142, 143, 144, 146, 151, 152, 153, 156, 157, 162, 163, 169, 170, 171, 174, 175, 176, 177, 178, 179, 194, 195, 213, 220, 229, 231, 239, 240, 242, 244, 247, 248, 250, 255, 256, 269, 270, 272, 277, 283, 284, 285, 287, 288, 290, 291], "exponenti": [3, 146, 213, 231, 269, 270, 272, 283, 284, 285], "real": [3, 40, 41, 43, 142, 152, 172, 173, 175, 176, 178, 194, 231, 240, 242, 244, 247, 248, 250, 256, 269, 270, 283, 284, 285, 287, 290, 291], "sinusoid": [3, 162, 194, 231, 269, 270, 285, 291], "to_complex_bb": [3, 269, 291], "x_r": [3, 269, 270], "complex_": [3, 7, 107, 113, 114, 115, 116, 123, 142, 144, 151, 152, 156, 157, 162, 169, 170, 239, 255, 269, 270, 275, 276], "passband": [3, 204, 205, 206, 207, 208, 223, 226, 262, 263, 265, 269, 270, 286, 291], "center": [3, 204, 205, 206, 207, 208, 226, 256, 263, 269, 270, 291], "f_": [3, 9, 16, 24, 27, 59, 60, 63, 84, 97, 107, 108, 122, 142, 143, 152, 153, 162, 163, 170, 171, 204, 205, 207, 208, 213, 215, 218, 221, 223, 231, 240, 241, 242, 244, 246, 247, 248, 249, 250, 253, 256, 266, 267, 268, 269, 270, 272, 283, 284, 285, 287, 289], "r": [3, 26, 27, 28, 33, 34, 36, 69, 70, 96, 97, 98, 103, 104, 106, 195, 213, 214, 215, 217, 220, 223, 231, 262, 265, 267, 269, 270, 272, 279, 280, 281, 282, 285, 286, 287, 289], "4": [3, 7, 17, 19, 26, 33, 36, 37, 40, 42, 44, 59, 80, 81, 84, 94, 96, 97, 103, 106, 134, 142, 143, 144, 152, 153, 156, 162, 166, 167, 168, 169, 170, 174, 175, 176, 177, 178, 179, 182, 183, 187, 190, 192, 194, 195, 196, 198, 199, 201, 204, 205, 206, 207, 208, 209, 212, 213, 214, 215, 217, 218, 220, 221, 222, 223, 224, 225, 226, 228, 229, 231, 232, 234, 238, 239, 240, 241, 242, 243, 244, 247, 248, 249, 252, 254, 255, 256, 257, 258, 259, 262, 263, 265, 266, 267, 268, 269, 270, 271, 272, 273, 275, 281, 283, 285, 286, 287, 288], "rate": [3, 5, 7, 9, 16, 24, 26, 27, 28, 30, 34, 44, 45, 46, 48, 49, 59, 60, 63, 69, 70, 84, 96, 97, 98, 100, 104, 107, 111, 121, 142, 152, 162, 166, 168, 170, 179, 180, 181, 183, 185, 188, 191, 209, 213, 214, 215, 217, 221, 231, 238, 240, 241, 242, 244, 246, 247, 248, 249, 250, 252, 253, 256, 266, 267, 269, 270, 272, 277, 290, 291], "baseband": [3, 7, 9, 142, 152, 162, 170, 231, 240, 249, 269, 270, 286, 287, 291], "x_c": [3, 269, 270], "c": [3, 9, 17, 19, 20, 21, 22, 23, 46, 47, 48, 49, 50, 107, 108, 123, 125, 142, 152, 162, 169, 170, 195, 198, 201, 222, 234, 255, 269, 270, 274, 287], "2": [3, 6, 7, 9, 17, 19, 22, 26, 29, 30, 33, 36, 37, 39, 40, 41, 42, 43, 44, 51, 55, 56, 57, 59, 60, 63, 80, 81, 84, 94, 96, 97, 99, 100, 103, 106, 107, 108, 117, 134, 142, 144, 152, 153, 156, 162, 163, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 182, 183, 187, 190, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 228, 229, 230, 231, 232, 234, 235, 237, 238, 239, 240, 241, 242, 243, 244, 246, 247, 248, 249, 252, 253, 254, 255, 256, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 275, 279, 282, 283, 284, 285, 286, 287, 288, 289], "to_real_pb": [3, 270, 286, 291], "2f_": [3, 270], "upsampl": [3, 96, 179, 272, 291], "factor": [3, 5, 9, 16, 25, 108, 125, 129, 130, 153, 163, 171, 202, 213, 272, 287], "downsampl": [3, 213, 291], "bsc_capac": [4, 201, 291], "p": [4, 8, 144, 146, 172, 173, 179, 181, 187, 188, 190, 191, 197, 198, 200, 201, 209, 212, 277], "calcul": [4, 5, 195, 198, 201, 220, 222, 234, 274, 291], "symmetr": [4, 200, 201, 212, 269, 270, 277, 290], "bsc": [4, 200, 201, 212, 277, 290, 291], "bec_capac": [4, 198, 291], "erasur": [4, 197, 198, 212, 277, 290], "bec": [4, 197, 198, 212, 277, 290, 291], "awgn_capac": [4, 195, 291], "addit": [4, 194, 195, 238, 239, 240, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 258, 272, 277, 290], "white": [4, 194, 195, 277, 290], "gaussian": [4, 6, 37, 94, 194, 195, 223, 277, 290, 291], "nois": [4, 9, 10, 11, 16, 22, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 111, 121, 125, 129, 132, 142, 152, 162, 166, 168, 170, 174, 175, 176, 177, 178, 194, 195, 214, 215, 217, 218, 238, 252, 267, 268, 277, 287, 290], "awgn": [4, 142, 152, 162, 166, 168, 170, 194, 195, 220, 238, 239, 252, 269, 270, 277, 288, 290, 291], "fspl": [4, 222], "distanc": [4, 219, 222, 227, 290, 291], "free": [4, 142, 152, 162, 170, 222, 290], "space": [4, 59, 84, 222, 290], "wavelength": [4, 274, 291], "lambda": [4, 222, 274], "electromagnet": [4, 274], "wave": [4, 142, 274], "frequenc": [4, 9, 17, 19, 21, 26, 37, 51, 59, 60, 63, 76, 84, 94, 96, 125, 142, 144, 146, 179, 204, 205, 206, 207, 208, 213, 221, 222, 231, 234, 241, 242, 244, 246, 247, 248, 253, 269, 270, 272, 274, 277, 289, 290, 291], "f": [4, 17, 19, 26, 42, 59, 60, 63, 84, 96, 144, 146, 179, 192, 194, 221, 222, 223, 231, 234, 266, 274, 275, 280, 283, 284, 285, 286, 287, 288, 289], "parabolic_antenna": [4, 234, 291], "tupl": [4, 26, 37, 39, 42, 44, 46, 49, 51, 59, 60, 63, 76, 84, 94, 96, 107, 113, 114, 134, 139, 140, 142, 152, 156, 159, 160, 162, 170, 174, 177, 179, 193, 216, 219, 227, 233, 234, 235, 239, 241, 242, 243, 244, 247, 248, 254, 255, 258], "gain": [4, 9, 12, 13, 14, 15, 16, 76, 77, 85, 94, 125, 126, 127, 129, 134, 141, 144, 145, 147, 156, 161, 192, 204, 205, 206, 207, 208, 222, 223, 226, 234, 262, 263, 265, 287, 290], "g": [4, 49, 234, 281], "beamwidth": [4, 234], "theta": [4, 144, 147, 149, 150, 234], "parabol": [4, 234], "reflector": [4, 234], "signal": [5, 7, 9, 17, 19, 22, 23, 26, 27, 37, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 58, 69, 70, 76, 78, 94, 96, 97, 107, 108, 119, 125, 128, 134, 135, 136, 138, 142, 144, 146, 151, 152, 153, 162, 163, 170, 171, 174, 175, 176, 177, 178, 179, 180, 193, 194, 195, 202, 203, 204, 205, 207, 208, 209, 213, 214, 215, 216, 217, 218, 219, 221, 222, 223, 227, 229, 230, 231, 233, 234, 235, 236, 240, 241, 242, 244, 246, 247, 248, 249, 250, 253, 256, 259, 264, 266, 267, 268, 269, 270, 272, 274, 284, 285, 287, 289, 290, 291], "peak_pow": [5, 233, 235, 291], "peak": [5, 142, 152, 170, 202, 220, 233, 235, 236], "average_pow": [5, 193, 233, 291], "averag": [5, 44, 134, 139, 140, 142, 152, 156, 159, 160, 170, 193, 194, 195, 220, 233, 246], "papr": [5, 142, 152, 170, 233, 286, 291], "ratio": [5, 22, 40, 42, 44, 46, 47, 48, 49, 50, 111, 121, 142, 152, 166, 168, 170, 175, 177, 194, 195, 214, 215, 217, 218, 233, 237, 238, 252, 260, 261, 267, 268], "peak_voltag": [5, 202, 236, 291], "bool": [5, 26, 28, 37, 38, 40, 41, 42, 43, 51, 53, 59, 67, 69, 71, 74, 76, 77, 79, 84, 92, 94, 95, 96, 98, 142, 152, 162, 166, 168, 170, 175, 176, 177, 178, 179, 181, 193, 216, 231, 235, 236, 239, 248, 250, 255, 256, 264], "rms_voltag": [5, 202, 264, 291], "root": [5, 6, 108, 153, 163, 171, 220, 240, 256, 264, 265, 275, 276, 284, 290], "mean": [5, 220, 246, 253, 264, 289], "squar": [5, 6, 108, 153, 163, 171, 220, 222, 234, 256, 264, 265, 284], "rm": [5, 134, 135, 136, 138, 202, 220, 264], "crest_factor": [5, 202, 233, 291], "crest": [5, 202], "euclidean": [5, 219, 290, 291], "y": [5, 6, 26, 27, 37, 51, 52, 58, 70, 76, 78, 94, 96, 97, 125, 128, 144, 146, 151, 179, 194, 197, 200, 210, 211, 212, 213, 219, 221, 227, 229, 231, 239, 244, 246, 253, 255, 266, 272, 287, 288], "between": [5, 26, 28, 38, 53, 67, 71, 74, 77, 79, 92, 95, 96, 98, 156, 179, 181, 219, 222, 227, 246, 250, 253, 287, 290], "two": [5, 204, 205, 219, 227, 240, 241, 242, 244, 246, 247, 248, 253, 275, 283, 284, 285], "ham": [5, 59, 204, 205, 207, 208, 227, 290, 291], "errorr": [5, 44, 45, 46, 47, 48, 49, 50, 288, 291], "A": [5, 9, 17, 19, 20, 21, 22, 23, 25, 27, 37, 44, 51, 52, 59, 84, 94, 97, 108, 125, 134, 153, 156, 163, 171, 192, 199, 204, 205, 207, 208, 224, 228, 229, 234, 262, 265, 278, 280, 287], "error": [5, 7, 9, 15, 16, 22, 44, 45, 46, 48, 49, 50, 107, 111, 121, 125, 129, 134, 137, 139, 140, 141, 142, 152, 156, 157, 159, 160, 161, 162, 166, 168, 170, 192, 201, 220, 238, 252, 287, 290, 291], "ber": [5, 7, 44, 107, 111, 142, 152, 162, 166, 170, 238, 288, 290, 291], "symbol": [5, 7, 44, 46, 49, 96, 107, 108, 112, 113, 114, 115, 116, 121, 122, 123, 134, 137, 142, 143, 152, 153, 156, 157, 162, 163, 166, 168, 169, 170, 171, 194, 214, 215, 217, 218, 220, 221, 223, 226, 239, 240, 249, 252, 255, 256, 262, 263, 265, 267, 268, 286, 287, 289, 290, 291], "ser": [5, 7, 44, 107, 121, 142, 152, 162, 168, 170, 252, 288, 290, 291], "evm": [5, 220, 290, 291], "x_hat": [5, 7, 44, 46, 220, 239, 288], "ref": [5, 134, 136, 138, 192, 204, 205, 206, 207, 208, 209, 220, 223, 225, 273], "vector": [5, 44, 59, 73, 84, 204, 205, 207, 208, 220, 246, 253, 290, 291], "magnitud": [5, 7, 196, 206, 220, 225, 241, 244, 273, 275, 290, 291], "hat": [5, 7, 46, 107, 113, 114, 134, 137, 142, 152, 156, 157, 162, 170, 220, 239, 255], "k": [5, 6, 7, 46, 107, 108, 112, 113, 114, 115, 116, 117, 134, 137, 142, 152, 156, 157, 162, 163, 170, 171, 210, 211, 214, 215, 217, 220, 239, 255, 256, 267, 286, 289], "linearmodul": [6, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 139, 140, 159, 160, 162, 255, 291], "amplitud": [6, 107, 108, 134, 135, 136, 138, 229, 277, 283, 287], "arbitrari": [6, 69, 70, 71, 72, 73, 74, 75, 107, 290, 291], "psk": [6, 134, 152, 156, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 194, 220, 221, 229, 238, 239, 240, 252, 255, 256, 266, 286, 287, 290, 291], "shift": [6, 142, 152, 162, 166, 167, 168, 169, 170, 275, 284, 285, 290, 291], "kei": [6, 142, 152, 162, 166, 167, 168, 169, 170, 290, 291], "demodul": [6, 107, 114, 142, 152, 162, 170, 291], "pimpsk": [6, 170, 171, 291], "pi": [6, 26, 80, 81, 84, 96, 97, 134, 144, 152, 156, 162, 170, 171, 179, 194, 213, 222, 223, 229, 231, 234, 241, 242, 243, 244, 247, 248, 254, 258, 269, 270, 272, 275, 283, 284, 285, 287, 290, 291], "m": [6, 76, 79, 83, 94, 107, 108, 112, 113, 114, 115, 116, 117, 123, 134, 142, 152, 156, 162, 163, 169, 170, 171, 212, 214, 215, 217, 222, 255, 267, 279, 280, 281, 282, 290, 291], "oqpsk": [6, 142, 152, 153, 154, 155, 291], "offset": [6, 17, 19, 26, 37, 96, 97, 107, 108, 118, 142, 143, 144, 146, 147, 149, 152, 153, 162, 163, 167, 170, 171, 179, 221, 231, 256, 266, 277, 287, 290, 291], "quadratur": [6, 142, 152, 229], "msk": [6, 142, 143, 249, 291], "rectangular": [6, 108, 153, 163, 171, 263, 286, 289, 290, 291], "span": [6, 7, 108, 153, 163, 171, 223, 226, 240, 249, 262, 263, 265, 286, 289], "half_sin": [6, 143, 226, 291], "half": [6, 142, 152, 209, 226, 234, 290, 291], "sine": [6, 142, 146, 226, 290, 291], "time_bandwidth": [6, 223], "raised_cosin": [6, 108, 153, 163, 171, 240, 262, 289, 291], "alpha": [6, 108, 153, 163, 171, 223, 257, 262, 265, 286, 289], "rais": [6, 37, 94, 108, 153, 163, 171, 240, 256, 262, 265, 284, 290], "cosin": [6, 37, 94, 108, 146, 153, 163, 171, 240, 256, 262, 265, 284, 290], "rc": [6, 108, 153, 163, 171, 262], "root_raised_cosin": [6, 37, 55, 56, 94, 108, 153, 163, 171, 240, 241, 242, 243, 244, 247, 248, 254, 258, 265, 284, 286, 288, 289, 291], "srrc": [6, 108, 152, 153, 162, 163, 170, 171, 240, 256, 265, 286, 288], "binary_cod": [6, 199, 291], "gener": [6, 142, 152, 162, 170, 194, 197, 199, 200, 212, 224, 251, 279, 288, 291], "code": [6, 26, 29, 37, 51, 55, 76, 80, 94, 96, 99, 107, 109, 142, 143, 152, 153, 154, 162, 163, 164, 169, 170, 171, 179, 182, 196, 199, 214, 215, 217, 224, 225, 239, 255, 267, 273, 276, 281, 288, 291], "gray_cod": [6, 224, 291], "grai": [6, 142, 143, 152, 153, 162, 163, 169, 170, 171, 224, 239, 255, 288, 290], "diff_encod": [6, 142, 152, 162, 166, 168, 170, 210, 211, 291], "y_prev": [6, 210, 211], "input": [6, 9, 17, 19, 22, 23, 26, 27, 28, 31, 37, 38, 51, 52, 53, 61, 65, 66, 69, 70, 71, 73, 76, 77, 78, 79, 86, 91, 94, 95, 96, 97, 98, 101, 125, 128, 144, 146, 152, 162, 166, 168, 170, 172, 179, 180, 181, 184, 194, 195, 197, 198, 200, 201, 203, 210, 211, 212, 213, 230, 232, 237, 243, 254, 260, 261, 271, 272, 277, 284, 285, 287], "data": [6, 134, 139, 156, 159, 210, 211, 228, 232, 256, 271, 290], "diff_decod": [6, 210, 211, 291], "decod": [6, 210], "use_styl": [7, 257], "appli": [7, 26, 96, 108, 179, 221, 229, 239, 240, 246, 253, 255, 256, 257, 266, 277], "default": [7, 61, 66, 143, 153, 163, 169, 171, 193, 216, 219, 227, 233, 235, 239, 242, 244, 247, 248, 250, 253, 255, 257, 288], "matplotlib": [7, 238, 239, 240, 242, 243, 244, 245, 246, 247, 248, 249, 250, 252, 253, 254, 255, 256, 257, 258, 283, 284, 285, 286, 287, 288, 289, 290], "rcparam": [7, 257], "time_domain": [7, 26, 37, 94, 96, 97, 142, 144, 152, 162, 170, 179, 194, 213, 225, 231, 256, 269, 270, 272, 273, 286, 287, 288, 289, 291], "ani": [7, 26, 37, 51, 59, 76, 84, 94, 96, 144, 146, 179, 196, 203, 213, 225, 230, 256, 272, 273, 276, 282], "dtype": [7, 26, 37, 51, 59, 76, 84, 94, 96, 142, 144, 146, 152, 162, 170, 179, 196, 225, 232, 256, 271, 273, 276, 287], "_scalartype_co": [7, 256], "t": [7, 9, 11, 16, 39, 125, 129, 132, 174, 223, 228, 256, 279, 283], "raster": [7, 240, 249, 250, 290, 291], "none": [7, 26, 37, 42, 51, 59, 61, 66, 69, 73, 84, 96, 108, 125, 133, 146, 153, 163, 171, 177, 179, 193, 194, 195, 197, 200, 204, 205, 207, 208, 212, 216, 219, 227, 232, 233, 235, 239, 240, 241, 242, 243, 244, 246, 247, 248, 249, 250, 253, 254, 255, 256, 271, 277, 283, 286, 288], "periodogram": [7, 213, 246, 269, 270, 272, 286, 290, 291], "power": [7, 142, 152, 162, 170, 193, 194, 195, 203, 220, 223, 225, 226, 230, 233, 234, 235, 246, 262, 263, 265, 273, 289, 290], "densiti": [7, 22, 246, 286, 289], "xx": [7, 246], "welch": [7, 246, 253], "spectrogram": [7, 253, 290, 291], "constel": [7, 142, 152, 162, 167, 170, 194, 220, 221, 229, 239, 266, 275, 290, 291], "symbol_map": [7, 107, 108, 123, 142, 152, 162, 167, 169, 170, 220, 255, 288, 291], "map": [7, 107, 108, 115, 123, 142, 152, 162, 169, 170, 220, 255, 290, 291], "ey": [7, 142, 152, 162, 170, 240, 290, 291], "diagram": [7, 9, 26, 37, 94, 96, 125, 144, 179, 210, 211, 240, 290, 291], "phase_tre": [7, 142, 249, 291], "tree": [7, 249, 291], "continu": [7, 142, 249, 283, 291], "cpm": [7, 249, 291], "kwarg": [7, 238, 239, 240, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 258], "e_b": [7, 46, 47, 48, 49, 50, 107, 111, 142, 152, 162, 166, 170, 195, 214, 215, 217, 238, 267, 290], "n_0": [7, 22, 46, 47, 48, 49, 50, 107, 111, 121, 142, 152, 162, 166, 168, 170, 194, 195, 214, 215, 217, 218, 220, 238, 239, 252, 267, 268, 288, 290], "e_": [7, 46, 47, 48, 49, 50, 107, 121, 142, 152, 162, 168, 170, 194, 195, 214, 217, 218, 220, 239, 252, 268, 288, 290], "roc": [7, 39, 42, 174, 177, 251, 291], "receiv": [7, 39, 40, 42, 44, 46, 107, 113, 114, 120, 134, 135, 137, 138, 142, 152, 156, 157, 162, 166, 168, 170, 174, 175, 176, 177, 178, 220, 222, 240, 245, 251, 291], "oper": [7, 39, 42, 174, 177, 251, 291], "characterist": [7, 39, 42, 174, 177, 251, 291], "curv": [7, 39, 42, 166, 168, 174, 177, 238, 251, 252, 291], "enr": [7, 174, 175, 177, 245], "impulse_respons": [7, 26, 37, 51, 61, 76, 86, 94, 96, 179, 204, 205, 206, 207, 208, 209, 223, 226, 243, 262, 263, 265, 284, 285, 289, 291], "step_respons": [7, 26, 37, 51, 66, 76, 91, 94, 96, 179, 254, 284, 285, 287, 291], "step": [7, 26, 37, 51, 66, 76, 91, 94, 96, 144, 146, 151, 179, 241, 254, 290], "zeros_pol": [7, 258, 285, 291], "zero": [7, 26, 27, 37, 51, 58, 73, 76, 77, 80, 81, 84, 93, 94, 96, 97, 98, 125, 146, 179, 181, 206, 225, 226, 232, 241, 242, 243, 244, 247, 248, 254, 258, 263, 269, 273, 284, 286, 287, 289, 290, 291], "pole": [7, 76, 77, 80, 81, 84, 88, 94, 241, 242, 243, 244, 247, 248, 254, 258, 284, 290], "magnitude_respons": [7, 37, 59, 84, 94, 204, 205, 206, 207, 208, 209, 226, 244, 262, 263, 265, 284, 285, 287, 289, 291], "omega": [7, 26, 37, 51, 59, 60, 63, 76, 84, 94, 96, 144, 147, 148, 150, 179, 241, 242, 244, 247, 248, 287], "phase_respons": [7, 59, 84, 248, 291], "angl": [7, 156, 248, 287], "phase_delai": [7, 26, 37, 51, 63, 96, 179, 247, 291], "tau_": [7, 26, 37, 51, 63, 96, 179, 247], "phi": [7, 26, 37, 51, 63, 96, 107, 108, 118, 142, 143, 152, 153, 162, 163, 167, 170, 171, 179, 221, 229, 231, 247], "group_delai": [7, 26, 37, 51, 60, 96, 179, 206, 242, 284, 285, 291], "group": [7, 26, 37, 51, 60, 96, 179, 206, 242, 290], "tau_g": [7, 26, 37, 51, 60, 96, 179, 242], "iir": [7, 9, 18, 61, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 