`scipy.signal._filter_design:bilinear_zpk`

source: build-install/usr/lib/python3.14/site-packages/scipy/signal/_filter_design.py:2952

Signature

def bilinear_zpk(z, p, k, fs)

Summary

Return a digital IIR filter from an analog one using a bilinear transform.

Extended Summary

Transform a set of poles and zeros from the analog s-plane to the digital z-plane using Tustin's method, which substitutes 2*fs*(z-1) / (z+1) for s, maintaining the shape of the frequency response.

Parameters

z : array_like: Zeros of the analog filter transfer function.
p : array_like: Poles of the analog filter transfer function.
k : float: System gain of the analog filter transfer function.
fs : float: Sample rate, as ordinary frequency (e.g., hertz). No prewarping is done in this function.

Returns

z : ndarray: Zeros of the transformed digital filter transfer function.
p : ndarray: Poles of the transformed digital filter transfer function.
k : float: System gain of the transformed digital filter.

Notes

Examples

import numpy as np
from scipy import signal
import matplotlib.pyplot as plt

✓

fs = 100
bf = 2 * np.pi * np.array([7, 13])
filts = signal.lti(*signal.butter(4, bf, btype='bandpass', analog=True,
                                  output='zpk'))
filtz = signal.lti(*signal.bilinear_zpk(filts.zeros, filts.poles,
                                        filts.gain, fs))
wz, hz = signal.freqz_zpk(filtz.zeros, filtz.poles, filtz.gain)
ws, hs = signal.freqs_zpk(filts.zeros, filts.poles, filts.gain,
                          worN=fs*wz)

✓

plt.semilogx(wz*fs/(2*np.pi), 20*np.log10(np.abs(hz).clip(1e-15)),
             label=r'$|H_z(e^{j \omega})|$')
plt.semilogx(wz*fs/(2*np.pi), 20*np.log10(np.abs(hs).clip(1e-15)),
             label=r'$|H(j \omega)|$')
plt.legend()
plt.xlabel('Frequency [Hz]')
plt.ylabel('Amplitude [dB]')

✗

Text(0, 0.5, 'Amplitude [dB]')

plt.grid(True)

✓

Aliases

scipy.signal.bilinear_zpk

Referenced by

This package

release:1.1.0-notes