scipy.signal.

iirpeak#

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

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:

w0float: 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.
Qfloat: Quality factor. Dimensionless parameter that characterizes peak filter -3 dB bandwidth bw relative to its center frequency, Q = w0/bw.
fsfloat, optional: The sampling frequency of the digital system.

Added in version 1.2.0.
xparray_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, andarray, 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()

../../_images/scipy-signal-iirpeak-1.png