bilinear_zpk(z, p, k, fs)
Transform a set of poles and zeros from the analog s-plane to the digital z-plane using Tustin's method, which substitutes (z-1) / (z+1)
for s
, maintaining the shape of the frequency response.
Zeros of the analog filter transfer function.
Poles of the analog filter transfer function.
System gain of the analog filter transfer function.
Sample rate, as ordinary frequency (e.g., hertz). No prewarping is done in this function.
Zeros of the transformed digital filter transfer function.
Poles of the transformed digital filter transfer function.
System gain of the transformed digital filter.
Return a digital IIR filter from an analog one using a bilinear transform.
>>> from scipy import signal
... import matplotlib.pyplot as plt
>>> fs = 100See :
... 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()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.signal._filter_design.bilinear
scipy.signal._filter_design.bilinear_zpk
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