# scipy.signal.iircomb

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

  Design IIR notching or peaking digital comb filter.

  A notching comb filter is a band-stop filter with a narrow bandwidth (high quality factor). It rejects a narrow frequency band and leaves the rest of the spectrum little changed.

  A peaking comb filter is a band-pass filter with a narrow bandwidth (high quality factor). It rejects components outside a narrow frequency band.

  Parameters
    w0 float

      Frequency to attenuate (notching) or boost (peaking). 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 it returns a filter with notches at frequencies `0`, `w0`, `2 * w0`, etc. If ‘peak’, then it returns a filter with peaks at frequencies `0.5 * w0`, `1.5 * w0`, `2.5 * w0``, etc. Default is ‘notch’.

    fs float, optional

      The sampling frequency of the signal. Default is 2.0.

  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

  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

      >>> 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))
      >>> 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()
      >>> ax[1].plot(freq, np.unwrap(np.angle(h))*180/np.pi, color='green')
      >>> ax[1].set_ylabel("Angle (degrees)", 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()
      >>> 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)

      >>> # 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))
      >>> 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()
      >>> ax[1].plot(freq, np.unwrap(np.angle(h))*180/np.pi, color='green')
      >>> ax[1].set_ylabel("Angle (degrees)", 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()
      >>> plt.show()

scipy.signal.iirpeak scipy.signal.lti