`scipy.signal._filter_design:iirpeak`

source: /scipy/signal/_filter_design.py :5466

Signature

   def     iirpeak (    w0    ,    Q    ,    fs    =  2.0   ,  * ,     xp    =  None   ,    device    =  None     )

Summary

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

Extended Summary

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.
versionadded 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.

Notes

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 dev-arrayapi for more information.

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
b, a = signal.iirpeak(f0, Q, fs)

✓

freq, h = signal.freqz(b, a, fs=fs)
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()

✓

Aliases

scipy.signal.iirpeak