125, 131, 241, 242, 243, 244, 247, 248, 254, 258, 284, 287, 290, 291], "q": [8, 142, 152, 172, 173, 174, 175, 176, 178, 179, 181, 185, 188, 209, 275, 291], "comput": [8, 26, 39, 40, 41, 42, 43, 59, 84, 107, 111, 121, 134, 142, 152, 156, 162, 166, 168, 170, 172, 173, 174, 175, 176, 177, 178, 193, 194, 216, 219, 222, 227, 233, 235, 284, 285, 287, 289, 291], "complementari": [8, 172, 173], "cumul": [8, 172, 173], "distribut": [8, 172, 173], "standard": [8, 172, 173], "normal": [8, 9, 11, 16, 125, 129, 132, 172, 173, 204, 205, 207, 208, 220, 223, 226, 241, 242, 244, 246, 247, 248, 253, 262, 263, 265, 287, 289], "mathcal": [8, 39, 172, 173, 174, 175, 176, 177, 178, 194, 212], "qinv": [8, 172, 173, 291], "invers": [8, 173], "closedlooppl": [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 278, 287, 291], "defin": [9, 51, 76, 194, 212, 223, 251, 275, 278, 285, 290], "perform": [9, 27, 52, 97, 166, 168, 206, 213, 272, 275, 278, 284, 285, 288, 290, 291], "close": [9, 16, 18, 278, 290, 291], "loop": [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 125, 126, 127, 128, 129, 130, 131, 132, 133, 144, 145, 146, 147, 148, 149, 150, 151, 278, 290, 291], "pll": [9, 10, 11, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 278, 290, 291], "meant": 9, "analysi": [9, 16, 280, 287, 290, 291], "onli": [9, 27, 35, 52, 58, 59, 64, 69, 73, 84, 89, 97, 105, 108, 134, 143, 153, 163, 169, 171, 189, 194, 204, 205, 207, 208, 222, 225, 226, 250, 263, 273, 282, 287, 288], "block": [9, 26, 37, 94, 96, 125, 144, 179, 210, 211], "bb": [9, 286, 287], "phase_err": [9, 287], "ped": [9, 15, 16, 129, 134, 138, 139, 140, 156, 157, 158, 159, 160, 161, 278, 287], "lf": [9, 287], "phase_est": [9, 287], "lo": [9, 287], "nco": [9, 12, 16, 129, 144, 145, 146, 147, 148, 149, 150, 151, 278, 287, 290, 291], "local": [9, 279, 287], "oscil": [9, 144, 147, 278, 287, 290, 291], "detector": [9, 15, 16, 39, 129, 134, 141, 156, 161, 174, 287, 291], "filter": [9, 13, 14, 16, 18, 26, 27, 28, 31, 32, 33, 35, 36, 37, 38, 51, 52, 53, 54, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 101, 102, 103, 105, 106, 107, 114, 120, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 142, 152, 162, 170, 179, 180, 181, 184, 186, 187, 189, 190, 204, 205, 206, 207, 208, 209, 213, 223, 226, 240, 241, 242, 243, 244, 247, 248, 254, 258, 259, 262, 263, 265, 272, 278, 289, 290, 291], "numer": [9, 144, 147, 278, 285, 287, 290, 291], "control": [9, 134, 144, 147, 262, 265, 278, 287, 290, 291], "The": [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 31, 32, 33, 34, 36, 37, 39, 40, 41, 42, 43, 44, 46, 47, 48, 49, 50, 51, 52, 53, 57, 58, 59, 60, 61, 62, 63, 65, 66, 68, 69, 70, 72, 73, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 90, 91, 93, 94, 96, 97, 98, 101, 102, 103, 104, 106, 107, 108, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 156, 157, 159, 160, 161, 162, 163, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 181, 184, 185, 186, 187, 188, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 279, 280, 281, 282, 284, 285, 287, 288, 289, 290, 292], "transfer": [9, 18, 37, 51, 76, 77, 94, 125, 223, 284, 285, 287], "2nd": [9, 125, 129, 278, 287, 291], "proport": [9, 13, 27, 97, 125, 126, 129, 222, 234, 278, 291], "plu": [9, 125, 129, 278, 291], "z": [9, 37, 51, 76, 94, 125, 144, 210, 211, 275, 284, 285, 287], "k_1": [9, 13, 125, 126, 287], "k_2": [9, 14, 125, 127, 287], "frac": [9, 17, 19, 22, 23, 37, 39, 40, 41, 43, 51, 57, 76, 94, 98, 125, 152, 162, 170, 174, 175, 176, 181, 192, 193, 194, 195, 202, 214, 215, 217, 218, 220, 222, 223, 229, 230, 231, 233, 234, 264, 267, 268, 274, 275, 287], "k_0": [9, 12, 16, 129, 144, 145, 147, 287], "k_p": [9, 15, 16, 129, 134, 141, 156, 161, 287], "refer": [9, 17, 19, 20, 21, 22, 23, 39, 40, 41, 43, 44, 69, 125, 134, 136, 137, 138, 156, 157, 166, 168, 174, 175, 176, 178, 192, 194, 202, 204, 205, 206, 207, 208, 209, 220, 221, 223, 225, 233, 259, 262, 265, 266, 273, 275, 285, 289, 290], "michael": [9, 17, 19, 20, 21, 22, 23, 125, 134, 156, 262, 265], "rice": [9, 17, 19, 20, 21, 22, 23, 125, 134, 156, 262, 265], "digit": [9, 17, 19, 20, 21, 22, 23, 125, 134, 156, 166, 168, 262, 265, 287, 290, 291], "commun": [9, 17, 19, 20, 21, 22, 23, 125, 134, 156, 166, 168, 209, 259, 262, 265, 287, 290], "discret": [9, 17, 19, 20, 21, 22, 23, 37, 94, 125, 134, 156, 194, 212, 218, 262, 265, 268, 277, 283, 287, 290, 291], "approach": [9, 17, 19, 20, 21, 22, 23, 125, 134, 156, 195, 198, 201, 262, 265, 287], "appendix": [9, 125, 262, 265], "lock": [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 125, 126, 127, 128, 129, 130, 131, 132, 133, 144, 145, 146, 147, 148, 149, 150, 151], "exampl": [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 29, 30, 33, 35, 36, 37, 38, 40, 42, 44, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 99, 100, 103, 105, 106, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 142, 144, 145, 146, 147, 148, 149, 150, 151, 152, 156, 162, 166, 167, 168, 169, 170, 172, 173, 175, 177, 179, 182, 183, 187, 189, 190, 192, 194, 195, 196, 197, 198, 199, 200, 201, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 217, 218, 220, 221, 222, 223, 224, 225, 226, 228, 229, 230, 231, 232, 234, 237, 238, 239, 240, 241, 242, 243, 244, 247, 248, 249, 252, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 287], "see": [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 35, 38, 47, 48, 49, 50, 51, 52, 53, 54, 57, 58, 62, 64, 65, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 85, 87, 88, 89, 90, 92, 93, 95, 105, 125, 126, 127, 128, 129, 130, 131, 132, 133, 142, 144, 145, 146, 147, 148, 149, 150, 151, 152, 162, 167, 169, 170, 179, 189, 204, 205, 207, 208, 213, 223, 226, 241, 242, 243, 244, 247, 248, 254, 258, 262, 263, 265, 290], "noise_bandwidth": [9, 16, 125, 129, 132], "damping_factor": [9, 16, 125, 129, 130], "creat": [9, 16, 26, 28, 37, 38, 44, 45, 51, 53, 69, 71, 76, 77, 79, 94, 95, 96, 97, 98, 107, 108, 125, 129, 142, 143, 144, 147, 152, 153, 162, 163, 167, 170, 171, 179, 181, 194, 196, 220, 221, 225, 231, 266, 269, 270, 273, 275, 283, 287, 289], "object": [9, 16, 26, 29, 30, 37, 44, 45, 51, 55, 56, 76, 80, 81, 94, 96, 99, 100, 107, 108, 109, 110, 142, 143, 152, 153, 154, 155, 162, 163, 164, 165, 170, 171, 179, 182, 183, 225, 241, 242, 243, 244, 247, 248, 254, 258, 273, 287, 291], "phase_lock_tim": [9, 23], "frequency_lock_tim": [9, 17], "freq_offset": [9, 17, 19], "lock_tim": [9, 19, 287], "phase_error_vari": [9, 22], "cn0": [9, 22], "varianc": [9, 22, 39, 41, 43, 176, 178, 194], "steadi": [9, 22], "state": [9, 22, 26, 27, 35, 37, 51, 52, 58, 64, 65, 67, 69, 73, 74, 76, 89, 90, 92, 94, 96, 97, 105, 179, 189, 291], "sample_r": [9, 16, 24, 26, 59, 60, 63, 84, 96, 97, 142, 152, 162, 170, 179, 213, 221, 231, 240, 241, 242, 244, 246, 247, 248, 249, 250, 253, 256, 269, 270, 272, 283, 287, 289], "bnt": [9, 11, 287], "bandwidth": [9, 10, 11, 16, 20, 125, 129, 132, 195, 204, 205, 223, 262, 265, 287, 289], "b_n": [9, 10, 11, 16, 17, 19, 22, 23, 125, 129, 132], "bn": [9, 10], "hz": [9, 10, 16, 17, 19, 22, 59, 60, 63, 84, 125, 129, 132, 195, 203, 213, 221, 222, 223, 230, 231, 234, 269, 270, 274, 283], "zeta": [9, 16, 25, 125, 129, 130], "damp": [9, 16, 25, 125, 129, 130, 287], "k0": [9, 12, 16, 129, 144, 145, 147, 287], "kp": [9, 15, 16, 129, 287], "k1": [9, 13, 125, 126, 287], "k2": [9, 14, 125, 127, 287], "repres": [9, 18, 197, 198], "omega_n": [9, 21, 287], "natur": [9, 21], "radian": [9, 20, 21, 22, 134, 137, 139, 140, 144, 146, 147, 148, 149, 150, 156, 157, 159, 160, 170, 287], "omega_3db": [9, 20], "3": [9, 17, 19, 20, 23, 26, 33, 36, 37, 39, 40, 44, 55, 56, 59, 80, 81, 84, 94, 96, 97, 103, 106, 134, 142, 144, 152, 156, 162, 166, 167, 168, 169, 170, 174, 175, 179, 182, 183, 187, 190, 192, 194, 195, 196, 197, 199, 200, 203, 204, 205, 206, 207, 208, 209, 212, 213, 214, 215, 217, 218, 220, 221, 222, 223, 224, 225, 226, 228, 229, 230, 231, 232, 234, 239, 240, 241, 242, 243, 244, 247, 248, 254, 256, 258, 259, 262, 263, 265, 266, 267, 269, 270, 271, 272, 273, 274, 275, 279, 280, 285, 287, 289, 290], "omega_": [9, 20], "textrm": [9, 20], "properti": [10, 11, 12, 13, 14, 15, 18, 20, 21, 24, 25, 31, 32, 33, 34, 36, 57, 62, 65, 67, 68, 72, 74, 75, 82, 83, 85, 87, 88, 90, 92, 93, 101, 102, 103, 104, 106, 112, 117, 118, 119, 120, 122, 123, 124, 126, 127, 130, 131, 132, 135, 136, 141, 145, 148, 149, 161, 167, 169, 184, 185, 186, 187, 188, 190, 191, 291], "paramet": [16, 17, 19, 22, 27, 28, 38, 40, 41, 42, 43, 46, 47, 48, 50, 52, 53, 59, 60, 61, 63, 66, 70, 71, 73, 77, 78, 79, 84, 86, 91, 95, 97, 98, 108, 111, 113, 114, 115, 116, 121, 128, 129, 137, 138, 139, 140, 143, 146, 147, 151, 153, 157, 159, 160, 163, 166, 168, 171, 172, 173, 175, 176, 177, 178, 181, 192, 193, 194, 195, 196, 197, 198, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 258, 259, 260, 261, 262, 263, 264, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275], "where": [16, 27, 52, 97, 108, 125, 129, 132, 163, 171, 174, 194, 195, 212, 214, 215, 217, 223, 267, 275, 284, 285, 290], "period": [16, 125, 129, 132, 142, 275], "second": [16, 17, 19, 23, 44, 125, 129, 132, 223], "critic": [16, 25, 125, 129, 130, 287], "underdamp": [16, 25, 125, 129, 130], "overdamp": [16, 25, 125, 129, 130], "ted": [16, 129], "t_": [17, 19, 23, 70, 223, 289], "fl": [17, 19], "delta": [17, 19, 26, 37, 51, 61, 76, 86, 94, 96, 179, 206, 243, 284, 285], "take": [17, 19, 23, 279], "onto": [17, 19, 23], "39": 17, "pl": [19, 23], "38": 19, "34": [20, 256], "33": 21, "sigma_": [22, 39, 40, 42], "theta_": [22, 134, 137, 156, 157], "carrier": [22, 162], "43": 22, "40": [23, 96, 179, 213], "less": [25, 192], "than": [25, 142, 143, 153, 163, 169, 171, 192, 226, 229, 239, 255, 263], "greater": [25, 262, 265], "fir": [26, 27, 28, 29, 30, 31, 33, 35, 36, 37, 38, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 96, 97, 98, 99, 100, 101, 103, 105, 106, 179, 180, 181, 182, 183, 184, 187, 189, 190, 204, 205, 206, 207, 208, 209, 240, 241, 242, 243, 244, 247, 248, 254, 258, 259, 286, 290, 291], "note": [26, 33, 36, 37, 39, 40, 41, 43, 51, 76, 94, 96, 103, 106, 125, 134, 144, 156, 174, 175, 176, 178, 179, 187, 190, 192, 194, 195, 198, 201, 206, 210, 211, 223, 229, 234, 240, 259, 275], "equival": [26, 96, 179, 194, 195, 204, 205, 206, 207, 208, 218, 225, 268, 273, 281, 283], "first": [26, 31, 44, 96, 98, 101, 142, 150, 152, 179, 181, 184, 232, 256, 271, 280, 282], "prototyp": [26, 33, 36, 96, 103, 106, 179, 187, 190], "feedforward": [26, 28, 33, 36, 37, 51, 53, 68, 76, 79, 83, 94, 96, 98, 103, 106, 179, 181, 187, 190, 241, 242, 243, 244, 247, 248, 254, 258, 284, 285], "coeffici": [26, 28, 51, 53, 76, 79, 96, 98, 107, 120, 124, 142, 152, 162, 170, 179, 181, 241, 242, 243, 244, 247, 248, 254, 258, 284, 285], "discard": [26, 179], "each": [26, 27, 52, 96, 97, 179, 220, 228, 246, 250, 253], "instead": [26, 96, 179, 239], "ar": [26, 27, 28, 33, 36, 38, 39, 44, 46, 47, 48, 50, 52, 53, 71, 77, 79, 95, 96, 97, 98, 103, 106, 107, 108, 120, 124, 142, 143, 146, 152, 153, 162, 163, 170, 171, 174, 179, 181, 187, 190, 195, 197, 198, 200, 201, 206, 222, 225, 226, 232, 239, 240, 241, 242, 244, 246, 247, 248, 249, 250, 253, 255, 256, 257, 259, 263, 269, 270, 273, 279, 281, 283, 285, 287, 289, 290, 292], "commut": [26, 96, 179], "parallel": [26, 96, 179], "output": [26, 27, 31, 37, 51, 52, 61, 66, 76, 77, 79, 86, 91, 94, 95, 96, 97, 98, 101, 114, 125, 128, 144, 146, 150, 151, 179, 181, 184, 194, 195, 196, 197, 198, 200, 201, 211, 212, 220, 225, 230, 232, 243, 254, 271, 273, 276, 279, 283, 284, 285, 287], "sum": [26, 39, 51, 76, 174, 289], "prevent": [26, 96, 152, 170, 179], "need": [26, 96, 179, 279, 280, 282], "done": [26, 279], "case": [26, 96, 170, 174, 179], "3x": [26, 96], "6": [26, 33, 36, 37, 44, 55, 56, 80, 81, 84, 94, 96, 97, 103, 106, 134, 142, 144, 152, 162, 169, 170, 175, 176, 178, 179, 187, 190, 192, 199, 203, 206, 212, 213, 214, 215, 220, 222, 224, 225, 228, 230, 234, 239, 240, 241, 242, 243, 244, 247, 248, 254, 255, 256, 258, 259, 262, 265, 269, 270, 272, 273, 275, 279, 280, 281, 282, 284, 285, 287, 288], "9": [26, 33, 36, 59, 84, 96, 97, 103, 106, 142, 152, 162, 170, 175, 179, 187, 190, 192, 199, 212, 220, 224, 225, 228, 259, 262, 265, 273, 279, 285, 286, 288, 289], "v": [26, 144, 203, 230, 279], "5": [26, 33, 36, 37, 39, 40, 41, 42, 43, 44, 55, 56, 59, 94, 96, 97, 103, 106, 134, 142, 144, 152, 162, 170, 175, 177, 179, 187, 190, 192, 194, 197, 199, 200, 201, 204, 205, 206, 207, 208, 212, 213, 214, 215, 217, 218, 220, 221, 222, 223, 224, 225, 228, 229, 234, 237, 240, 241, 242, 243, 244, 247, 248, 254, 256, 258, 259, 262, 265, 266, 267, 268, 269, 270, 272, 273, 275, 279, 283, 284, 285, 286, 287, 288, 289], "7": [26, 29, 30, 33, 36, 96, 97, 99, 100, 103, 106, 134, 142, 152, 156, 162, 169, 170, 175, 179, 187, 190, 192, 199, 206, 207, 209, 212, 220, 224, 225, 228, 259, 273, 275, 279, 285, 287], "8": [26, 33, 36, 37, 40, 42, 59, 80, 81, 84, 94, 96, 97, 103, 106, 108, 134, 142, 143, 144, 152, 153, 156, 162, 163, 166, 167, 168, 169, 170, 171, 175, 177, 179, 187, 190, 192, 194, 195, 196, 198, 199, 201, 204, 205, 206, 207, 208, 209, 212, 213, 220, 222, 223, 224, 225, 226, 228, 231, 234, 238, 239, 240, 241, 242, 243, 244, 247, 248, 249, 252, 254, 255, 256, 257, 258, 259, 262, 263, 265, 269, 270, 272, 273, 275, 284, 285, 286, 287, 289], "summat": 26, "bottom": [26, 96, 179], "top": [26, 96, 179], "adder": [26, 125, 144, 210, 211, 287], "relat": [26, 33, 36, 96, 103, 106, 179, 187, 190, 195, 223], "In": [26, 27, 28, 29, 30, 33, 36, 37, 38, 40, 42, 44, 52, 53, 55, 56, 59, 67, 71, 74, 77, 79, 80, 81, 84, 92, 94, 95, 96, 97, 98, 99, 100, 103, 106, 134, 142, 144, 152, 156, 162, 166, 167, 168, 169, 170, 172, 173, 175, 177, 179, 181, 182, 183, 187, 190, 192, 194, 195, 196, 197, 198, 199, 200, 201, 203, 204, 205, 206, 207, 208, 209, 210, 211, 212, 213, 214, 215, 217, 218, 220, 221, 222, 223, 224, 225, 226, 228, 229, 230, 231, 232, 234, 237, 238, 239, 240, 241, 242, 243, 244, 247, 248, 249, 252, 254, 255, 256, 257, 258, 259, 260, 261, 262, 263, 265, 266, 267, 268, 269, 270, 271, 272, 273, 274, 275, 283, 288], "np": [26, 33, 36, 40, 42, 59, 80, 81, 84, 96, 97, 103, 106, 107, 119, 123, 142, 144, 152, 162, 166, 168, 169, 170, 175, 177, 179, 187, 190, 192, 194, 195, 196, 197, 198, 200, 201, 212, 213, 220, 221, 222, 225, 229, 231, 238, 239, 240, 241, 242, 243, 244, 247, 248, 249, 252, 254, 256, 258, 259, 266, 269, 270, 272, 273, 275, 283, 284, 285, 286, 287, 288, 289], "co": [26, 96, 97, 179, 231], "64": [26, 206, 228, 285], "arang": [26, 33, 36, 96, 97, 103, 106, 179, 187, 190, 194, 196, 213, 225, 231, 259, 269, 270, 272, 273, 275, 283, 287], "280": 26, "out": [26, 29, 33, 36, 44, 55, 59, 80, 84, 96, 97, 99, 103, 106, 134, 142, 152, 162, 167, 169, 170, 172, 173, 179, 182, 187, 190, 196, 197, 199, 200, 203, 210, 211, 212, 214, 215, 217, 218, 220, 222, 224, 225, 230, 232, 234, 237, 257, 259, 260, 261, 267, 268, 271, 273, 274], "plt": [26, 37, 40, 42, 94, 96, 97, 134, 142, 144, 152, 156, 162, 166, 167, 168, 169, 170, 175, 177, 179, 192, 194, 195, 196, 198, 201, 204, 205, 206, 207, 208, 209, 213, 220, 221, 222, 223, 225, 226, 229, 231, 238, 239, 240, 241, 242, 243, 244, 247, 248, 249, 252, 254, 255, 256, 258, 262, 263, 265, 266, 269, 270, 272, 273, 275, 283, 284, 285, 286, 287, 288, 289], "figur": [26, 37, 40, 42, 94, 96, 97, 134, 142, 144, 152, 156, 162, 166, 167, 168, 169, 170, 175, 177, 179, 192, 194, 195, 196, 198, 201, 204, 205, 206, 207, 208, 209, 213, 220, 221, 222, 223, 225, 226, 229, 231, 238, 239, 240, 241, 242, 243, 244, 247, 248, 249, 252, 254, 255, 256, 257, 258, 262, 263, 265, 266, 269, 270, 272, 273, 275, 283, 284, 285, 286, 287, 288, 289], "figsiz": [26, 37, 40, 42, 94, 96, 97, 134, 142, 144, 152, 156, 162, 166, 167, 168, 169, 170, 175, 177, 179, 192, 194, 195, 196, 198, 201, 204, 205, 206, 207, 208, 209, 213, 220, 221, 222, 223, 225, 226, 229, 231, 238, 239, 240, 241, 242, 243, 244, 247, 248, 249, 252, 254, 255, 256, 257, 258, 262, 263, 265, 266, 269, 270, 272, 273, 275, 283, 284, 