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bundles / scipy 1.17.1 / scipy / signal / _filter_design / bilinear_zpk

function

scipy.signal._filter_design:bilinear_zpk

source: /scipy/signal/_filter_design.py :2932

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

Array API Standard Support

bilinear_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 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]')
✗
plt.grid(True)
✓

See also

bilinear
lp2bp_zpk
lp2bs_zpk
lp2hp_zpk
lp2lp_zpk

Aliases

  • scipy.signal.bilinear_zpk

Referenced by

This package