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scipy.signal.

# iircomb

scipy.signal.iircomb(w0, Q, ftype='notch', fs=2.0, *, pass_zero=False)

  Design IIR notching or peaking digital comb filter.

  A notching comb filter consists of regularly-spaced band-stop filters with a narrow bandwidth (high quality factor). Each rejects a narrow frequency band and leaves the rest of the spectrum little changed.

  A peaking comb filter consists of regularly-spaced band-pass filters with a narrow bandwidth (high quality factor). Each rejects components outside a narrow frequency band.

  Parameters:
    w0 float

      The fundamental frequency of the comb filter (the spacing between its peaks). This must evenly divide the sampling frequency. If `fs` is specified, this is in the same units as `fs`. By default, it is a normalized scalar that must satisfy `0 < w0 < 1`, with `w0 = 1` corresponding to half of the sampling frequency.

    Q float

      Quality factor. Dimensionless parameter that characterizes notch filter -3 dB bandwidth `bw` relative to its center frequency, `Q = w0/bw`.

    ftype{‘notch’, ‘peak’}

      The type of comb filter generated by the function. If ‘notch’, then the Q factor applies to the notches. If ‘peak’, then the Q factor applies to the peaks. Default is ‘notch’.

    fs float, optional

      The sampling frequency of the signal. Default is 2.0.

    pass_zero bool, optional

      If False (default), the notches (nulls) of the filter are centered on frequencies [0, w0, 2*w0, …], and the peaks are centered on the midpoints [w0/2, 3*w0/2, 5*w0/2, …]. If True, the peaks are centered on [0, w0, 2*w0, …] (passing zero frequency) and vice versa.

      Added in version 1.9.0.

  Returns:
    b, a ndarray, ndarray

      Numerator (`b`) and denominator (`a`) polynomials of the IIR filter.

  Raises:
    ValueError

      If w0 is less than or equal to 0 or greater than or equal to `fs/2`, if `fs` is not divisible by w0, if ftype is not ‘notch’ or ‘peak’

  See also

  `iirnotch`
  `iirpeak`

  Notes

  For implementation details, see [1]. The TF implementation of the comb filter is numerically stable even at higher orders due to the use of a single repeated pole, which won’t suffer from precision loss.

  References

  [1]

  Sophocles J. Orfanidis, “Introduction To Signal Processing”, Prentice-Hall, 1996, ch. 11, “Digital Filter Design”

  Examples

  Design and plot notching comb filter at 20 Hz for a signal sampled at 200 Hz, using quality factor Q = 30

      >>> from scipy import signal
      >>> import matplotlib.pyplot as plt
      >>> import numpy as np

      >>> fs = 200.0  # Sample frequency (Hz)
      >>> f0 = 20.0  # Frequency to be removed from signal (Hz)
      >>> Q = 30.0  # Quality factor
      >>> # Design notching comb filter
      >>> b, a = signal.iircomb(f0, Q, ftype='notch', fs=fs)

      >>> # Frequency response
      >>> freq, h = signal.freqz(b, a, fs=fs)
      >>> response = abs(h)
      >>> # To avoid divide by zero when graphing
      >>> response[response == 0] = 1e-20
      >>> # Plot
      >>> fig, ax = plt.subplots(2, 1, figsize=(8, 6), sharex=True)
      >>> ax[0].plot(freq, 20*np.log10(abs(response)), color='blue')
      >>> ax[0].set_title("Frequency Response")
      >>> ax[0].set_ylabel("Amplitude [dB]", color='blue')
      >>> ax[0].set_xlim([0, 100])
      >>> ax[0].set_ylim([-30, 10])
      >>> ax[0].grid(True)
      >>> ax[1].plot(freq, (np.angle(h)*180/np.pi+180)%360 - 180, color='green')
      >>> ax[1].set_ylabel("Phase [deg]", color='green')
      >>> ax[1].set_xlabel("Frequency [Hz]")
      >>> ax[1].set_xlim([0, 100])
      >>> ax[1].set_yticks([-90, -60, -30, 0, 30, 60, 90])
      >>> ax[1].set_ylim([-90, 90])
      >>> ax[1].grid(True)
      >>> plt.show()

  Design and plot peaking comb filter at 250 Hz for a signal sampled at 1000 Hz, using quality factor Q = 30

      >>> fs = 1000.0  # Sample frequency (Hz)
      >>> f0 = 250.0  # Frequency to be retained (Hz)
      >>> Q = 30.0  # Quality factor
      >>> # Design peaking filter
      >>> b, a = signal.iircomb(f0, Q, ftype='peak', fs=fs, pass_zero=True)

      >>> # Frequency response
      >>> freq, h = signal.freqz(b, a, fs=fs)
      >>> response = abs(h)
      >>> # To avoid divide by zero when graphing
      >>> response[response == 0] = 1e-20
      >>> # Plot
      >>> fig, ax = plt.subplots(2, 1, figsize=(8, 6), sharex=True)
      >>> ax[0].plot(freq, 20*np.log10(np.maximum(abs(h), 1e-5)), color='blue')
      >>> ax[0].set_title("Frequency Response")
      >>> ax[0].set_ylabel("Amplitude [dB]", color='blue')
      >>> ax[0].set_xlim([0, 500])
      >>> ax[0].set_ylim([-80, 10])
      >>> ax[0].grid(True)
      >>> ax[1].plot(freq, (np.angle(h)*180/np.pi+180)%360 - 180, color='green')
      >>> ax[1].set_ylabel("Phase [deg]", color='green')
      >>> ax[1].set_xlabel("Frequency [Hz]")
      >>> ax[1].set_xlim([0, 500])
      >>> ax[1].set_yticks([-90, -60, -30, 0, 30, 60, 90])
      >>> ax[1].set_ylim([-90, 90])
      >>> ax[1].grid(True)
      >>> plt.show()