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scipy.signal.

# iirpeak

scipy.signal.iirpeak(w0, Q, fs=2.0, *, xp=None, device=None)

  Design second-order IIR peak (resonant) digital filter.

  A peak 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 be retained in a signal. 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 peak filter -3 dB bandwidth `bw` relative to its center frequency, `Q = w0/bw`.

    fs float, optional

      The sampling frequency of the digital system.

      Added in version 1.2.0.

    xp array_namespace, optional

      Optional array namespace. Should be compatible with the array API standard, or supported by array-api-compat. Default: `numpy`

    device: any

      optional device specification for output. Should match one of the supported device specification in `xp`.

  Returns:
    b, a ndarray, ndarray

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

  See also

  `iirnotch`

  Notes

  Added in version 0.19.0.

  Array API Standard Support

  `iirpeak` has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable `SCIPY_ARRAY_API=1` and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

  Library | CPU | GPU
  --- | --- | ---
  NumPy | ✅ | n/a
  CuPy | n/a | ✅
  PyTorch | ✅ | ✅
  JAX | ✅ | ✅
  Dask | ✅ | n/a

  > See Support for the array API standard for more information.

  References

  [1]

  Sophocles J. Orfanidis, “Introduction To Signal Processing”, Prentice-Hall, 1996

  Examples

  Design and plot filter to remove the frequencies other than the 300 Hz component from a signal sampled at 1000 Hz, using a quality factor Q = 30

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

      >>> fs = 1000.0  # Sample frequency (Hz)
      >>> f0 = 300.0  # Frequency to be retained (Hz)
      >>> Q = 30.0  # Quality factor
      >>> # Design peak filter
      >>> b, a = signal.iirpeak(f0, Q, fs)

      >>> # Frequency response
      >>> freq, h = signal.freqz(b, a, fs=fs)
      >>> # 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([-50, 10])
      >>> ax[0].grid(True)
      >>> ax[1].plot(freq, np.unwrap(np.angle(h))*180/np.pi, 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()