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Module « scipy.signal »

Fonction bilinear_zpk - module scipy.signal

Signature de la fonction bilinear_zpk

def bilinear_zpk(z, p, k, fs) 

Description

help(scipy.signal.bilinear_zpk)

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)`` 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.

See Also
--------
lp2lp_zpk, lp2hp_zpk, lp2bp_zpk, lp2bs_zpk
bilinear

Notes
-----
.. versionadded:: 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('Amplitude [dB]')
>>> plt.grid(True)

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