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Module « scipy.signal »

Fonction freqz_zpk - module scipy.signal

Signature de la fonction freqz_zpk

def freqz_zpk(z, p, k, worN=512, whole=False, fs=6.283185307179586) 

Description

help(scipy.signal.freqz_zpk)

Compute the frequency response of a digital filter in ZPK form.

Given the Zeros, Poles and Gain of a digital filter, compute its frequency
response:

:math:`H(z)=k \prod_i (z - Z[i]) / \prod_j (z - P[j])`

where :math:`k` is the `gain`, :math:`Z` are the `zeros` and :math:`P` are
the `poles`.

Parameters
----------
z : array_like
    Zeroes of a linear filter
p : array_like
    Poles of a linear filter
k : scalar
    Gain of a linear filter
worN : {None, int, array_like}, optional
    If a single integer, then compute at that many frequencies (default is
    N=512).

    If an array_like, compute the response at the frequencies given.
    These are in the same units as `fs`.
whole : bool, optional
    Normally, frequencies are computed from 0 to the Nyquist frequency,
    fs/2 (upper-half of unit-circle). If `whole` is True, compute
    frequencies from 0 to fs. Ignored if w is array_like.
fs : float, optional
    The sampling frequency of the digital system. Defaults to 2*pi
    radians/sample (so w is from 0 to pi).

    .. versionadded:: 1.2.0

Returns
-------
w : ndarray
    The frequencies at which `h` was computed, in the same units as `fs`.
    By default, `w` is normalized to the range [0, pi) (radians/sample).
h : ndarray
    The frequency response, as complex numbers.

See Also
--------
freqs : Compute the frequency response of an analog filter in TF form
freqs_zpk : Compute the frequency response of an analog filter in ZPK form
freqz : Compute the frequency response of a digital filter in TF form

Notes
-----
.. versionadded:: 0.19.0

Examples
--------
Design a 4th-order digital Butterworth filter with cut-off of 100 Hz in a
system with sample rate of 1000 Hz, and plot the frequency response:

>>> import numpy as np
>>> from scipy import signal
>>> z, p, k = signal.butter(4, 100, output='zpk', fs=1000)
>>> w, h = signal.freqz_zpk(z, p, k, fs=1000)

>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> ax1 = fig.add_subplot(1, 1, 1)
>>> ax1.set_title('Digital filter frequency response')

>>> ax1.plot(w, 20 * np.log10(abs(h)), 'b')
>>> ax1.set_ylabel('Amplitude [dB]', color='b')
>>> ax1.set_xlabel('Frequency [Hz]')
>>> ax1.grid(True)

>>> ax2 = ax1.twinx()
>>> phase = np.unwrap(np.angle(h))
>>> ax2.plot(w, phase, 'g')
>>> ax2.set_ylabel('Phase [rad]', color='g')

>>> plt.axis('tight')
>>> plt.show()

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