scipy.signal.bilinear_zpk#
- scipy.signal.bilinear_zpk(z, p, k, fs)[source]#
Return a digital IIR filter from an analog one using a bilinear transform.
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)
fors
, maintaining the shape of the frequency response.- Parameters:
- zarray_like
Zeros of the analog filter transfer function.
- parray_like
Poles of the analog filter transfer function.
- kfloat
System gain of the analog filter transfer function.
- fsfloat
Sample rate, as ordinary frequency (e.g., hertz). No prewarping is done in this function.
- Returns:
- zndarray
Zeros of the transformed digital filter transfer function.
- pndarray
Poles of the transformed digital filter transfer function.
- kfloat
System gain of the transformed digital filter.
Notes
New in version 1.1.0.
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('Magnitude [dB]') >>> plt.grid(True)