285, 286, 287, 288, 289], "plot": [26, 37, 40, 42, 59, 60, 61, 63, 66, 84, 86, 91, 94, 96, 97, 134, 142, 144, 152, 156, 162, 166, 167, 168, 169, 170, 175, 177, 179, 194, 195, 196, 198, 201, 204, 205, 206, 207, 208, 209, 213, 220, 221, 222, 223, 225, 226, 229, 231, 238, 239, 240, 241, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 257, 258, 262, 263, 265, 266, 269, 270, 272, 273, 275, 283, 284, 285, 287, 288, 289, 290, 291], "marker": [26, 96, 97, 144, 179, 239, 255, 256, 283, 284, 285, 288], "label": [26, 37, 40, 42, 94, 96, 97, 134, 143, 153, 156, 163, 166, 168, 171, 175, 177, 179, 192, 194, 204, 205, 206, 207, 208, 220, 221, 223, 225, 229, 238, 240, 241, 242, 244, 245, 246, 247, 248, 249, 250, 252, 253, 256, 262, 265, 266, 273, 283, 286, 287, 288, 289], "o": [26, 96, 97, 179, 283], "titl": [26, 37, 94, 96, 134, 142, 144, 152, 156, 166, 168, 179, 192, 194, 195, 196, 198, 201, 213, 220, 221, 225, 229, 231, 238, 252, 256, 266, 269, 270, 272, 273, 275, 283, 286, 287, 288, 289], "tight_layout": [26, 37, 94, 96, 134, 142, 144, 152, 156, 166, 168, 179, 192, 194, 195, 196, 198, 201, 213, 220, 221, 222, 225, 231, 238, 252, 256, 266, 269, 270, 272, 273, 275, 286, 287, 288, 289], "preserv": [26, 28, 38, 53, 67, 71, 74, 77, 79, 92, 95, 96, 98, 179, 181, 240, 250], "call": [26, 27, 28, 38, 52, 53, 67, 71, 74, 77, 79, 92, 95, 96, 97, 98, 179, 181], "true": [26, 40, 41, 42, 43, 59, 84, 96, 97, 134, 139, 140, 142, 152, 156, 159, 160, 162, 166, 168, 170, 175, 176, 177, 178, 179, 192, 193, 195, 197, 198, 200, 201, 212, 216, 222, 225, 231, 235, 236, 239, 248, 250, 255, 256, 257, 264, 273, 286, 287, 288], "y1": [26, 96, 97, 179, 229], "70": [26, 228], "y2": [26, 96, 97, 179, 229], "140": [26, 213], "y3": [26, 96, 97, 179], "210": 26, "y4": [26, 96, 179], "y5": [26, 96, 179], "flush": [26, 27, 37, 51, 52, 58, 96, 97, 179, 291], "y_1": [26, 96, 179, 229], "y_2": [26, 96, 179, 229], "y_3": [26, 96, 179], "y_4": [26, 96, 179], "y_5": [26, 96, 179], "__call__": [26, 27, 28, 37, 38, 51, 52, 53, 67, 69, 70, 71, 74, 76, 77, 78, 79, 92, 94, 95, 96, 97, 98, 125, 128, 134, 137, 144, 146, 156, 157, 179, 180, 181, 291], "full": [26, 27, 52, 96, 97, 179, 180, 196, 225, 273], "__len__": [26, 37, 51, 54, 96, 179], "__repr__": [26, 29, 37, 51, 55, 76, 80, 94, 96, 99, 107, 109, 142, 152, 154, 162, 164, 170, 179, 182], "style": [26, 29, 37, 51, 55, 76, 80, 94, 96, 99, 107, 109, 142, 152, 154, 162, 164, 170, 179, 182, 257], "__str__": [26, 30, 37, 51, 56, 76, 81, 94, 96, 100, 107, 110, 142, 152, 155, 162, 165, 170, 179, 183], "human": [26, 30, 37, 51, 56, 76, 81, 94, 96, 100, 107, 110, 142, 152, 155, 162, 165, 170, 179, 183], "readabl": [26, 30, 37, 51, 56, 76, 81, 94, 96, 100, 107, 110, 142, 152, 155, 162, 165, 170, 179, 183], "reset": [26, 35, 37, 51, 64, 69, 73, 76, 89, 94, 96, 105, 125, 133, 144, 150, 179, 189], "when": [26, 35, 37, 51, 58, 61, 64, 66, 76, 86, 89, 91, 94, 96, 105, 179, 189, 194, 195, 197, 198, 200, 201, 218, 225, 241, 242, 243, 244, 247, 248, 254, 268, 273, 275, 283, 284, 285], "pass": [26, 37, 51, 58, 96, 179, 194, 197, 200, 212, 220, 238, 239, 240, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 258, 277, 279, 281, 284, 285, 291], "through": [26, 37, 51, 58, 96, 152, 170, 179, 197, 200, 212, 277, 284, 285, 287], "indic": [26, 28, 31, 37, 38, 41, 42, 43, 51, 53, 67, 69, 71, 74, 76, 77, 79, 92, 94, 95, 96, 98, 101, 107, 108, 142, 143, 152, 153, 162, 163, 166, 168, 170, 171, 175, 176, 177, 178, 179, 181, 184, 193, 216, 223, 226, 229, 231, 235, 236, 240, 248, 249, 250, 256, 262, 263, 264, 265, 273], "whether": [26, 28, 37, 38, 41, 42, 43, 51, 53, 67, 69, 71, 74, 76, 77, 79, 92, 94, 95, 96, 98, 166, 168, 175, 176, 177, 178, 179, 181, 193, 216, 231, 235, 236, 248, 250, 256, 264], "consist": [26, 37, 46, 47, 48, 49, 50, 51, 65, 96, 179], "previou": [26, 28, 37, 38, 51, 53, 65, 71, 73, 77, 79, 95, 96, 98, 179, 181, 210, 211], "u": [26, 37, 51, 66, 76, 91, 94, 96, 179, 192, 254, 275, 276, 284, 285], "frequency_respons": [26, 37, 51, 59, 76, 84, 94, 96, 179, 291], "numpi": [26, 37, 51, 59, 76, 84, 94, 96, 146, 179, 194, 197, 200, 212, 271, 283, 284, 285, 286, 287, 288, 289, 290], "float64": [26, 37, 51, 59, 76, 84, 94, 96, 144, 146, 179, 196, 225, 273, 276], "complex128": [26, 37, 51, 59, 76, 84, 94, 96, 144, 146, 179], "custom": [26, 32, 96, 102, 108, 153, 163, 171, 179, 186, 204, 205, 207, 208, 291], "multir": [26, 27, 28, 32, 96, 97, 98, 102, 179, 181, 186, 209, 259, 291], "polyphase_tap": [26, 30, 33, 36, 96, 97, 100, 103, 106, 179, 183, 187, 190], "index": [26, 31, 69, 73, 96, 101, 107, 142, 152, 162, 170, 179, 184, 225, 240, 249, 250, 255, 273, 276, 279], "correspond": [26, 31, 44, 49, 96, 101, 179, 184, 250], "mode": [27, 28, 35, 38, 52, 53, 58, 64, 67, 69, 71, 73, 74, 77, 79, 89, 92, 95, 97, 98, 105, 180, 181, 189, 196, 225, 273, 275], "l": [27, 52, 78, 97, 206], "stream": [27, 28, 29, 30, 35, 38, 52, 53, 55, 56, 58, 64, 67, 69, 71, 73, 74, 77, 79, 80, 81, 89, 92, 95, 97, 98, 99, 100, 105, 142, 152, 162, 170, 181, 182, 183, 189, 285], "convolut": [27, 52, 96, 97], "ha": [27, 52, 96, 97, 142, 152, 162, 194, 204, 205, 206, 207, 208, 213, 222, 223, 234, 272, 275, 287, 288, 289], "align": [27, 52, 97, 98, 152, 181, 225, 273, 283], "howev": [27, 46, 47, 48, 50, 52, 97, 125, 198, 201, 225, 273, 283], "produc": [27, 52, 96, 97, 179, 223, 289], "final": [27, 52, 97], "dictat": [27, 52, 97], "argument": [27, 28, 52, 97, 98, 181, 238, 239, 240, 242, 243, 244, 245, 246, 247, 248, 249, 250, 251, 252, 253, 254, 255, 256, 258, 284, 285], "specif": [28, 49, 59, 84, 98, 181, 282, 289], "npt": [28, 59, 84, 98, 108, 143, 153, 163, 171, 181, 204, 205, 207, 208, 241, 242, 243, 244, 247, 248, 254, 258], "string": [29, 30, 55, 56, 80, 81, 99, 100, 108, 109, 110, 153, 154, 155, 163, 164, 165, 171, 182, 183, 228, 246, 253, 291], "represent": [29, 30, 55, 56, 80, 81, 99, 100, 109, 110, 154, 155, 164, 165, 182, 183, 255, 291], "print": [30, 56, 81, 100, 183, 228, 283, 284, 285, 287], "167": [30, 100], "24": [30, 100, 183], "shape": [30, 56, 81, 97, 100, 107, 108, 114, 116, 119, 120, 124, 142, 152, 153, 162, 163, 170, 171, 183, 223, 226, 240, 256, 262, 263, 265, 285, 290, 291], "12": [30, 96, 142, 152, 162, 170, 176, 178, 192, 199, 209, 224, 259, 284, 288, 291], "befor": [33, 36, 103, 106, 187, 190, 292], "decomposit": [33, 36, 103, 106, 187, 190, 291], "after": [33, 36, 103, 106, 187, 190], "10": [33, 36, 37, 40, 42, 44, 94, 96, 97, 103, 106, 108, 142, 152, 153, 162, 163, 166, 168, 170, 171, 175, 177, 179, 187, 190, 192, 193, 194, 199, 203, 204, 205, 207, 208, 212, 214, 215, 216, 217, 218, 221, 222, 223, 224, 225, 226, 228, 229, 230, 231, 233, 234, 235, 236, 238, 239, 241, 242, 243, 244, 247, 248, 252, 254, 256, 258, 259, 262, 263, 264, 265, 266, 267, 268, 273, 283, 284, 285, 286, 287, 288, 289], "puls": [37, 94, 107, 108, 114, 116, 119, 120, 124, 142, 152, 153, 162, 163, 170, 171, 223, 226, 240, 256, 262, 263, 265, 290, 291], "deriv": 37, "d": [37, 51, 57, 219, 222, 227, 234, 279, 281, 290], "lfloor": [37, 51, 57], "rfloor": [37, 51, 57], "null": [39, 174, 289], "altern": [39, 174, 285], "hypothes": [39, 174], "follow": [39, 44, 107, 142, 152, 162, 170, 229, 239, 250, 253, 255, 257, 259, 287], "assum": [39, 174, 194, 212, 232, 256, 271], "valu": [39, 107, 108, 111, 121, 142, 143, 152, 153, 162, 163, 166, 168, 170, 171, 172, 173, 196, 203, 210, 211, 223, 225, 229, 230, 239, 242, 244, 247, 248, 255, 273, 285, 291], "random": [39, 142, 152, 162, 170, 194, 197, 200, 212, 220, 221, 229, 239, 240, 249, 256, 266, 286, 287, 288], "process": [39, 40, 41, 43, 174, 175, 176, 178, 209, 259, 285, 287, 290], "w": [39, 174, 194, 283, 284, 285, 286, 287, 288, 289], "sigma": [39, 40, 41, 42, 43, 174, 175, 176, 177, 178, 194, 195], "_0": [39, 174], "_1": [39, 174], "test": [39, 174, 281, 290], "statist": [39, 40, 41, 43, 174, 175, 176, 178], "limits_": [39, 51, 76, 174], "left": [39, 40, 41, 76, 152, 156, 162, 170, 174, 175, 176, 178, 192, 193, 194, 195, 216, 219, 220, 222, 223, 229, 231, 234, 235, 236, 264, 275], "right": [39, 40, 41, 76, 152, 156, 162, 170, 174, 175, 176, 178, 192, 193, 194, 195, 216, 219, 220, 222, 223, 229, 231, 234, 235, 236, 264, 275], "gamma": [39, 41, 43, 174, 176, 178, 192], "sim": [39, 174, 194, 280], "chi_": [39, 40, 41], "2n": [39, 40, 41], "text": [39, 170, 174, 192, 193, 194, 195, 198, 201, 202, 203, 209, 220, 221, 222, 230, 233, 235, 236, 264, 266], "under": [39, 174], "detect": [39, 40, 41, 42, 43, 134, 137, 139, 140, 156, 157, 159, 160, 174, 175, 176, 177, 178, 192, 245, 251, 291], "threshold": [39, 41, 43, 174, 176, 178], "q_": [39, 40, 41, 43], "chi_n": [39, 40, 41, 43], "steven": [39, 40, 41, 43, 174, 175, 176, 178], "kai": [39, 40, 41, 43, 174, 175, 176, 178], "fundament": [39, 40, 41, 43, 174, 175, 176, 178], "theori": [39, 40, 41, 43, 174, 175, 176, 178], "section": [39, 46, 47, 48, 49, 50, 134, 156, 174, 285, 287], "static": [39, 40, 41, 42, 43, 174, 175, 176, 177, 178, 280], "n_nc": [39, 40, 41, 42, 43, 192], "number": [40, 41, 42, 43, 44, 46, 47, 50, 59, 60, 61, 63, 66, 84, 86, 91, 107, 108, 112, 122, 139, 140, 142, 143, 151, 152, 153, 159, 160, 162, 163, 170, 171, 192, 194, 197, 200, 212, 214, 215, 217, 223, 226, 228, 232, 239, 240, 241, 242, 243, 244, 246, 247, 248, 249, 253, 254, 259, 262, 263, 265, 267, 271], "For": [40, 41, 43, 175, 176, 178, 194, 213, 222, 272, 279, 284], "linspac": [40, 59, 84, 166, 168, 175, 195, 198, 201, 222, 238, 252, 285, 286, 287, 288], "20": [40, 42, 96, 97, 142, 144, 152, 162, 170, 175, 179, 192, 195, 197, 200, 203, 212, 220, 221, 228, 229, 230, 236, 259, 264, 272, 286, 288, 291], "101": [40, 42, 175, 177, 204, 205, 207, 208], "25": [40, 197, 200, 206, 212, 237, 240, 260, 261, 283, 286, 287, 289], "1e": [40, 175, 221, 288], "sigma2": [41, 43, 176, 178], "If": [42, 73, 108, 146, 153, 163, 171, 177, 179, 193, 194, 195, 212, 216, 232, 235, 236, 239, 240, 241, 242, 243, 244, 246, 247, 248, 249, 250, 253, 254, 255, 256, 264, 269, 271, 290], "logspac": [42, 59, 84, 177, 192], "theoret": [42, 166, 168, 238, 252, 288, 291], "variou": [42, 280, 289], "100": [42, 59, 76, 84, 86, 91, 94, 144, 166, 168, 192, 194, 195, 198, 201, 203, 204, 205, 207, 208, 220, 230, 231, 238, 240, 241, 243, 249, 252, 254, 266, 269, 270, 272, 283, 287], "1_000": [42, 194, 221, 222, 229, 266, 286], "000": [42, 221], "5_000": 42, "measur": [44, 46, 134, 139, 140, 156, 159, 160, 193, 194, 202, 203, 216, 219, 220, 227, 230, 233, 235, 236, 264, 287, 290, 291], "new": [44, 45, 69, 71, 107, 108, 142, 143, 152, 153, 162, 163, 170, 171, 266], "accumul": [44, 144, 146, 147, 148, 150, 287], "from": [44, 60, 63, 76, 77, 94, 98, 107, 123, 142, 152, 162, 169, 170, 181, 203, 214, 215, 217, 218, 230, 237, 246, 253, 260, 261, 267, 268, 279, 284, 285, 287, 290], "contain": [44, 194, 228], "add": [44, 46, 49, 142, 152, 162, 170, 194, 221, 226, 250, 263, 266, 277, 288, 292], "total": [44, 223, 226, 262, 263, 265, 289], "count": [44, 47, 220], "error_r": [44, 48, 49, 288], "everi": [44, 283], "can": [44, 46, 47, 48, 50, 125, 142, 194, 220, 223, 225, 232, 240, 246, 253, 273, 281, 284, 285, 288, 290, 292], "obtain": 44, "tabul": [44, 45], "all": [44, 49, 146, 220, 240, 249, 250, 280, 282, 290], "ascend": [44, 49], "other": [46, 47, 48, 50, 283, 292], "quantiti": [46, 47, 48, 49, 50], "user": [46, 47, 48, 50, 284, 285], "caution": [46, 47, 48, 50], "instanc": [46, 47, 48, 50, 142], "transmit": [46, 107, 124, 134, 137, 142, 152, 156, 157, 162, 170, 220, 240], "e": [49, 134, 144, 156, 174, 175, 176, 177, 178, 193, 197, 198, 216, 275, 280, 281, 284, 285, 288], "whatev": 49, "wa": [49, 195], "provid": [49, 107, 111, 121, 142, 152, 162, 166, 168, 170, 250, 280, 290], "wrapper": [51, 76], "scipi": [51, 76, 204, 205, 207, 208, 246, 253, 289, 290], "convolv": 51, "It": [51, 76, 96, 108, 125, 134, 153, 163, 171, 194, 240], "support": [51, 76, 291], "one": [51, 76, 143, 152, 153, 163, 169, 171, 223, 228, 240, 241, 242, 244, 246, 247, 248, 253, 269, 284, 285, 286, 289], "its": [51, 76, 77, 94, 194, 284, 285, 289], "sum_": [51, 76, 176, 178, 193, 194, 195, 216, 219, 220, 227, 264], "valid": [52, 222, 240, 249, 250, 275], "same": [52, 97, 134, 156, 256, 284], "0013559842808217807": [55, 56], "005995136544658217": [55, 56], "008698817681933214": [55, 56], "0024103767414047302": [55, 56], "010205586837665018": [55, 56], "018983779931504997": [55, 56], "011950905288150394": [55, 56], "01518393864077397": [55, 56], "051622191325047306": [55, 56], "07210389837804473": [55, 56], "04745944982876247": [55, 56], "039173517569276436": [55, 56], "17918683372907862": [55, 56], "3367363220550604": [55, 56], "4611457574513795": [55, 56], "5084040873607553": [55, 56], "30": [56, 96, 179, 213, 241, 243, 254, 269, 270, 285, 291], "31": [56, 284], "15": [56, 134, 142, 177, 199, 224, 225, 259, 272, 273], "remain": [58, 213, 232], "1024": [59, 60, 63, 84, 241, 242, 244, 247, 248, 286, 289], "whole": [59, 84, 289], "decad": [59, 84, 241, 242, 244, 247, 248, 284, 287], "point": [59, 84, 139, 140, 159, 160, 246, 253], "endpoint": [59, 84, 285], "includ": [59, 84, 280, 281, 282, 290], "integ": [59, 84, 232], "maximum": [59, 84, 107, 113, 114, 134, 142, 152, 162, 170, 223, 226, 239, 255, 262, 263, 265, 278, 287], "max_f": [59, 84], "log10": [59, 84], "evenli": [59, 84], "00000000e": [59, 84, 169, 170, 285], "00": [59, 84, 169, 170, 285], "76562500e": [59, 84], "04": [59, 84, 228, 285], "95312500e": [59, 84], "03": [59, 84, 228, 285], "97070312e": [59, 84], "01": [59, 84, 169, 170, 228, 285, 287], "98046875e": [59, 84], "99023438e": [59, 84], "95337172": 59, "30202676j": 59, "8178049": 59, "5759632j": 59, "6058636": 59, "79630028j": 59, "rad": [59, 84], "0000000000000002": 59, "0j": [59, 84, 143, 153, 163, 171], "sever": [59, 84], "200": [59, 84, 213, 283, 288], "300": [59, 84, 269, 270], "400": [59, 84, 213, 283], "1000": [59, 84, 139, 140, 142, 152, 159, 160, 162, 170, 220, 222, 269, 270, 288], "00391660e": 59, "14686183e": 59, "17j": 59, "53081763e": 59, "88127210e": 59, "62720131e": 59, "03715849e": 59, "83622458e": 59, "27280811e": 59, "resampl": [69, 70, 71, 72, 73, 74, 75, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 209, 259, 290, 291], "http": [69, 192, 202, 204, 205, 206, 207, 208, 209, 223, 225, 233, 273, 275, 279, 280, 281], "wirelesspi": 69, "com": [69, 192, 204, 205, 206, 207, 208, 209, 223, 225, 273, 280, 281], "structur": 69, "should": [73, 134, 142, 240, 281], "equal": [73, 142], "three": [73, 283, 289], "lfilter": 76, "b_i": [76, 79, 83, 94, 241, 242, 243, 244, 247, 248, 254, 258, 285], "feedback": [76, 79, 82, 94, 241, 242, 243, 244, 247, 248, 254, 258, 285], "a_j": [76, 79, 82, 94, 241, 242, 243, 244, 247, 248, 254, 258, 285], "These": [76, 152, 162, 170, 257, 281, 287], "differ": [76, 143, 153, 163, 169, 171, 204, 205, 206, 207, 208, 225, 256, 273, 275, 289], "a_0": 76, "classmethod": [76, 77, 94], "zerospol": [76, 77, 80, 81, 84, 94, 241, 242, 243, 244, 247, 248, 254, 258, 285], "self": [76, 77, 94], "b_tap": [76, 81, 83, 94, 285], "a_tap": [76, 81, 82, 94, 285], "exp": [80, 81, 84, 146, 152, 162, 170, 213, 223, 229, 231, 241, 242, 243, 244, 247, 248, 254, 258, 270, 272, 275, 283, 285, 287], "1j": [80, 81, 84, 213, 231, 241, 242, 243, 244, 247, 248, 254, 258, 270, 272, 283, 285, 287], "conj": [80, 81, 84, 241, 242, 243, 244, 247, 248, 254, 258, 285, 287], "478207252018059": [80, 81, 285], "6400000000000001": [80, 81, 285], "7391036260090295": [81, 285], "3061467458920719j": [81, 285], "4722987": 84, "47271105": 84, "0041658j": 84, "47394825": 84, "00830241j": 84, "47601067": 84, "01238051j": 84, "472298696877605": 84, "36961426": 84, "9678537j": 84, "57338213": 84, "77694738j": 84, "52496713": 84, "3885743j": 84, "51520024": 84, "1706839j": 84, "insert": [96, 179], "multipli": [96, 179], "hold": [96, 98, 179, 181, 232, 291], "recommend": 96, "wai": [96, 281], "11": [96, 142, 152, 162, 170, 199, 209, 224, 225, 259, 273, 279], "zoh": [96, 98, 102, 179, 181, 186], "13": [96, 142, 152, 162, 170, 174, 175, 176, 178, 196, 199, 224, 256, 259, 