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Module « scipy.signal »

Fonction bilinear - module scipy.signal

Signature de la fonction bilinear

def bilinear(b, a, fs=1.0) 

Description

help(scipy.signal.bilinear)

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
----------
b : array_like
    Numerator of the analog filter transfer function.
a : array_like
    Denominator of the analog filter transfer function.
fs : float
    Sample rate, as ordinary frequency (e.g., hertz). No prewarping is
    done in this function.

Returns
-------
b : ndarray
    Numerator of the transformed digital filter transfer function.
a : ndarray
    Denominator of the transformed digital filter transfer function.

See Also
--------
lp2lp, lp2hp, lp2bp, lp2bs
bilinear_zpk

Examples
--------
>>> from scipy import signal
>>> import matplotlib.pyplot as plt
>>> import numpy as np

>>> fs = 100
>>> bf = 2 * np.pi * np.array([7, 13])
>>> filts = signal.lti(*signal.butter(4, bf, btype='bandpass',
...                                   analog=True))
>>> filtz = signal.lti(*signal.bilinear(filts.num, filts.den, fs))
>>> wz, hz = signal.freqz(filtz.num, filtz.den)
>>> ws, hs = signal.freqs(filts.num, filts.den, 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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