bundles / scipy latest / scipy / signal / _filter_design / freqz_zpk

function

`scipy.signal._filter_design:freqz_zpk`

source: build-install/usr/lib/python3.14/site-packages/scipy/signal/_filter_design.py:586

Signature

def freqz_zpk(z, p, k, worN = 512, whole = False, fs = 6.283185307179586)

Summary

Compute the frequency response of a digital filter in ZPK form.

Extended Summary

Given the Zeros, Poles and Gain of a digital filter, compute its frequency response:

$H (z) = k \prod_{i} (z - Z [i]) / \prod_{j} (z - P [j])$

where $k$ is the gain, $Z$ are the zeros and $P$ are the poles.

Parameters

z : array_like

Zeroes of a linear filter

p : array_like

Poles of a linear filter

k : scalar

Gain of a linear filter

worN : {None, int, array_like}, optional

If a single integer, then compute at that many frequencies (default is N=512).

If an array_like, compute the response at the frequencies given. These are in the same units as fs.

whole : bool, optional

Normally, frequencies are computed from 0 to the Nyquist frequency, fs/2 (upper-half of unit-circle). If whole is True, compute frequencies from 0 to fs. Ignored if w is array_like.

fs : float, optional

The sampling frequency of the digital system. Defaults to 2*pi radians/sample (so w is from 0 to pi).

Returns

w : ndarray: The frequencies at which h was computed, in the same units as fs. By default, w is normalized to the range [0, pi) (radians/sample).
h : ndarray: The frequency response, as complex numbers.

Notes

Examples

Design a 4th-order digital Butterworth filter with cut-off of 100 Hz in a system with sample rate of 1000 Hz, and plot the frequency response:

import numpy as np
from scipy import signal
z, p, k = signal.butter(4, 100, output='zpk', fs=1000)
w, h = signal.freqz_zpk(z, p, k, fs=1000)

✓

import matplotlib.pyplot as plt
fig = plt.figure()
ax1 = fig.add_subplot(1, 1, 1)

✓

ax1.set_title('Digital filter frequency response')

✗

Text(0.5, 1.0, 'Digital filter frequency response')

ax1.plot(w, 20 * np.log10(abs(h)), 'b')
ax1.set_ylabel('Amplitude [dB]', color='b')
ax1.set_xlabel('Frequency [Hz]')

✗

Text(0.5, 0, 'Frequency [Hz]')

ax1.grid(True)

✓

ax2 = ax1.twinx()
phase = np.unwrap(np.angle(h))

✓

ax2.plot(w, phase, 'g')
ax2.set_ylabel('Phase [rad]', color='g')

✗

Text(0, 0.5, 'Phase [rad]')

plt.axis('tight')

✗

(np.float64(-24.951171875), np.float64(523.974609375), np.float64(-6.594609448570726), np.float64(0.3140290213605108))

plt.show()

✓

Aliases

scipy.signal.freqz_zpk