291], "matlab": [96, 98, 102, 179, 181, 186, 290], "iter": 97, "concaten": [97, 285], "linearli": [98, 181], "2r": 98, "ramp": [98, 125, 181], "advanc": [98, 181], "ones": [98, 181, 204, 205, 207, 208, 287], "84": 100, "modul": [107, 108, 116, 117, 119, 134, 139, 140, 142, 144, 152, 153, 156, 159, 160, 162, 163, 166, 168, 170, 171, 214, 215, 217, 220, 238, 240, 249, 252, 255, 256, 267, 279, 282, 288, 290, 291], "nomenclatur": [107, 142, 152, 162, 170], "variabl": [107, 142, 144, 146, 152, 162, 170, 228, 287], "name": [107, 142, 152, 162, 170], "decis": [107, 113, 114, 134, 137, 140, 142, 152, 156, 157, 160, 162, 170, 240, 287], "tild": [107, 113, 114, 134, 137, 142, 152, 156, 157, 162, 170], "map_symbol": [107, 115, 142, 152, 162, 170, 194, 220, 221, 229, 239, 240, 266, 286, 287, 288, 291], "decide_symbol": [107, 113, 142, 152, 162, 170, 287, 288, 291], "a_tild": [107, 113, 142, 152, 162, 170, 287, 288], "likelihood": [107, 113, 114, 134, 142, 152, 162, 170, 278, 287], "mle": 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"semant": 292, "major": 292, "minor": 292, "patch": 292, "introduc": 292, "featur": 292, "backward": 292, "compat": 292, "bug": 292, "There": 292, "guarante": 292, "them": 292}, "objects": {"": [[3, 0, 0, 1, "sdr", ""]], "sdr": [[9, 1, 1, "", "ClosedLoopPLL", "A class that defines the performance of a closed-loop PLL."], [26, 1, 1, "", "Decimator", "Implements a polyphase decimating FIR filter."], [37, 1, 1, "", "Differentiator", "Implements a differentiator FIR filter."], [39, 1, 1, "", "EnergyDetector", "Implements an energy detector."], [44, 1, 1, "", "ErrorRate", "A class for measuring bit error rates (BER) or symbol error rates (SER)."], [51, 1, 1, "", "FIR", "Implements a finite impulse response (FIR) filter."], [69, 1, 1, "", "FarrowResampler", "Implements a cubic Farrow arbitrary resampler."], [76, 1, 1, "", "IIR", "Implements an infinite impulse response (IIR) filter."], [94, 1, 1, "", "Integrator", "Implements an integrator IIR filter."], [96, 1, 1, "", "Interpolator", "Implements a polyphase interpolating FIR filter."], [107, 1, 1, "", "LinearModulation", "Implements linear phase/amplitude modulation with arbitrary symbol mapping."], [125, 1, 1, "", "LoopFilter", "Implements a 2nd order, proportional-plus-integrator (PPI) loop filter."], [134, 1, 1, "", "MLPED", "Implements a maximum-likelihood phase error detector (ML-PED)."], [142, 1, 1, "", "MSK", "Implements minimum-shift keying (MSK) modulation and demodulation."], [144, 1, 1, "", "NCO", "Implements a numerically-controlled oscillator (NCO)."], [152, 1, 1, "", "OQPSK", "Implements offset quadrature phase-shift keying (OQPSK) modulation and demodulation."], [156, 1, 1, "", "PED", "Implements a heuristic phase error detector (PED)."], [162, 1, 1, "", "PSK", "Implements phase-shift keying (PSK) modulation and demodulation."], [170, 1, 1, "", "PiMPSK", "Implements $pi/M$ phase-shift keying ($pi/M$ PSK) modulation and demodulation."], [172, 5, 1, "", "Q", "Computes the complementary cumulative distribution function $Q(x)$ of the standard normal distribution $mathcal{N}(0, 1)$."], [173, 5, 1, "", "Qinv", "Computes the inverse complementary cumulative distribution function $Q^{-1}(p)$ of the standard normal distribution $mathcal{N}(0, 1)$."], [174, 1, 1, "", "ReplicaCorrelator", "Implements an clairvoyant replica-correlator detector."], [179, 1, 1, "", "Resampler", "Implements a polyphase rational resampling FIR filter."], [192, 5, 1, "", "albersheim", "Estimates the minimum required single-sample SNR, given $N_{NC}$ non-coherent combinations, to achieve a probability of detection $P_D$ and probability of false alarm $P_{FA}$. This function implements Albersheim's equation."], [193, 5, 1, "", "average_power", "Measures the average power of a time-domain signal $x[n]$."], [194, 5, 1, "", "awgn", "Adds additive white Gaussian noise (AWGN) to the time-domain signal $x[n]$."], [195, 5, 1, "", "awgn_capacity", "Calculates the capacity of an additive white Gaussian noise (AWGN) channel."], [196, 5, 1, "", "barker", "Returns the Barker code/sequence of length $N$."], [197, 5, 1, "", "bec", "Passes the binary input sequence $x$ through a binary erasure channel (BEC) with erasure probability $p$."], [198, 5, 1, "", "bec_capacity", "Calculates the capacity of a binary erasure channel (BEC)."], [199, 5, 1, "", "binary_code", "Generates a binary code of length $2^n$."], [200, 5, 1, "", "bsc", "Passes the binary input sequence $x$ through a binary symmetric channel (BSC) with transition probability $p$."], [201, 5, 1, "", "bsc_capacity", "Calculates the capacity of a binary symmetric channel (BSC)."], [202, 5, 1, "", "crest_factor", "Measures the crest factor of a time-domain signal $x[n]$."], [203, 5, 1, "", "db", "Converts from linear units to decibels."], [204, 5, 1, "", "design_bandpass_fir", "Designs a bandpass FIR filter impulse response $h[n]$ using the window method."], [205, 5, 1, "", "design_bandstop_fir", "Designs a bandstop FIR filter impulse response $h[n]$ using the window method."], [206, 5, 1, "", "design_frac_delay_fir", "Designs a fractional delay FIR filter impulse response $h[n]$ using the Kaiser window method."], [207, 5, 1, "", "design_highpass_fir", "Designs a highpass FIR filter impulse response $h[n]$ using the window method."], [208, 5, 1, "", "design_lowpass_fir", "Designs a lowpass FIR filter impulse response $h[n]$ using the window method."], [209, 5, 1, "", "design_multirate_fir", "Designs a multirate FIR filter impulse response $h[n]$ using the Kaiser window method."], [210, 5, 1, "", "diff_decode", "Differentially decodes the input data $y[k]$."], [211, 5, 1, "", "diff_encode", "Differentially encodes the input data $x[k]$."], [212, 5, 1, "", "dmc", "Passes the input sequence $x$ through a discrete memoryless channel (DMC) with transition probability matrix $P$."], [213, 5, 1, "", "downsample", "Downsamples the time-domain signal $x[n]$ by the factor $r$."], [214, 5, 1, "", "ebn0_to_esn0", "Converts from $E_b/N_0$ to $E_s/N_0$."], [215, 5, 1, "", "ebn0_to_snr", "Converts from $E_b/N_0$ to $S/N$."], [216, 5, 1, "", "energy", "Measures the energy of a time-domain signal $x[n]$."], [217, 5, 1, "", "esn0_to_ebn0", "Converts from $E_s/N_0$ to $E_b/N_0$."], [218, 5, 1, "", "esn0_to_snr", "Converts from $E_s/N_0$ to $S/N$."], [219, 5, 1, "", "euclidean", "Measures the Euclidean distance between two signals $x[n]$ and $y[n]$."], [220, 5, 1, "", "evm", "Calculates the error-vector magnitude (EVM) of the complex symbols $hat{x}[k]$."], [221, 5, 1, "", "frequency_offset", "Applies a frequency and phase offset to the time-domain signal $x[n]$."], [222, 5, 1, "", "fspl", "Calculates the free-space path loss (FSPL) in dB."], [223, 5, 1, "", "gaussian", "Returns a Gaussian pulse shape."], [224, 5, 1, "", "gray_code", "Generates a Gray code of length $2^n$."], [225, 5, 1, "", "hadamard", "Returns the Hadamard code/sequence of length $N$."], [226, 5, 1, "", "half_sine", "Returns a half-sine pulse shape."], [227, 5, 1, "", "hamming", "Measures the Hamming distance between two signals $x[n]$ and $y[n]$."], [228, 5, 1, "", "hexdump", "Returns a hexdump of the specified data."], [229, 5, 1, "", "iq_imbalance", "Applies IQ imbalance to the complex time-domain signal $x[n]$."], [230, 5, 1, "", "linear", "Converts from decibels to linear units."], [231, 5, 1, "", "mix", "Mixes the time-domain signal $x[n]$ with a complex exponential or real sinusoid."], [232, 5, 1, "", "pack", "Packs a binary array into an array with multiple bits per element."], [233, 5, 1, "", "papr", "Measures the peak-to-average power ratio (PAPR) of a time-domain signal $x[n]$."], [234, 5, 1, "", "parabolic_antenna", "Calculates the gain $G$ and beamwidth $theta$ of a parabolic reflector."], [235, 5, 1, "", "peak_power", "Measures the peak power of a time-domain signal $x[n]$."], [236, 5, 1, "", "peak_voltage", "Measures the peak voltage of a time-domain signal $x[n]$."], [237, 5, 1, "", "percent", "Converts from a ratio to a percentage."], [259, 5, 1, "", "polyphase_decompose", "Decomposes the FIR filter taps $h_i$ into the polyphase matrix $H_{i, j}$ with $B$ phases."], [260, 5, 1, "", "ppb", "Converts from a ratio to parts per billion (ppb)."], [261, 5, 1, "", "ppm", "Converts from a ratio to parts per million (ppm)."], [262, 5, 1, "", "raised_cosine", "Returns a raised cosine (RC) pulse shape."], [263, 5, 1, "", "rectangular", "Returns a rectangular pulse shape."], [264, 5, 1, "", "rms_voltage", "Measures the root-mean-square (RMS) voltage of a time-domain signal $x[n]$."], [265, 5, 1, "", "root_raised_cosine", "Returns a square root raised cosine (SRRC) pulse shape."], [266, 5, 1, "", "sample_rate_offset", "Applies a sample rate offset to the time-domain signal $x[n]$."], [267, 5, 1, "", "snr_to_ebn0", "Converts from $S/N$ to $E_b/N_0$."], [268, 5, 1, "", "snr_to_esn0", "Converts from $S/N$ to $E_s/N_0$."], [269, 5, 1, "", "to_complex_bb", "Converts the real passband signal $x_r[n]$ centered at $f_{s,r}/4$ with sample rate $f_{s,r}$ to a complex baseband signal $x_c[n]$ centered at $0$ with sample rate $f_{s,c} = f_{s,r}/2$."], [270, 5, 1, "", "to_real_pb", "Converts the complex baseband signal $x_c[n]$ centered at $0$ with sample rate $f_{s,c}$ to a real passband signal $x_r[n]$ centered at $f_{s,r}/4$ with sample rate $f_{s,r} = 2f_{s,c}$."], [271, 5, 1, "", "unpack", "Unpacks an array with multiple bits per element into a binary array."], [272, 5, 1, "", "upsample", "Upsamples the time-domain signal $x[n]$ by the factor $r$."], [273, 5, 1, "", "walsh", "Returns the Walsh code/sequence of length $N$."], [274, 5, 1, "", "wavelength", "Calculates the wavelength $lambda$ of an electromagnetic wave with frequency $f$."], [275, 5, 1, "", "zadoff_chu", "Returns the root-$u$ Zadoff-Chu sequence of length $N$."]], "sdr.ClosedLoopPLL": [[10, 2, 1, "", "Bn", "The noise bandwidth $B_n$ of the PLL in Hz."], [11, 2, 1, "", "BnT", "The normalized noise bandwidth $B_n T$ of the PLL."], [12, 2, 1, "", "K0", "The NCO gain $K_0$."], [13, 2, 1, "", "K1", "The proportional gain $K_1$ of the loop filter."], [14, 2, 1, "", "K2", "The integral gain $K_2$ of the loop filter."], [15, 2, 1, "", "Kp", "The phase error detector (PED) gain $K_p$."], [16, 3, 1, "", "__init__", "Creates a closed-loop PLL analysis object."], [17, 3, 1, "", "frequency_lock_time", "Returns the frequency lock time of the PLL."], [18, 2, 1, "", "iir", "The IIR filter that represents the closed-loop transfer function of the PLL."], [19, 3, 1, "", "lock_time", "Returns the lock time of the PLL."], [20, 2, 1, "", "omega_3dB", "The 3-dB bandwidth $omega_{3textrm{dB}}$ of the PLL in radians/s."], [21, 2, 1, "", "omega_n", "The natural frequency $omega_n$ of the PLL in radians/s."], [22, 3, 1, "", "phase_error_variance", "Returns the variance of the phase error of the PLL in steady state."], [23, 3, 1, "", "phase_lock_time", "Returns the phase lock time of the PLL."], [24, 2, 1, "", "sample_rate", "The sample rate $f_s$ of the PLL in samples/s."], [25, 2, 1, "", "zeta", "The damping factor $zeta$ of the PLL."]], "sdr.ClosedLoopPLL.__init__": [[16, 4, 2, "p-K0", "K0", "The NCO gain $K_0$."], [16, 4, 2, "p-Kp", "Kp", "The gain $K_p$ of the phase error detector (PED) or time error detector (TED)."], [16, 4, 2, "p-damping_factor", "damping_factor", "The damping factor $zeta$ of the loop filter. $zeta = 1$ is critically damped, $zeta < 1$ is underdamped, and $zeta > 1$ is overdamped."], [16, 4, 2, "p-noise_bandwidth", "noise_bandwidth", "The normalized noise bandwidth $B_n T$ of the loop filter, where $B_n$ is the noise bandwidth in Hz and $T$ is the sampling period in seconds."], [16, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the PLL in Hz."]], "sdr.ClosedLoopPLL.frequency_lock_time": [[17, 4, 2, "p-freq_offset", "freq_offset", "The frequency offset $Delta f$ of the input signal in Hz."]], "sdr.ClosedLoopPLL.lock_time": [[19, 4, 2, "p-freq_offset", "freq_offset", "The frequency offset $Delta f$ of the input signal in Hz."]], "sdr.ClosedLoopPLL.phase_error_variance": [[22, 4, 2, "p-cn0", "cn0", "The carrier-to-noise density ratio $C/N_0$ of the input signal in dB-Hz."]], "sdr.Decimator": [[27, 3, 1, "", "__call__", "Filters and decimates the input signal $x[n]$ with the polyphase FIR filter."], [28, 3, 1, "", "__init__", "Creates a polyphase FIR decimating filter."], [29, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [30, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [31, 2, 1, "", "delay", "The delay of FIR filter in samples. The delay indicates the output sample index that corresponds to the first input sample."], [32, 2, 1, "", "method", "The method used to design the multirate filter."], [33, 2, 1, "", "polyphase_taps", "The polyphase feedforward taps $h_{i, j}$."], [34, 2, 1, "", "rate", "The decimation rate $r$."], [35, 3, 1, "", "reset", "Resets the filter state. Only useful when using streaming mode."], [36, 2, 1, "", "taps", "The prototype feedforward taps $h_i$."]], "sdr.Decimator.__call__": [[27, 4, 2, "p-mode", "mode", "The non-streaming convolution mode."], [27, 4, 2, "p-x", "x", "The input signal $x[n]$ with sample rate $f_s$ and length $L$."]], "sdr.Decimator.__init__": [[28, 4, 2, "p-rate", "rate", "The decimation rate $r$."], [28, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs are preserved between calls to __call__()."], [28, 4, 2, "p-taps", "taps", "The multirate filter design specification."]], "sdr.Differentiator": [[38, 3, 1, "", "__init__", "Creates a differentiator FIR filter."]], "sdr.Differentiator.__init__": [[38, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs are preserved between calls to __call__()."]], "sdr.EnergyDetector": [[40, 3, 1, "", "p_d", "Computes the probability of detection $P_D$."], [41, 3, 1, "", "p_fa", "Computes the probability of false alarm $P_{FA}$."], [42, 3, 1, "", "roc", "Computes the receiver operating characteristic (ROC) curve."], [43, 3, 1, "", "threshold", "Computes the threshold $gamma'$."]], "sdr.EnergyDetector.p_d": [[40, 4, 2, "p-N_nc", "N_nc", "The number of samples $N_{NC}$ to non-coherently integrate."], [40, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$."], [40, 4, 2, "p-snr", "snr", "The received signal-to-noise ratio $sigma_s^2 / sigma^2$ in dB."]], "sdr.EnergyDetector.p_fa": [[41, 4, 2, "p-N_nc", "N_nc", "The number of samples $N_{NC}$ to non-coherently integrate."], [41, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [41, 4, 2, "p-sigma2", "sigma2", "The noise variance $sigma^2$."], [41, 4, 2, "p-threshold", "threshold", "The threshold $gamma'$."]], "sdr.EnergyDetector.roc": [[42, 4, 2, "p-N_nc", "N_nc", "The number of samples $N_{NC}$ to non-coherently integrate."], [42, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [42, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$. If None, the ROC curve is computed for p_fa = np.logspace(-10, 0, 101)."], [42, 4, 2, "p-snr", "snr", "The received signal-to-noise ratio $sigma_s^2 / sigma^2$ in dB."]], "sdr.EnergyDetector.threshold": [[43, 4, 2, "p-N_nc", "N_nc", "The number of samples $N_{NC}$ to non-coherently integrate."], [43, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [43, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$."], [43, 4, 2, "p-sigma2", "sigma2", "The noise variance $sigma^2$."]], "sdr.ErrorRate": [[45, 3, 1, "", "__init__", "Creates a new error rate tabulation object."], [46, 3, 1, "", "add", "Measures the number of bit or symbol errors at the given signal-to-noise ratio (SNR)."], [47, 3, 1, "", "counts", "Returns the number of counts at the specified signal-to-noise ratio (SNR)."], [48, 3, 1, "", "error_rate", "Returns the error rate at the specified signal-to-noise ratio (SNR)."], [49, 3, 1, "", "error_rates", "Returns all signal-to-noise ratios (SNRs) in ascending order and their corresponding error rates."], [50, 3, 1, "", "errors", "Returns the number of errors at the specified signal-to-noise ratio (SNR)."]], "sdr.ErrorRate.add": [[46, 