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

function

`scipy.signal._filter_design:freqz_zpk`

source: /scipy/signal/_filter_design.py :576

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

Array API Standard Support

freqz_zpk 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 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')

✗

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

✗

plt.axis('tight')

✗

plt.show()

✓

Aliases

scipy.signal.freqz_zpk