`scipy.signal._filter_design:freqs_zpk`

source: /scipy/signal/_filter_design.py :253

Signature

def freqs_zpk ( z , p , k , worN = 200 )

Summary

Compute frequency response of analog filter.

Extended Summary

Given the zeros z, poles p, and gain k of a filter, compute its frequency response

           (jw-z[0]) * (jw-z[1]) * ... * (jw-z[-1])
H(w) = k * ----------------------------------------
           (jw-p[0]) * (jw-p[1]) * ... * (jw-p[-1])

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 None, then compute at 200 frequencies around the interesting parts of the response curve (determined by pole-zero locations). If a single integer, then compute at that many frequencies. Otherwise, compute the response at the angular frequencies (e.g., rad/s) given in worN.

Returns

w : ndarray: The angular frequencies at which h was computed.
h : ndarray: The frequency response.

Notes

Array API Standard Support

freqs_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                   ⚠️ no JIT             ⛔                   
Dask                  ⚠️ computes graph     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

import numpy as np
from scipy.signal import freqs_zpk, iirfilter

✓

z, p, k = iirfilter(4, [1, 10], 1, 60, analog=True, ftype='cheby1',
                    output='zpk')

✓

w, h = freqs_zpk(z, p, k, worN=np.logspace(-1, 2, 1000))

✓

import matplotlib.pyplot as plt

✓

plt.semilogx(w, 20 * np.log10(abs(h)))
plt.xlabel('Frequency [rad/s]')
plt.ylabel('Amplitude response [dB]')

✗

plt.grid(True)
plt.show()

✓

Aliases

scipy.signal.freqs_zpk