4, 2, "p-snr", "snr", "The signal-to-noise ratio (SNR) in dB. This can be $E_b/N_0$, $E_s/N_0$, $S/N$, $C/N_0$, or other SNR quantities. However, users are cautioned to be consistent for a given class instance."], [46, 4, 2, "p-x", "x", "The transmitted bits or symbols $x[k]$."], [46, 4, 2, "p-x_hat", "x_hat", "The received bits or symbols $hat{x}[k]$."]], "sdr.ErrorRate.counts": [[47, 4, 2, "p-snr", "snr", "The signal-to-noise ratio (SNR) in dB. This can be $E_b/N_0$, $E_s/N_0$, $S/N$, $C/N_0$, or other SNR quantities. However, users are cautioned to be consistent for a given class instance."]], "sdr.ErrorRate.error_rate": [[48, 4, 2, "p-snr", "snr", "The signal-to-noise ratio (SNR) in dB. This can be $E_b/N_0$, $E_s/N_0$, $S/N$, $C/N_0$, or other SNR quantities. However, users are cautioned to be consistent for a given class instance."]], "sdr.ErrorRate.errors": [[50, 4, 2, "p-snr", "snr", "The signal-to-noise ratio (SNR) in dB. This can be $E_b/N_0$, $E_s/N_0$, $S/N$, $C/N_0$, or other SNR quantities. However, users are cautioned to be consistent for a given class instance."]], "sdr.FIR": [[52, 3, 1, "", "__call__", "Filters the input signal $x[n]$ with the FIR filter."], [53, 3, 1, "", "__init__", "Creates a FIR filter with feedforward coefficients $h_i$."], [54, 3, 1, "", "__len__", "Returns the filter length $N + 1$."], [55, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [56, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [57, 2, 1, "", "delay", "The delay of the FIR filter $d = lfloor frac{N + 1}{2} rfloor$ in samples."], [58, 3, 1, "", "flush", "Flushes the filter state by passing zeros through the filter. Only useful when using streaming mode."], [59, 3, 1, "", "frequency_response", "Returns the frequency response $H(omega)$ of the FIR filter."], [60, 3, 1, "", "group_delay", "Returns the group delay $tau_g(omega)$ of the FIR filter."], [61, 3, 1, "", "impulse_response", "Returns the impulse response $h[n]$ of the FIR filter. The impulse response $h[n]$ is the filter output when the input is an impulse $delta[n]$."], [62, 2, 1, "", "order", "The order of the FIR filter $N$."], [63, 3, 1, "", "phase_delay", "Returns the phase delay $tau_{phi}(omega)$ of the FIR filter."], [64, 3, 1, "", "reset", "Resets the filter state. Only useful when using streaming mode."], [65, 2, 1, "", "state", "The filter state consisting of the previous $N$ inputs."], [66, 3, 1, "", "step_response", "Returns the step response $s[n]$ of the FIR filter. The step response $s[n]$ is the filter output when the input is a unit step $u[n]$."], [67, 2, 1, "", "streaming", "Indicates whether the filter is in streaming mode."], [68, 2, 1, "", "taps", "The feedforward taps $h_i$ for $i = 0,...,N$."]], "sdr.FIR.__call__": [[52, 4, 2, "p-mode", "mode", "The non-streaming convolution mode."], [52, 4, 2, "p-x", "x", "The input signal $x[n]$ with length $L$."]], "sdr.FIR.__init__": [[53, 4, 2, "p-h", "h", "The feedforward coefficients $h_i$ for $i = 0,...N$."], [53, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs are preserved between calls to __call__()."]], "sdr.FIR.frequency_response": [[59, 4, 2, "p-decades", "decades", "Only used if freqs is an integer."], [59, 4, 2, "p-freqs", "freqs", "The frequency specification."], [59, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the filter in samples/s."], [59, 4, 2, "p-whole", "whole", "Only used if freqs is an integer."]], "sdr.FIR.group_delay": [[60, 4, 2, "p-N", "N", "The number of samples in the group delay."], [60, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the filter in samples/s."]], "sdr.FIR.impulse_response": [[61, 4, 2, "p-N", "N", "The number of samples to return. The default is the filter length."]], "sdr.FIR.phase_delay": [[63, 4, 2, "p-N", "N", "The number of samples in the phase delay."], [63, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the filter in samples/s."]], "sdr.FIR.step_response": [[66, 4, 2, "p-N", "N", "The number of samples to return. The default is the filter length."]], "sdr.FarrowResampler": [[70, 3, 1, "", "__call__", "Resamples the input signal $x[n]$ by the given arbitrary rate $r$."], [71, 3, 1, "", "__init__", "Creates a new Farrow arbitrary resampler."], [72, 2, 1, "", "order", "The order of the filter."], [73, 3, 1, "", "reset", "Streaming-mode only: Resets the filter state and fractional sample index."], [74, 2, 1, "", "streaming", "Indicates whether the filter is in streaming mode."], [75, 2, 1, "", "taps", "The Farrow filter taps."]], "sdr.FarrowResampler.__call__": [[70, 4, 2, "p-rate", "rate", "The resampling rate $r$."], [70, 4, 2, "p-x", "x", "The input signal $x[n] = x(n T_s)$."]], "sdr.FarrowResampler.__init__": [[71, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs are preserved between calls to __call__()."]], "sdr.FarrowResampler.reset": [[73, 4, 2, "p-state", "state", "The filter state to reset to. The state vector should equal the previous three inputs. If None, the filter state will be reset to zero."]], "sdr.IIR": [[77, 3, 1, "", "ZerosPoles", "Creates an IIR filter from its zeros, poles, and gain."], [78, 3, 1, "", "__call__", "Filters the input signal $x[n]$ with the IIR filter."], [79, 3, 1, "", "__init__", "Creates an IIR filter with feedforward coefficients $b_i$ and feedback coefficients $a_j$."], [80, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [81, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [82, 2, 1, "", "a_taps", "The feedback taps $a_j$ for $j = 0,...,N$."], [83, 2, 1, "", "b_taps", "The feedforward taps $b_i$ for $i = 0,...,M$."], [84, 3, 1, "", "frequency_response", "Returns the frequency response $H(omega)$ of the IIR filter."], [85, 2, 1, "", "gain", "The gain of the IIR filter."], [86, 3, 1, "", "impulse_response", "Returns the impulse response $h[n]$ of the IIR filter. The impulse response $h[n]$ is the filter output when the input is an impulse $delta[n]$."], [87, 2, 1, "", "order", "The order of the IIR filter $N$."], [88, 2, 1, "", "poles", "The poles of the IIR filter."], [89, 3, 1, "", "reset", "Resets the filter state. Only useful when using streaming mode."], [90, 2, 1, "", "state", "The filter state."], [91, 3, 1, "", "step_response", "Returns the step response $s[n]$ of the IIR filter. The step response $s[n]$ is the filter output when the input is a unit step $u[n]$."], [92, 2, 1, "", "streaming", "Indicates whether the filter is in streaming mode."], [93, 2, 1, "", "zeros", "The zeros of the IIR filter."]], "sdr.IIR.ZerosPoles": [[77, 4, 2, "p-gain", "gain", "The gain of the transfer function."], [77, 4, 2, "p-poles", "poles", "The poles of the transfer function."], [77, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs and outputs are preserved between calls to __call__()."], [77, 4, 2, "p-zeros", "zeros", "The zeros of the transfer function."]], "sdr.IIR.__call__": [[78, 4, 2, "p-x", "x", "The input signal $x[n]$ with length $L$."]], "sdr.IIR.__init__": [[79, 4, 2, "p-a", "a", "The feedback coefficients $a_j$ for $j = 0,...,N$."], [79, 4, 2, "p-b", "b", "The feedforward coefficients $b_i$ for $i = 0,...,M$."], [79, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs and outputs are preserved between calls to __call__()."]], "sdr.IIR.frequency_response": [[84, 4, 2, "p-decades", "decades", "Only used if freqs is an integer."], [84, 4, 2, "p-freqs", "freqs", "The frequency specification."], [84, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the filter in samples/s."], [84, 4, 2, "p-whole", "whole", "Only used if freqs is an integer."]], "sdr.IIR.impulse_response": [[86, 4, 2, "p-N", "N", "The number of samples to return."]], "sdr.IIR.step_response": [[91, 4, 2, "p-N", "N", "The number of samples to return."]], "sdr.Integrator": [[95, 3, 1, "", "__init__", "Creates an integrating IIR filter."]], "sdr.Integrator.__init__": [[95, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs and outputs are preserved between calls to __call__()."]], "sdr.Interpolator": [[97, 3, 1, "", "__call__", "Interpolates and filters the input signal $x[n]$ with the polyphase FIR filter."], [98, 3, 1, "", "__init__", "Creates a polyphase FIR interpolating filter."], [99, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [100, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [101, 2, 1, "", "delay", "The delay of FIR filter in samples. The delay indicates the output sample index that corresponds to the first input sample."], [102, 2, 1, "", "method", "The method used to design the multirate filter."], [103, 2, 1, "", "polyphase_taps", "The polyphase feedforward taps $h_{i, j}$."], [104, 2, 1, "", "rate", "The interpolation rate $r$."], [105, 3, 1, "", "reset", "Resets the filter state. Only useful when using streaming mode."], [106, 2, 1, "", "taps", "The prototype feedforward taps $h_i$."]], "sdr.Interpolator.__call__": [[97, 4, 2, "p-mode", "mode", "The non-streaming convolution mode."], [97, 4, 2, "p-x", "x", "The input signal $x[n]$ with sample rate $f_s$ and length $L$."]], "sdr.Interpolator.__init__": [[98, 4, 2, "p-rate", "rate", "The interpolation rate $r$."], [98, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs are preserved between calls to __call__()."], [98, 4, 2, "p-taps", "taps", "The multirate filter design specification."]], "sdr.LinearModulation": [[108, 3, 1, "", "__init__", "Creates a new linear phase/amplitude modulation object."], [109, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [110, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [111, 3, 1, "", "ber", "Computes the bit error rate (BER) at the provided $E_b/N_0$ values."], [112, 2, 1, "", "bps", "The number of bits per symbol $k = log_2 M$."], [113, 3, 1, "", "decide_symbols", "Converts the received complex symbols $tilde{a}[k]$ into decimal symbol decisions $hat{s}[k]$ and complex symbol decisions $hat{a}[k]$ using maximum-likelihood estimation (MLE)."], [114, 3, 1, "", "demodulate", "Demodulates the pulse-shaped complex samples $tilde{x}[n]$ into decimal symbol decisions $hat{s}[k]$ using matched filtering and maximum-likelihood estimation."], [115, 3, 1, "", "map_symbols", "Converts the decimal symbols $s[k]$ to complex symbols $a[k]$."], [116, 3, 1, "", "modulate", "Modulates the decimal symbols $s[k]$ into pulse-shaped complex samples $x[n]$."], [117, 2, 1, "", "order", "The modulation order $M = 2^k$."], [118, 2, 1, "", "phase_offset", "The phase offset $phi$ in degrees."], [119, 2, 1, "", "pulse_shape", "The pulse shape $h[n]$ of the modulated signal."], [120, 2, 1, "", "rx_filter", "The receive decimating matched filter. The filter coefficients are matched to the pulse shape $h[-n]^*$."], [121, 3, 1, "", "ser", "Computes the symbol error rate (SER) at the provided $E_s/N_0$ values."], [122, 2, 1, "", "sps", "The number of samples per symbol $f_s / f_{sym}$."], [123, 2, 1, "", "symbol_map", "The symbol map ${0, dots, M-1} mapsto mathbb{C}$. This maps decimal symbols from $0$ to $M-1$ to complex symbols."], [124, 2, 1, "", "tx_filter", "The transmit interpolating pulse shaping filter. The filter coefficients are the pulse shape $h[n]$."]], "sdr.LinearModulation.__init__": [[108, 4, 2, "p-alpha", "alpha", "The roll-off factor of the pulse shape. If None, 0.2 is used for \"rc\" and \"srrc\"."], [108, 4, 2, "p-phase_offset", "phase_offset", "A phase offset $phi$ in degrees to apply to symbol_map."], [108, 4, 2, "p-pulse_shape", "pulse_shape", "The pulse shape $h[n]$ of the modulated signal."], [108, 4, 2, "p-span", "span", "The span of the pulse shape in symbols. This is only used if pulse_shape is a string. If None, 1 is used for \"rect\" and 10 is used for \"rc\" and \"srrc\"."], [108, 4, 2, "p-sps", "sps", "The number of samples per symbol $f_s / f_{sym}$."], [108, 4, 2, "p-symbol_map", "symbol_map", "The symbol mapping ${0, dots, M-1} mapsto mathbb{C}$. An $M$-length array whose indices are decimal symbols $s[k]$ and whose values are complex symbols $a[k]$, where $M$ is the modulation order."]], "sdr.LinearModulation.ber": [[111, 4, 2, "p-ebn0", "ebn0", "Bit energy $E_b$ to noise PSD $N_0$ ratio in dB."]], "sdr.LinearModulation.decide_symbols": [[113, 4, 2, "p-a_tilde", "a_tilde", "The received complex symbols $tilde{a}[k]$."]], "sdr.LinearModulation.demodulate": [[114, 4, 2, "p-x_tilde", "x_tilde", "The received pulse-shaped complex samples $tilde{x}[n]$ to demodulate, with sps samples per symbol and length sps * s_hat.size + pulse_shape.size - 1."]], "sdr.LinearModulation.map_symbols": [[115, 4, 2, "p-s", "s", "The decimal symbols $s[k]$ to map, $0$ to $M-1$."]], "sdr.LinearModulation.modulate": [[116, 4, 2, "p-s", "s", "The decimal symbols $s[k]$ to modulate, $0$ to $M-1$."]], "sdr.LinearModulation.ser": [[121, 4, 2, "p-esn0", "esn0", "Symbol energy $E_s$ to noise PSD $N_0$ ratio in dB."]], "sdr.LoopFilter": [[126, 2, 1, "", "K1", "The proportional gain $K_1$ of the loop filter."], [127, 2, 1, "", "K2", "The integral gain $K_2$ of the loop filter."], [128, 3, 1, "", "__call__", "Filters the input signal $x[n]$."], [129, 3, 1, "", "__init__", "Creates a 2nd order, proportional-plus-integrator (PPI) loop filter."], [130, 2, 1, "", "damping_factor", "The damping factor $zeta$ of the loop filter. $zeta = 1$ is critically damped, $zeta < 1$ is underdamped, and $zeta > 1$ is overdamped."], [131, 2, 1, "", "iir", "The underlying IIR filter used to implement the loop filter."], [132, 2, 1, "", "noise_bandwidth", "The normalized noise bandwidth $B_n T$ of the loop filter, where $B_n$ is the noise bandwidth in Hz and $T$ is the sampling period in seconds."], [133, 3, 1, "", "reset", "Resets the loop filter."]], "sdr.LoopFilter.__call__": [[128, 4, 2, "p-x", "x", "The input signal $x[n]$."]], "sdr.LoopFilter.__init__": [[129, 4, 2, "p-K0", "K0", "The NCO gain $K_0$."], [129, 4, 2, "p-Kp", "Kp", "The gain $K_p$ of the phase error detector (PED) or time error detector (TED)."], [129, 4, 2, "p-damping_factor", "damping_factor", "The damping factor $zeta$ of the loop filter. $zeta = 1$ is critically damped, $zeta < 1$ is underdamped, and $zeta > 1$ is overdamped."], [129, 4, 2, "p-noise_bandwidth", "noise_bandwidth", "The normalized noise bandwidth $B_n T$ of the loop filter, where $B_n$ is the noise bandwidth in Hz and $T$ is the sampling period in seconds."]], "sdr.MLPED": [[135, 2, 1, "", "A_received", "(Settable) The received signal RMS amplitude $A_{rx,rms}$."], [136, 2, 1, "", "A_reference", "(Settable) The reference signal RMS amplitude $A_{ref,rms}$."], [137, 3, 1, "", "__call__", "Detects the phase error."], [138, 3, 1, "", "__init__", "Initializes the ML-PED."], [139, 3, 1, "", "data_aided_error", "Measures the average phase error of the data-aided PED using the specified modulation scheme."], [140, 3, 1, "", "decision_directed_error", "Measures the average phase error of the decision-directed PED using the specified modulation scheme."], [141, 2, 1, "", "gain", "The gain of the phase error detector $K_p$."]], "sdr.MLPED.__call__": [[137, 4, 2, "p-received", "received", "The received complex symbols $tilde{a}[k]$."], [137, 4, 2, "p-reference", "reference", "The reference complex symbols, either the known transmitted complex symbols $a[k]$ or the complex symbols decisions $hat{a}[k]$."]], "sdr.MLPED.__init__": [[138, 4, 2, "p-A_received", "A_received", "The received signal RMS amplitude $A_{rx,rms}$."], [138, 4, 2, "p-A_reference", "A_reference", "The reference signal RMS amplitude $A_{ref,rms}$."]], "sdr.MLPED.data_aided_error": [[139, 4, 2, "p-modem", "modem", "The linear modulation scheme."], [139, 4, 2, "p-n_points", "n_points", "The number of points to use to measure the phase error."]], "sdr.MLPED.decision_directed_error": [[140, 4, 2, "p-modem", "modem", "The linear modulation scheme."], [140, 4, 2, "p-n_points", "n_points", "The number of points to use to measure the phase error."]], "sdr.MSK": [[143, 3, 1, "", "__init__", "Creates a new MSK object."]], "sdr.MSK.