freqz_zpk(z, p, k, worN=512, whole=False, fs=6.283185307179586)
Given the Zeros, Poles and Gain of a digital filter, compute its frequency response:
$H(z)=k \prod_i (z - Z[i]) / \prod_j (z - P[j])$
where $k$
is the :None:None:`gain`, $Z$
are the zeros
and $P$
are the :None:None:`poles`.
Zeroes of a linear filter
Poles of a linear filter
Gain of a linear filter
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 :None:None:`fs`.
Normally, frequencies are computed from 0 to the Nyquist frequency, fs/2 (upper-half of unit-circle). If :None:None:`whole` is True, compute frequencies from 0 to fs. Ignored if w is array_like.
The sampling frequency of the digital system. Defaults to 2*pi radians/sample (so w is from 0 to pi).
The frequencies at which h was computed, in the same units as :None:None:`fs`. By default, w is normalized to the range [0, pi) (radians/sample).
The frequency response, as complex numbers.
Compute the frequency response of a digital filter in ZPK form.
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
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:
>>> 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()
>>> ax2 = ax1.twinx()
... angles = np.unwrap(np.angle(h))
... ax2.plot(w, angles, 'g')
... ax2.set_ylabel('Angle [radians]', color='g')
>>> plt.axis('tight')
... plt.show()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.signal._filter_design.bilinear_zpk
scipy.signal._filter_design.freqz
scipy.signal._filter_design.freqz_zpk
scipy.signal._filter_design.freqs_zpk
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