__init__": [[143, 4, 2, "p-phase_offset", "phase_offset", "The absolute phase offset $phi$ in degrees."], [143, 4, 2, "p-sps", "sps", "The number of samples per symbol $f_s / f_{sym}$."], [143, 4, 2, "p-symbol_labels", "symbol_labels", "The decimal symbol labels of consecutive complex symbols."]], "sdr.NCO": [[145, 2, 1, "", "K0", "(Settable) The NCO gain $K_0$."], [146, 3, 1, "", "__call__", "Steps the NCO with variable frequency and/or phase signals."], [147, 3, 1, "", "__init__", "Creates a numerically-controlled oscillator (NCO)."], [148, 2, 1, "", "increment", "(Settable) The constant phase accumulation $omega$ of the NCO in radians/sample."], [149, 2, 1, "", "offset", "(Settable) The absolute phase offset $theta$ of the NCO in radians."], [150, 3, 1, "", "reset", "Resets the NCO."], [151, 3, 1, "", "step", "Steps the NCO forward by $N$ samples."]], "sdr.NCO.__call__": [[146, 4, 2, "p-freq", "freq", "The variable frequency signal $f[n]$ in radians/sample. This input signal varies the per-sample phase increment of the NCO. If None, the signal is all zeros."], [146, 4, 2, "p-output", "output", "The format of the output signal $y[n]$. Options are the accumulated phase, sine, cosine, or complex exponential."], [146, 4, 2, "p-phase", "phase", "The variable phase signal $p[n]$ in radians. This input signal varies the per-sample phase offset of the NCO. If None, the signal is all zeros."]], "sdr.NCO.__init__": [[147, 4, 2, "p-K0", "K0", "The NCO gain $K_0$."], [147, 4, 2, "p-increment", "increment", "The constant accumulation $omega$ of the NCO in radians/sample."], [147, 4, 2, "p-offset", "offset", "The absolute offset $theta$ of the NCO in radians."]], "sdr.NCO.step": [[151, 4, 2, "p-N", "N", "The number of samples $N$ to step the NCO forward."]], "sdr.OQPSK": [[153, 3, 1, "", "__init__", "Creates a new OQPSK object."], [154, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [155, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."]], "sdr.OQPSK.__init__": [[153, 4, 2, "p-alpha", "alpha", "The roll-off factor of the pulse shape. If None, 0.2 is used for \"rc\" and \"srrc\"."], [153, 4, 2, "p-phase_offset", "phase_offset", "The absolute phase offset $phi$ in degrees."], [153, 4, 2, "p-pulse_shape", "pulse_shape", "The pulse shape $h[n]$ of the modulated signal."], [153, 4, 2, "p-span", "span", "The span of the pulse shape in symbols. This is only used if pulse_shape is a string. If None, 1 is used for \"rect\" and 10 is used for \"rc\" and \"srrc\"."], [153, 4, 2, "p-sps", "sps", "The number of samples per symbol $f_s / f_{sym}$."], [153, 4, 2, "p-symbol_labels", "symbol_labels", "The decimal symbol labels of consecutive complex symbols."]], "sdr.PED": [[157, 3, 1, "", "__call__", "Detects the phase error."], [158, 3, 1, "", "__init__", "Initializes the PED."], [159, 3, 1, "", "data_aided_error", "Measures the average phase error of the data-aided PED using the specified modulation scheme."], [160, 3, 1, "", "decision_directed_error", "Measures the average phase error of the decision-directed PED using the specified modulation scheme."], [161, 2, 1, "", "gain", "The gain of the phase error detector $K_p$."]], "sdr.PED.__call__": [[157, 4, 2, "p-received", "received", "The received complex symbols $tilde{a}[k]$."], [157, 4, 2, "p-reference", "reference", "The reference complex symbols, either the known transmitted complex symbols $a[k]$ or the complex symbols decisions $hat{a}[k]$."]], "sdr.PED.data_aided_error": [[159, 4, 2, "p-modem", "modem", "The linear modulation scheme."], [159, 4, 2, "p-n_points", "n_points", "The number of points to use to measure the phase error."]], "sdr.PED.decision_directed_error": [[160, 4, 2, "p-modem", "modem", "The linear modulation scheme."], [160, 4, 2, "p-n_points", "n_points", "The number of points to use to measure the phase error."]], "sdr.PSK": [[163, 3, 1, "", "__init__", "Creates a new PSK object."], [164, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [165, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [166, 3, 1, "", "ber", "Computes the bit error rate (BER) at the provided $E_b/N_0$ values."], [167, 2, 1, "", "phase_offset", "The phase offset $phi$ in degrees."], [168, 3, 1, "", "ser", "Computes the symbol error rate (SER) at the provided $E_s/N_0$ values."], [169, 2, 1, "", "symbol_map", "The symbol map ${0, dots, M-1} mapsto mathbb{C}$. This maps decimal symbols from $0$ to $M-1$ to complex symbols."]], "sdr.PSK.__init__": [[163, 4, 2, "p-alpha", "alpha", "The roll-off factor of the pulse shape. If None, 0.2 is used for \"rc\" and \"srrc\"."], [163, 4, 2, "p-order", "order", "The modulation order $M = 2^k$, where $k ge 1$ is the bits per symbol."], [163, 4, 2, "p-phase_offset", "phase_offset", "The phase offset $phi$ in degrees."], [163, 4, 2, "p-pulse_shape", "pulse_shape", "The pulse shape $h[n]$ of the modulated signal."], [163, 4, 2, "p-span", "span", "The span of the pulse shape in symbols. This is only used if pulse_shape is a string. If None, 1 is used for \"rect\" and 10 is used for \"rc\" and \"srrc\"."], [163, 4, 2, "p-sps", "sps", "The number of samples per symbol $f_s / f_{sym}$."], [163, 4, 2, "p-symbol_labels", "symbol_labels", "The decimal symbol labels of consecutive complex symbols."]], "sdr.PSK.ber": [[166, 4, 2, "p-diff_encoded", "diff_encoded", "Indicates whether the input symbols were differentially encoded."], [166, 4, 2, "p-ebn0", "ebn0", "Bit energy $E_b$ to noise PSD $N_0$ ratio in dB."]], "sdr.PSK.ser": [[168, 4, 2, "p-diff_encoded", "diff_encoded", "Indicates whether the input symbols were differentially encoded."], [168, 4, 2, "p-esn0", "esn0", "Symbol energy $E_s$ to noise PSD $N_0$ ratio in dB."]], "sdr.PiMPSK": [[171, 3, 1, "", "__init__", "Creates a new $pi/M$ PSK object."]], "sdr.PiMPSK.__init__": [[171, 4, 2, "p-alpha", "alpha", "The roll-off factor of the pulse shape. If None, 0.2 is used for \"rc\" and \"srrc\"."], [171, 4, 2, "p-order", "order", "The modulation order $M = 2^k$, where $k ge 1$ is the bits per symbol."], [171, 4, 2, "p-phase_offset", "phase_offset", "The absolute phase offset $phi$ in degrees."], [171, 4, 2, "p-pulse_shape", "pulse_shape", "The pulse shape $h[n]$ of the modulated signal."], [171, 4, 2, "p-span", "span", "The span of the pulse shape in symbols. This is only used if pulse_shape is a string. If None, 1 is used for \"rect\" and 10 is used for \"rc\" and \"srrc\"."], [171, 4, 2, "p-sps", "sps", "The number of samples per symbol $f_s / f_{sym}$."], [171, 4, 2, "p-symbol_labels", "symbol_labels", "The decimal symbol labels of consecutive complex symbols."]], "sdr.Q": [[172, 4, 2, "p-x", "x", "The real-valued input $x$."]], "sdr.Qinv": [[173, 4, 2, "p-p", "p", "The probability $p$ of exceeding the returned value $x$."]], "sdr.ReplicaCorrelator": [[175, 3, 1, "", "p_d", "Computes the probability of detection $P_D$."], [176, 3, 1, "", "p_fa", "Computes the probability of false alarm $P_{FA}$."], [177, 3, 1, "", "roc", "Computes the receiver operating characteristic (ROC) curve."], [178, 3, 1, "", "threshold", "Computes the threshold $gamma'$."]], "sdr.ReplicaCorrelator.p_d": [[175, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [175, 4, 2, "p-enr", "enr", "The received energy-to-noise ratio $mathcal{E}/sigma^2$ in dB."], [175, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$."]], "sdr.ReplicaCorrelator.p_fa": [[176, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [176, 4, 2, "p-energy", "energy", "The received energy $mathcal{E} = sum_{i=0}^{N-1} left| s[n] right|^2$."], [176, 4, 2, "p-sigma2", "sigma2", "The noise variance $sigma^2$."], [176, 4, 2, "p-threshold", "threshold", "The threshold $gamma'$."]], "sdr.ReplicaCorrelator.roc": [[177, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [177, 4, 2, "p-enr", "enr", "The received energy-to-noise ratio $mathcal{E}/sigma^2$ in dB."], [177, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$. If None, the ROC curve is computed for p_fa = np.logspace(-10, 0, 101)."]], "sdr.ReplicaCorrelator.threshold": [[178, 4, 2, "p-complex", "complex", "Indicates whether the signal is complex."], [178, 4, 2, "p-energy", "energy", "The received energy $mathcal{E} = sum_{i=0}^{N-1} left| s[n] right|^2$."], [178, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$."], [178, 4, 2, "p-sigma2", "sigma2", "The noise variance $sigma^2$."]], "sdr.Resampler": [[180, 3, 1, "", "__call__", "Resamples and filters the input signal $x[n]$ with the polyphase FIR filter."], [181, 3, 1, "", "__init__", "Creates a polyphase FIR rational resampling filter."], [182, 3, 1, "", "__repr__", "Returns a code-styled string representation of the object."], [183, 3, 1, "", "__str__", "Returns a human-readable string representation of the object."], [184, 2, 1, "", "delay", "The delay of FIR filter in samples. The delay indicates the output sample index that corresponds to the first input sample."], [185, 2, 1, "", "down", "The decimation rate $Q$."], [186, 2, 1, "", "method", "The method used to design the multirate filter."], [187, 2, 1, "", "polyphase_taps", "The polyphase feedforward taps $h_{i, j}$."], [188, 2, 1, "", "rate", "The resampling rate $P/Q$."], [189, 3, 1, "", "reset", "Resets the filter state. Only useful when using streaming mode."], [190, 2, 1, "", "taps", "The prototype feedforward taps $h_i$."], [191, 2, 1, "", "up", "The interpolation rate $P$."]], "sdr.Resampler.__init__": [[181, 4, 2, "p-down", "down", "The decimation rate $Q$."], [181, 4, 2, "p-streaming", "streaming", "Indicates whether to use streaming mode. In streaming mode, previous inputs are preserved between calls to __call__()."], [181, 4, 2, "p-taps", "taps", "The multirate filter design specification."], [181, 4, 2, "p-up", "up", "The interpolation rate $P$."]], "sdr.albersheim": [[192, 4, 2, "p-N_nc", "N_nc", "The number of non-coherent combinations $N_{NC} ge 1$."], [192, 4, 2, "p-p_d", "p_d", "The desired probability of detection $P_D$ in $(0, 1)$."], [192, 4, 2, "p-p_fa", "p_fa", "The desired probability of false alarm $P_{FA}$ in $(0, 1)$."]], "sdr.average_power": [[193, 4, 2, "p-axis", "axis", "Axis or axes along which to compute the average power. The default is None, which computes the average power of the entire array."], [193, 4, 2, "p-db", "db", "Indicates whether to return the result in decibels (dB)."], [193, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.awgn": [[194, 4, 2, "p-noise", "noise", "The noise power (variance) in linear units. If noise is None, snr must be specified."], [194, 4, 2, "p-seed", "seed", "The seed for the random number generator. This is passed to numpy.random.default_rng()."], [194, 4, 2, "p-snr", "snr", "The desired signal-to-noise ratio (SNR) in dB. If specified, the average signal power is measured explicitly. It is assumed that $x[n]$ contains signal only. If the signal power is known, the desired noise variance can be computed and passed in noise. If snr is None, noise must be specified."], [194, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to which AWGN is added."]], "sdr.awgn_capacity": [[195, 4, 2, "p-bandwidth", "bandwidth", "The bandwidth $B$ of the channel in Hz. If specified, the capacity is calculated in bits/s. If None, the capacity is calculated in bits/2D."], [195, 4, 2, "p-snr", "snr", "The signal-to-noise ratio $S / N$ in dB of the channel."]], "sdr.barker": [[196, 4, 2, "p-length", "length", "The length $N$ of the Barker code/sequence."], [196, 4, 2, "p-output", "output", "The output format of the Barker code/sequence."]], "sdr.bec": [[197, 4, 2, "p-p", "p", "The probability $p$ of a bit erasure."], [197, 4, 2, "p-seed", "seed", "The seed for the random number generator. This is passed to numpy.random.default_rng()."], [197, 4, 2, "p-x", "x", "The input sequence $x$ with $x_i in {0, 1}$."]], "sdr.bec_capacity": [[198, 4, 2, "p-p", "p", "The erasure probability $p$ of the BEC channel."]], "sdr.binary_code": [[199, 4, 2, "p-n", "n", "The length of the binary code."]], "sdr.bsc": [[200, 4, 2, "p-p", "p", "The probability $p$ of a bit flip."], [200, 4, 2, "p-seed", "seed", "The seed for the random number generator. This is passed to numpy.random.default_rng()."], [200, 4, 2, "p-x", "x", "The input sequence $x$ with $x_i in {0, 1}$."]], "sdr.bsc_capacity": [[201, 4, 2, "p-p", "p", "The transition probability $p$ of the BSC channel."]], "sdr.crest_factor": [[202, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.db": [[203, 4, 2, "p-type", "type", "The type of input value or signal."], [203, 4, 2, "p-x", "x", "The input value or signal."]], "sdr.design_bandpass_fir": [[204, 4, 2, "p-atten", "atten", "The sidelobe attenuation in dB. Only used if window is \"chebyshev\" or \"kaiser\"."], [204, 4, 2, "p-bandwidth", "bandwidth", "The two-sided bandwidth about $f_{center}$, normalized to the Nyquist frequency $f_s / 2$."], [204, 4, 2, "p-center_freq", "center_freq", "The center frequency $f_{center}$, normalized to the Nyquist frequency $f_s / 2$."], [204, 4, 2, "p-order", "order", "The filter order $N$. Must be even."], [204, 4, 2, "p-window", "window", "The time-domain window to use."]], "sdr.design_bandstop_fir": [[205, 4, 2, "p-atten", "atten", "The sidelobe attenuation in dB. Only used if window is \"chebyshev\" or \"kaiser\"."], [205, 4, 2, "p-bandwidth", "bandwidth", "The two-sided bandwidth about $f_{center}$, normalized to the Nyquist frequency $f_s / 2$."], [205, 4, 2, "p-center_freq", "center_freq", "The center frequency $f_{center}$, normalized to the Nyquist frequency $f_s / 2$."], [205, 4, 2, "p-order", "order", "The filter order $N$. Must be even."], [205, 4, 2, "p-window", "window", "The time-domain window to use."]], "sdr.design_frac_delay_fir": [[206, 4, 2, "p-delay", "delay", "The fractional delay $0 le Delta n le 1$."], [206, 4, 2, "p-length", "length", "The filter length $L$. Filters with even length have best performance. Filters with odd length are equivalent to an even-length filter with an appended zero."]], "sdr.design_highpass_fir": [[207, 4, 2, "p-atten", "atten", "The sidelobe attenuation in dB. Only used if window is \"chebyshev\" or \"kaiser\"."], [207, 4, 2, "p-cutoff_freq", "cutoff_freq", "The cutoff frequency $f_c$, normalized to the Nyquist frequency $f_s / 2$."], [207, 4, 2, "p-order", "order", "The filter order $N$. Must be even."], [207, 4, 2, "p-window", "window", "The time-domain window to use."]], "sdr.design_lowpass_fir": [[208, 4, 2, "p-atten", "atten", "The sidelobe attenuation in dB. Only used if window is \"chebyshev\" or \"kaiser\"."], [208, 4, 2, "p-cutoff_freq", "cutoff_freq", "The cutoff frequency $f_c$, normalized to the Nyquist frequency $f_s / 2$."], [208, 4, 2, "p-order", "order", "The filter order $N$. Must be even."], [208, 4, 2, "p-window", "window", "The time-domain window to use."]], "sdr.design_multirate_fir": [[209, 4, 2, "p-A_stop", "A_stop", "The stopband attenuation $A_{text{stop}}$ in dB."], [209, 4, 2, "p-down", "down", "The decimation rate $Q$."], [209, 4, 2, "p-half_length", "half_length", "The half-length of the polyphase filters."], [209, 4, 2, "p-up", "up", "The interpolation rate $P$."]], "sdr.diff_decode": [[210, 4, 2, "p-y", "y", "The input encoded data $y[k]$."], [210, 4, 2, "p-y_prev", "y_prev", "The previous value of the encoded data $y[k-1]$."]], "sdr.diff_encode": [[211, 4, 2, "p-x", "x", "The input uncoded data $x[k]$."], [211, 4, 2, "p-y_prev", "y_prev", "The previous value of the output encoded data $y[k-1]$."]], "sdr.dmc": [[212, 4, 2, "p-P", "P", "The $m times n$ transition probability matrix $P$, where $P_{i,j} = Pr(Y = y_j | X = x_i)$."], [212, 4, 2, "p-X", "X", "The input alphabet $mathcal{X}$ of size $m$. If None, it is assumed that $mathcal{X} = {0, 1, ldots, m-1}$."], [212, 4, 2, "p-Y", "Y", "The output alphabet $mathcal{Y}$ of size $n$. If None, it is assumed that $mathcal{Y} = {0, 1, ldots, n-1}$."], [212, 4, 2, "p-seed", "seed", "The seed for the random number generator. This is passed to numpy.random.default_rng()."], [212, 4, 2, "p-x", "x", "The input sequence $x$ with $x_i in mathcal{X}$."]], "sdr.downsample": [[213, 4, 2, "p-rate", "rate", "The downsampling factor $r$."], [213, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ with sample rate $f_s$."]], "sdr.ebn0_to_esn0": [[214, 4, 2, "p-bps", "bps", "Bits per symbol $log_2 M$, where $M$ is the modulation order."], [214, 4, 2, "p-ebn0", "ebn0", "Bit energy $E_b$ to noise PSD $N_0$ ratio in dB."], [214, 4, 2, "p-rate", "rate", "Code rate $r = k/n$, where $k$ is the number of information bits and $n$ is the number of coded bits."]], "sdr.ebn0_to_snr": [[215, 4, 2, "p-bps", "bps", "Bits per symbol $log_2 M$, where $M$ is the modulation order."], [215, 4, 2, "p-ebn0", "ebn0", "Bit energy $E_b$ to noise PSD $N_0$ ratio in dB."], [215, 4, 2, "p-rate", "rate", "Code rate $r = k/n$, where $k$ is the number of information bits and $n$ is the number of coded bits."], [215, 4, 2, "p-sps", "sps", "Samples per symbol $f_s / f_{sym}$."]], "sdr.energy": [[216, 4, 2, "p-axis", "axis", "Axis or axes along which to compute the energy. The default is None, which computes the energy of the entire array."], [216, 4, 2, "p-db", "db", "Indicates whether to return the result in decibels (dB)."], [216, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.esn0_to_ebn0": [[217, 4, 2, "p-bps", "bps", "Bits per symbol $log_2 M$, where $M$ is the modulation order."], [217, 4, 2, "p-esn0", "esn0", "Symbol energy $E_s$ to noise PSD $N_0$ ratio in dB."], [217, 4, 2, "p-rate", "rate", "Code rate $r = k/n$, where $k$ is the number of information bits and $n$ is the number of coded bits."]], "sdr.esn0_to_snr": [[218, 4, 2, "p-esn0", "esn0", "Symbol energy $E_s$ to noise PSD $N_0$ ratio in dB."], [218, 4, 2, "p-sps", "sps", "Samples per symbol $f_s / f_{sym}$."]], "sdr.euclidean": [[219, 4, 2, "p-axis", "axis", "Axis or axes along which to compute the distance. The default is None, which computes the distance across the entire array."], [219, 4, 2, "p-x", "x", "The time-domain signal $x[n]$."], [219, 4, 2, "p-y", "y", "The time-domain signal $y[n]$."]], "sdr.evm": [[220, 4, 2, "p-norm", "norm", "The normalization source used in the EVM calculation."], [220, 4, 2, "p-output", "output", "The output type of the EVM calculation."], [220, 4, 2, "p-ref", "ref", "The complex reference symbols $x[k]$. This can be the noiseless transmitted symbols or the modulation's symbol map."], [220, 4, 2, "p-x_hat", "x_hat", "The complex symbols $hat{x}[k]$ to be measured."]], "sdr.frequency_offset": [[221, 4, 2, "p-freq", "freq", "The frequency offset $f$ in Hz (or in cycles/sample if sample_rate=1)."], [221, 4, 2, "p-freq_rate", "freq_rate", "The frequency offset rate $f_{text{rate}}$ in Hz/s (or in cycles/sample^2 if sample_rate=1)."], [221, 4, 2, "p-phase", "phase", "The phase offset $phi$ in degrees."], [221, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ in samples/s."], [221, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to which the frequency offset is applied."]], "sdr.fspl": [[222, 4, 2, "p-distance", "distance", "The distance $d$ in meters between the transmitter and receiver."], [222, 4, 2, "p-freq", "freq", "The frequency $f$ in Hz of the signal."]], "sdr.gaussian": [[223, 4, 2, "p-norm", "norm", "Indicates how to normalize the pulse shape."], [223, 4, 2, "p-span", "span", "The length of the filter in symbols. The length of the filter is span * sps + 1 samples. The filter order span * sps must be even."], [223, 4, 2, "p-sps", "sps", "The number of samples per symbol."], [223, 4, 2, "p-time_bandwidth", "time_bandwidth", "The time-bandwidth product $B T_{sym}$ of the filter, where $B$ is the one-sided 3-dB bandwidth in Hz and $T_{sym}$ is the symbol time in seconds. The time-bandwidth product can also be thought of as the fractional bandwidth $B / f_{sym}$. Smaller values produce wider pulses."]], "sdr.gray_code": [[224, 4, 2, "p-n", "n", "The length of the Gray code."]], "sdr.hadamard": [[225, 4, 2, "p-index", "index", "The index $i$ of the Hadamard code."], [225, 4, 2, "p-length", "length", "The length $N$ of the Hadamard code/sequence. Must be a power of 2."], [225, 4, 2, "p-output", "output", "The output format of the Hadamard code/sequence."]], "sdr.half_sine": [[226, 4, 2, "p-norm", "norm", "Indicates how to normalize the pulse shape."], [226, 4, 2, "p-span", "span", "The length of the filter in symbols. The length of the filter is span * sps samples, but only the center sps samples are non-zero. The only reason for span to be larger than 1 is to add delay to the filter."], [226, 4, 2, "p-sps", "sps", "The number of samples per symbol."]], "sdr.hamming": [[227, 4, 2, "p-axis", "axis", "Axis or axes along which to compute the distance. The default is None, which computes the distance across the entire array."], [227, 4, 2, "p-x", "x", "The time-domain signal $x[n]$."], [227, 4, 2, "p-y", "y", "The time-domain signal $y[n]$."]], "sdr.hexdump": [[228, 4, 2, "p-data", "data", "The data to display. Each element is considered one byte. Use sdr.pack() or sdr.unpack() to convert data with variable bits per element."], [228, 4, 2, "p-width", "width", "The number of bytes per line."]], "sdr.iq_imbalance": [[229, 4, 2, "p-amplitude", "amplitude", "The amplitude imbalance $A$ in dB. A positive value indicates that the in-phase component is larger than the quadrature component."], [229, 4, 2, "p-phase", "phase", "The phase imbalance $phi$ in degrees. A positive value indicates that the quadrature component leads the in-phase component."], [229, 4, 2, "p-x", "x", "The complex time-domain signal $x[n]$ to which IQ imbalance is applied."]], "sdr.linear": [[230, 4, 2, "p-type", "type", "The type of output value or signal."], [230, 4, 2, "p-x", "x", "The input value or signal in dB."]], "sdr.mix": [[231, 4, 2, "p-complex", "complex", "Indicates whether to mix by a complex exponential or real sinusoid."], [231, 4, 2, "p-freq", "freq", "The frequency $f$ of the sinusoid in Hz (or 1/samples if sample_rate=1). The frequency must satisfy $-f_s/2 le f le f_s/2$."], [231, 4, 2, "p-phase", "phase", "The phase $phi$ of the sinusoid in degrees."], [231, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal."], [231, 4, 2, "p-x", "x", "The time-domain signal $x[n]$."]], "sdr.pack": [[232, 4, 2, "p-bpe", "bpe", "The number of bits per element in the output array."], [232, 4, 2, "p-dtype", "dtype", "The data type of the output array. If None, the smallest unsigned integer dtype that can hold bpe bits is used."], [232, 4, 2, "p-x", "x", "The input binary array with 1 bit per element."]], "sdr.papr": [[233, 4, 2, "p-axis", "axis", "Axis or axes along which to compute the PAPR. The default is None, which computes the PAPR of the entire array."], [233, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.parabolic_antenna": [[234, 4, 2, "p-diameter", "diameter", "The diameter $d$ in meters of the parabolic reflector."], [234, 4, 2, "p-efficiency", "efficiency", "The efficiency $0 le eta le 1$ of the parabolic reflector."], [234, 4, 2, "p-freq", "freq", "The frequency $f$ in Hz of the signal."]], "sdr.peak_power": [[235, 4, 2, "p-axis", "axis", "Axis or axes along which to compute the peak power. The default is None, which computes the peak power of the entire array."], [235, 4, 2, "p-db", "db", "Indicates whether to return the result in decibels (dB)."], [235, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.peak_voltage": [[236, 4, 2, "p-db", "db", "Indicates whether to return the result in decibels (dB)."], [236, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.percent": [[237, 4, 2, "p-x", "x", "The input ratio."]], "sdr.plot": [[238, 5, 1, "", "ber", "Plots the bit error rate (BER) as a function of $E_b/N_0$."], [239, 5, 1, "", "constellation", "Plots the constellation of the complex symbols $hat{x}[k]$."], [240, 5, 1, "", "eye", "Plots the eye diagram of the baseband modulated signal $x[n]$."], [241, 5, 1, "", "filter", "Plots the magnitude response $|H(omega)|^2$, impulse response $h[n]$, step response $s[n]$, and zeros and poles of the filter."], [242, 5, 1, "", "group_delay", "Plots the group delay $tau_g(omega)$ of the IIR filter."], [243, 5, 1, "", "impulse_response", "Plots the impulse response $h[n]$ of a filter."], [244, 5, 1, "", "magnitude_response", "Plots the magnitude response $|H(omega)|^2$ of the filter."], [245, 5, 1, "", "p_d", "Plots the probability of detection $P_D$ as a function of received SNR or ENR."], [246, 5, 1, "", "periodogram", "Plots the estimated power spectral density $P_{xx}$ of a time-domain signal $x[n]$ using Welch's method."], [247, 5, 1, "", "phase_delay", "Plots the phase delay $tau_{phi}(omega)$ of the filter."], [248, 5, 1, "", "phase_response", "Plots the phase response $angle H(omega)$ of the filter."], [249, 5, 1, "", "phase_tree", "Plots the phase tree of a continuous-phase modulated (CPM) signal signal $x[n]$."], [250, 5, 1, "", "raster", "Plots a raster of the time-domain signal $x[n]$."], [251, 5, 1, "", "roc", "Plots the receiver operating characteristic (ROC) curve as a function of $P_{FA}$."], [252, 5, 1, "", "ser", "Plots the symbol error rate (SER) as a function of $E_s/N_0$."], [253, 5, 1, "", "spectrogram", "Plots the spectrogram of a time-domain signal $x[n]$ using Welch's method."], [254, 5, 1, "", "step_response", "Plots the step response $s[n]$ of a filter."], [255, 5, 1, "", "symbol_map", "Plots the symbol map of the complex symbols $hat{x}[k]$."], [256, 5, 1, "", "time_domain", "Plots a time-domain signal $x[n]$."], [257, 5, 1, "", "use_style", "Applies sdr's default matplotlib rcParams."], [258, 5, 1, "", "zeros_poles", "Plots the zeros and poles of the filter."]], "sdr.plot.ber": [[238, 4, 2, "p-ber", "ber", "The bit error rate $P_{be}$."], [238, 4, 2, "p-ebn0", "ebn0", "The bit energy $E_b$ to noise PSD $N_0$ ratio (dB)."], [238, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.semilogy()."]], "sdr.plot.constellation": [[239, 4, 2, "p-heatmap", "heatmap", "If True, a heatmap is plotted instead of a scatter plot."], [239, 4, 2, "p-kwargs", "kwargs", "If heatmap=False, additional keyword arguments to pass to matplotlib.pyplot.scatter(). The following keyword arguments are set by default. The defaults may be overwritten."], [239, 4, 2, "p-limits", "limits", "The axis limits, which apply to both the x- and y-axis. If None, the axis limits are set to 10% larger than the maximum value."], [239, 4, 2, "p-x_hat", "x_hat", "The complex symbols $hat{x}[k]$."]], "sdr.plot.eye": [[240, 4, 2, "p-color", "color", "Indicates how to color the rasters. If \"index\", the rasters are colored based on their index. If a valid Matplotlib color, the rasters are all colored with that color."], [240, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to sdr.plot.raster()."], [240, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Samples\"."], [240, 4, 2, "p-span", "span", "The number of symbols per raster."], [240, 4, 2, "p-sps", "sps", "The number of samples per symbol."], [240, 4, 2, "p-x", "x", "The baseband modulated signal $x[n]$. If x is complex, the real and imaginary rasters are interleaved. Time order is preserved."]], "sdr.plot.filter": [[241, 4, 2, "p-N_freq", "N_freq", "The number of samples $N_f$ in the frequency response."], [241, 4, 2, "p-N_time", "N_time", "The number of samples $N_t$ in the time domain. If None, the length of b is used for FIR filters and 100 for IIR filters."], [241, 4, 2, "p-decades", "decades", "The number of decades to plot when x_axis=\"log\"."], [241, 4, 2, "p-filter", "filter", "The filter definition."], [241, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Normalized Frequency\"."], [241, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum, a two-sided spectrum, or one-sided spectrum with a logarithmic frequency axis."]], "sdr.plot.group_delay": [[242, 4, 2, "p-N", "N", "The number of samples $N$ in the frequency response."], [242, 4, 2, "p-decades", "decades", "The number of decades to plot when x_axis=\"log\"."], [242, 4, 2, "p-filter", "filter", "The filter definition."], [242, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [242, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Normalized Frequency\"."], [242, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum, a two-sided spectrum, or one-sided spectrum with a logarithmic frequency axis. The default is \"auto\" which selects \"one-sided\" for real-valued filters and \"two-sided\" for complex-valued filters."]], "sdr.plot.impulse_response": [[243, 4, 2, "p-N", "N", "The number of samples $N$ to plot. If None, the length of b is used for FIR filters and 100 for IIR filters."], [243, 4, 2, "p-filter", "filter", "The filter definition."], [243, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."]], "sdr.plot.magnitude_response": [[244, 4, 2, "p-N", "N", "The number of samples $N$ in the frequency response."], [244, 4, 2, "p-decades", "decades", "The number of decades to plot when x_axis=\"log\"."], [244, 4, 2, "p-filter", "filter", "The filter definition."], [244, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [244, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Normalized Frequency\"."], [244, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum, a two-sided spectrum, or one-sided spectrum with a logarithmic frequency axis. The default is \"auto\" which selects \"one-sided\" for real-valued filters and \"two-sided\" for complex-valued filters."], [244, 4, 2, "p-y_axis", "y_axis", "The y-axis scaling. Options are to display a linear or logarithmic magnitude response."]], "sdr.plot.p_d": [[245, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [245, 4, 2, "p-p_d", "p_d", "The probability of detection $P_D$."], [245, 4, 2, "p-x", "x", "The SNR or ENR in dB."], [245, 4, 2, "p-x_label", "x_label", "The x-axis label to use."]], "sdr.plot.periodogram": [[246, 4, 2, "p-average", "average", "The type of averaging to use. Options are to average the periodograms using the mean or median."], [246, 4, 2, "p-detrend", "detrend", "The type of detrending to apply. Options are to remove the mean or a linear trend from each segment."], [246, 4, 2, "p-fft", "fft", "The number of points to use in the FFT. If None, the FFT length is set to length."], [246, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [246, 4, 2, "p-length", "length", "The length of each segment in samples. If None, the length is set to 256."], [246, 4, 2, "p-overlap", "overlap", "The number of samples to overlap between segments. If None, the overlap is set to length // 2."], [246, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Normalized Frequency\"."], [246, 4, 2, "p-window", "window", "The windowing function to use. This can be a string or a vector of length length."], [246, 4, 2, "p-x", "x", "The time-domain signal $x[n]$."], [246, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum, a two-sided spectrum, or one-sided spectrum with a logarithmic frequency axis."], [246, 4, 2, "p-y_axis", "y_axis", "The y-axis scaling. Options are to display a linear or logarithmic power spectral density."]], "sdr.plot.phase_delay": [[247, 4, 2, "p-N", "N", "The number of samples $N$ in the phase delay."], [247, 4, 2, "p-decades", "decades", "The number of decades to plot when x_axis=\"log\"."], [247, 4, 2, "p-filter", "filter", "The filter definition."], [247, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [247, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Normalized Frequency\"."], [247, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum, a two-sided spectrum, or one-sided spectrum with a logarithmic frequency axis. The default is \"auto\" which selects \"one-sided\" for real-valued filters and \"two-sided\" for complex-valued filters."]], "sdr.plot.phase_response": [[248, 4, 2, "p-N", "N", "The number of samples $N$ in the phase response."], [248, 4, 2, "p-decades", "decades", "The number of decades to plot when x_axis=\"log\"."], [248, 4, 2, "p-filter", "filter", "The filter definition."], [248, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [248, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Normalized Frequency\"."], [248, 4, 2, "p-unwrap", "unwrap", "Indicates whether to unwrap the phase response."], [248, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum, a two-sided spectrum, or one-sided spectrum with a logarithmic frequency axis. The default is \"auto\" which selects \"one-sided\" for real-valued filters and \"two-sided\" for complex-valued filters."]], "sdr.plot.phase_tree": [[249, 4, 2, "p-color", "color", "Indicates how to color the rasters. If \"index\", the rasters are colored based on their index. If a valid Matplotlib color, the rasters are all colored with that color."], [249, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to sdr.plot.raster()."], [249, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Samples\"."], [249, 4, 2, "p-span", "span", "The number of symbols per raster."], [249, 4, 2, "p-sps", "sps", "The number of samples per symbol."], [249, 4, 2, "p-x", "x", "The baseband CPM signal $x[n]$."]], "sdr.plot.raster": [[250, 4, 2, "p-color", "color", "Indicates how to color the rasters. If \"index\", the rasters are colored based on their index. If a valid Matplotlib color, the rasters are all colored with that color."], [250, 4, 2, "p-colorbar", "colorbar", "Indicates whether to add a colorbar to the plot. This is only added if color=\"index\"."], [250, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.collections.LineCollection. The following keyword arguments are set by default. The defaults may be overwritten."], [250, 4, 2, "p-length", "length", "The length of each raster in samples. This must be provided if x is 1D."], [250, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Samples\"."], [250, 4, 2, "p-stride", "stride", "The stride between each raster in samples. If None, the stride is set to length."], [250, 4, 2, "p-x", "x", "The time-domain signal $x[n]$. If x is complex, the real and imaginary rasters are interleaved. Time order is preserved. If x is 1D, the rastering is determined by length and stride. If x is 2D, the rows correspond to each raster."]], "sdr.plot.roc": [[251, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to the plotting function defined by type."], [251, 4, 2, "p-p_d", "p_d", "The probability of detection $P_D$."], [251, 4, 2, "p-p_fa", "p_fa", "The probability of false alarm $P_{FA}$."], [251, 4, 2, "p-type", "type", "The type of plot to generate."]], "sdr.plot.ser": [[252, 4, 2, "p-esn0", "esn0", "The symbol energy $E_s$ to noise PSD $N_0$ ratio (dB)."], [252, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.semilogy()."], [252, 4, 2, "p-ser", "ser", "The symbol error rate $P_{se}$."]], "sdr.plot.spectrogram": [[253, 4, 2, "p-detrend", "detrend", "The type of detrending to apply. Options are to remove the mean or a linear trend from each segment."], [253, 4, 2, "p-fft", "fft", "The number of points to use in the FFT. If None, the FFT length is set to length."], [253, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.pcolormesh(). The following keyword arguments are set by default. The defaults may be overwritten."], [253, 4, 2, "p-length", "length", "The length of each segment in samples. If None, the length is set to 256."], [253, 4, 2, "p-overlap", "overlap", "The number of samples to overlap between segments. If None, the overlap is set to length // 2."], [253, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be label as \"Samples\" and the y-axis as \"Normalized Frequency\"."], [253, 4, 2, "p-window", "window", "The windowing function to use. This can be a string or a vector of length length."], [253, 4, 2, "p-x", "x", "The time-domain signal $x[n]$."], [253, 4, 2, "p-x_axis", "x_axis", "The x-axis scaling. Options are to display a one-sided spectrum or two-sided spectrum."]], "sdr.plot.step_response": [[254, 4, 2, "p-N", "N", "The number of samples $N$ to plot. If None, the length of b is used for FIR filters and 100 for IIR filters."], [254, 4, 2, "p-filter", "filter", "The filter definition."], [254, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."]], "sdr.plot.symbol_map": [[255, 4, 2, "p-annotate", "annotate", "If True, the symbols are annotated with their index. If \"bin\", the symbols are annotated with their binary representation."], [255, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot(). The following keyword arguments are set by default. The defaults may be overwritten."], [255, 4, 2, "p-limits", "limits", "The axis limits, which apply to both the x- and y-axis. If None, the axis limits are set to 50% larger than the maximum value."], [255, 4, 2, "p-modulation", "modulation", "The linear modulation or symbol map ${0, dots, M-1} mapsto mathbb{C}$."]], "sdr.plot.time_domain": [[256, 4, 2, "p-centered", "centered", "Indicates whether to center the x-axis about 0. This argument is mutually exclusive with offset."], [256, 4, 2, "p-diff", "diff", "Indicates how to differentiate the real and imaginary parts of a complex signal. If \"color\", the real and imaginary parts will have different colors based on the current Matplotlib color cycle. If \"line\", the real part will have a solid line and the imaginary part will have a dashed line, and both lines will share the same color."], [256, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."], [256, 4, 2, "p-offset", "offset", "The x-axis offset to apply to the first sample. The units of the offset are $1/f_s$. This argument is mutually exclusive with centered."], [256, 4, 2, "p-sample_rate", "sample_rate", "The sample rate $f_s$ of the signal in samples/s. If None, the x-axis will be labeled as \"Samples\"."], [256, 4, 2, "p-t", "t", "The time signal $t[n]$. The units are assumed to be $1/f_s$."], [256, 4, 2, "p-x", "x", "The time-domain signal $x[n]$."]], "sdr.plot.zeros_poles": [[258, 4, 2, "p-filter", "filter", "The filter definition."], [258, 4, 2, "p-kwargs", "kwargs", "Additional keyword arguments to pass to matplotlib.pyplot.plot()."]], "sdr.polyphase_decompose": [[259, 4, 2, "p-phases", "phases", "The number of phases $B$."], [259, 4, 2, "p-taps", "taps", "The multirate FIR filter taps $h_i$."]], "sdr.ppb": [[260, 4, 2, "p-x", "x", "The input ratio."]], "sdr.ppm": [[261, 4, 2, "p-x", "x", "The input ratio."]], "sdr.raised_cosine": [[262, 4, 2, "p-alpha", "alpha", "The excess bandwidth $0 le alpha le 1$ of the filter."], [262, 4, 2, "p-norm", "norm", "Indicates how to normalize the pulse shape."], [262, 4, 2, "p-span", "span", "The length of the filter in symbols. The length of the filter is span * sps + 1 samples. The filter order span * sps must be even."], [262, 4, 2, "p-sps", "sps", "The number of samples per symbol."]], "sdr.rectangular": [[263, 4, 2, "p-norm", "norm", "Indicates how to normalize the pulse shape."], [263, 4, 2, "p-span", "span", "The length of the filter in symbols. The length of the filter is span * sps samples, but only the center sps samples are non-zero. The only reason for span to be larger than 1 is to add delay to the filter."], [263, 4, 2, "p-sps", "sps", "The number of samples per symbol."]], "sdr.rms_voltage": [[264, 4, 2, "p-db", "db", "Indicates whether to return the result in decibels (dB)."], [264, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to measure."]], "sdr.root_raised_cosine": [[265, 4, 2, "p-alpha", "alpha", "The excess bandwidth $0 le alpha le 1$ of the filter."], [265, 4, 2, "p-norm", "norm", "Indicates how to normalize the pulse shape."], [265, 4, 2, "p-span", "span", "The length of the filter in symbols. The length of the filter is span * sps + 1 samples. The filter order span * sps must be even."], [265, 4, 2, "p-sps", "sps", "The number of samples per symbol."]], "sdr.sample_rate_offset": [[266, 4, 2, "p-ppm", "ppm", "The sample rate offset $f_{s,text{new}} / f_s$ in parts per million (ppm)."], [266, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ to which the sample rate offset is applied."]], "sdr.snr_to_ebn0": [[267, 4, 2, "p-bps", "bps", "Bits per symbol $log_2 M$, where $M$ is the modulation order."], [267, 4, 2, "p-rate", "rate", "Code rate $r = k/n$, where $k$ is the number of information bits and $n$ is the number of coded bits."], [267, 4, 2, "p-snr", "snr", "Signal-to-noise ratio $S/N$ in dB."], [267, 4, 2, "p-sps", "sps", "Samples per symbol $f_s / f_{sym}$."]], "sdr.snr_to_esn0": [[268, 4, 2, "p-snr", "snr", "Signal-to-noise ratio $S/N$ in dB."], [268, 4, 2, "p-sps", "sps", "Samples per symbol $f_s / f_{sym}$."]], "sdr.to_complex_bb": [[269, 4, 2, "p-x_r", "x_r", "The real passband signal $x_r[n]$ centered at $f_{s,r}/4$ with sample rate $f_{s,r}$. If the length is odd, one zero is appended to the end."]], "sdr.to_real_pb": [[270, 4, 2, "p-x_c", "x_c", "The complex baseband signal $x_c[n]$ centered at $0$ with sample rate $f_{s,c}$."]], "sdr.unpack": [[271, 4, 2, "p-bpe", "bpe", "The number of bits per element in the input array."], [271, 4, 2, "p-dtype", "dtype", "The data type of the output array. If None, numpy.uint8 is used."], [271, 4, 2, "p-x", "x", "The input array with bpe bits per element."]], "sdr.upsample": [[272, 4, 2, "p-rate", "rate", "The upsampling factor $r$."], [272, 4, 2, "p-x", "x", "The time-domain signal $x[n]$ with sample rate $f_s$."]], "sdr.walsh": [[273, 4, 2, "p-index", "index", "The index $i$ of the Walsh code. Indicates how many transitions there are in the code."], [273, 4, 2, "p-length", "length", "The length $N$ of the Walsh code/sequence. Must be a power of 2."], [273, 4, 2, "p-output", "output", "The output format of the Walsh code/sequence."]], "sdr.wavelength": [[274, 4, 2, "p-freq", "freq", "The frequency $f$ in Hz of the signal."]], "sdr.zadoff_chu": [[275, 4, 2, "p-length", "length", "The length $N$ of the Zadoff-Chu sequence."], [275, 4, 2, "p-root", "root", "The root $0 < u < N$ of the Zadoff-Chu sequence. The root must be relatively prime to the length, i.e., $gcd(u, N) = 1$."], [275, 4, 2, "p-shift", "shift", "The shift $q in mathbb{Z}$ of the Zadoff-Chu sequence. When $q ne 0$, the returned sequence is a cyclic shift of the root-$u$ Zadoff-Chu sequence."]]}, "objtypes": {"0": "py:module", "1": "py:class", "2": "py:property", "3": "py:method", "4": "py:parameter", "5": "py:function"}, "objnames": {"0": ["py", "module", "Python module"], "1": ["py", "class", "Python class"], "2": ["py", "property", "Python property"], "3": ["py", "method", "Python method"], "4": ["py", "parameter", "Python parameter"], "5": ["py", "function", "Python function"]}, "titleterms": {"convers": 0, "decibel": 0, "ratio": 0, "from": [0, 280, 281, 282], "e_b": 0, "n_0": 0, "e_": 0, "": [0, 284, 285], "n": [0, 283, 284, 285], "data": 1, "manipul": [1, 3], "detect": [2, 7], "detector": [2, 278], "theoret": 2, "limit": 2, "digit": [3, 285], "signal": [3, 277, 283, 286], "process": 3, "fir": [3, 284], "filter": [3, 7, 284, 285, 287], "iir": [3, 285], "multir": 3, "arbitrari": [3, 283], "resampl": [3, 283], "correl": 3, "link": 4, "budget": 4, "channel": [4, 277], "capac": 4, 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ain/https://mhostetter.github.io/sdr/latest/api/sdr.PSK/https://mhostetter.github.io/sdr/latest/api/sdr.PSK.__init__/https://mhostetter.github.io/sdr/latest/api/sdr.PSK.__repr__/https://mhostetter.github.io/sdr/latest/api/sdr.PSK.__str__/https://mhostetter.github.io/sdr/latest/api/sdr.PSK.ber/https://mhostetter.github.io/sdr/latest/api/sdr.PSK.phase_offset/https://mhostetter.github.io/sdr/latest/api/sdr.PSK.ser/https://mhostetter.github.io/sdr/latest/api/sdr.PSK.symbol_map/https://mhostetter.github.io/sdr/latest/api/sdr.PiMPSK/https://mhostetter.github.io/sdr/latest/api/sdr.PiMPSK.__init__/https://mhostetter.github.io/sdr/latest/api/sdr.Q/https://mhostetter.github.io/sdr/latest/api/sdr.Qinv/https://mhostetter.github.io/sdr/latest/api/sdr.ReplicaCorrelator/https://mhostetter.github.io/sdr/latest/api/sdr.ReplicaCorrelator.p_d/https://mhostetter.github.io/sdr/latest/api/sdr.ReplicaCorrelator.p_fa/https://mhostetter.github.io/sdr/latest/api/sdr.ReplicaCorrelator.roc/https://mhostetter.github.io/sdr/latest/api/sdr.ReplicaCorrelator.threshold/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler.__call__/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler.__init__/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler.__repr__/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler.__str__/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler.delay/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler.down/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler.method/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler.polyphase_taps/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler.rate/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler.reset/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler.taps/https://mhostetter.github.io/sdr/latest/api/sdr.Resampler.up/https://mhostetter.github.io/sdr/latest/api/sdr.albersheim/https://mhostetter.github.io/sdr/latest/api/sdr.average_power/https://mhostetter.github.io/sdr/latest/api/sdr.awgn/https://mhostetter.github.io/sdr/latest/api/sdr.awgn_capacity/https://mhostetter.github.io/sdr/latest/api/sdr.barker/https://mhostetter.github.io/sdr/latest/api/sdr.bec/https://mhostetter.github.io/sdr/latest/api/sdr.bec_capacity/https://mhostetter.github.io/sdr/latest/api/sdr.binary_code/https://mhostetter.github.io/sdr/latest/api/sdr.bsc/https://mhostetter.github.io/sdr/latest/api/sdr.bsc_capacity/https://mhostetter.github.io/sdr/latest/api/sdr.crest_factor/https://mhostetter.github.io/sdr/latest/api/sdr.db/https://mhostetter.github.io/sdr/latest/api/sdr.design_bandpass_fir/https://mhostetter.github.io/sdr/latest/api/sdr.design_bandstop_fir/https://mhostetter.github.io/sdr/latest/api/sdr.design_frac_delay_fir/https://mhostetter.github.io/sdr/latest/api/sdr.design_highpass_fir/https://mhostetter.github.io/sdr/latest/api/sdr.design_lowpass_fir/https://mhostetter.github.io/sdr/latest/api/sdr.design_multirate_fir/https://mhostetter.github.io/sdr/latest/api/sdr.diff_decode/https://mhostetter.github.io/sdr/latest/api/sdr.diff_encode/https://mhostetter.github.io/sdr/latest/api/sdr.dmc/https://mhostetter.github.io/sdr/latest/api/sdr.downsample/https://mhostetter.github.io/sdr/latest/api/sdr.ebn0_to_esn0/https://mhostetter.github.io/sdr/latest/api/sdr.ebn0_to_snr/https://mhostetter.github.io/sdr/latest/api/sdr.energy/https://mhostetter.github.io/sdr/latest/api/sdr.esn0_to_ebn0/https://mhostetter.github.io/sdr/latest/api/sdr.esn0_to_snr/https://mhostetter.github.io/sdr/latest/api/sdr.euclidean/https://mhostetter.github.io/sdr/latest/api/sdr.evm/https://mhostetter.github.io/sdr/latest/api/sdr.frequency_offset/https://mhostetter.github.io/sdr/latest/api/sdr.fspl/https://mhostetter.github.io/sdr/latest/api/sdr.gaussian/https://mhostetter.github.io/sdr/latest/api/sdr.gray_code/https://mhostetter.github.io/sdr/latest/api/sdr.hadamard/https://mhostetter.github.io/sdr/latest/api/sdr.half_sine/https://mhostetter.github.io/sdr/latest/api/sdr.hamming/https://mhostetter.github.io/sdr/latest/api/sdr.hexdump/https://mhostetter.github.io/sdr/latest/api/sdr.iq_imbalance/https://mhostetter.github.io/sdr/latest/api/sdr.linear/https://mhostetter.github.io/sdr/latest/api/sdr.mix/https://mhostetter.github.io/sdr/latest/api/sdr.pack/https://mhostetter.github.io/sdr/latest/api/sdr.papr/https://mhostetter.github.io/sdr/latest/api/sdr.parabolic_antenna/https://mhostetter.github.io/sdr/latest/api/sdr.peak_power/https://mhostetter.github.io/sdr/latest/api/sdr.peak_voltage/https://mhostetter.github.io/sdr/latest/api/sdr.percent/https://mhostetter.github.io/sdr/latest/api/sdr.plot.ber/https://mhostetter.github.io/sdr/latest/api/sdr.plot.constellation/https://mhostetter.github.io/sdr/latest/api/sdr.plot.eye/https://mhostetter.github.io/sdr/latest/api/sdr.plot.filter/https://mhostetter.github.io/sdr/latest/api/sdr.plot.group_delay/https://mhostetter.github.io/sdr/latest/api/sdr.plot.impulse_response/https://mhostette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