sosfreqz(sos, worN=512, whole=False, fs=6.283185307179586)
Given :None:None:`sos`, an array with shape (n, 6) of second order sections of a digital filter, compute the frequency response of the system function:
B0(z) B1(z) B{n-1}(z)
H(z) = ----- * ----- * ... * ---------
A0(z) A1(z) A{n-1}(z)
for z = exp(omega*1j), where B{k}(z) and A{k}(z) are numerator and denominator of the transfer function of the k-th second order section.
Array of second-order filter coefficients, must have shape (n_sections, 6)
. Each row corresponds to a second-order section, with the first three columns providing the numerator coefficients and the last three providing the denominator coefficients.
If a single integer, then compute at that many frequencies (default is N=512). Using a number that is fast for FFT computations can result in faster computations (see Notes of freqz
).
If an array_like, compute the response at the frequencies given (must be 1-D). 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.
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 SOS format.
Design a 15th-order bandpass filter in SOS format.
>>> from scipy import signal
... sos = signal.ellip(15, 0.5, 60, (0.2, 0.4), btype='bandpass',
... output='sos')
Compute the frequency response at 1500 points from DC to Nyquist.
>>> w, h = signal.sosfreqz(sos, worN=1500)
Plot the response.
>>> import matplotlib.pyplot as plt
... plt.subplot(2, 1, 1)
... db = 20*np.log10(np.maximum(np.abs(h), 1e-5))
... plt.plot(w/np.pi, db)
... plt.ylim(-75, 5)
... plt.grid(True)
... plt.yticks([0, -20, -40, -60])
... plt.ylabel('Gain [dB]')
... plt.title('Frequency Response')
... plt.subplot(2, 1, 2)
... plt.plot(w/np.pi, np.angle(h))
... plt.grid(True)
... plt.yticks([-np.pi, -0.5*np.pi, 0, 0.5*np.pi, np.pi],
... [r'$-\pi$', r'$-\pi/2$', '0', r'$\pi/2$', r'$\pi$'])
... plt.ylabel('Phase [rad]')
... plt.xlabel('Normalized frequency (1.0 = Nyquist)')
... plt.show()
If the same filter is implemented as a single transfer function, numerical error corrupts the frequency response:
>>> b, a = signal.ellip(15, 0.5, 60, (0.2, 0.4), btype='bandpass',
... output='ba')
... w, h = signal.freqz(b, a, worN=1500)
... plt.subplot(2, 1, 1)
... db = 20*np.log10(np.maximum(np.abs(h), 1e-5))
... plt.plot(w/np.pi, db)
... plt.ylim(-75, 5)
... plt.grid(True)
... plt.yticks([0, -20, -40, -60])
... plt.ylabel('Gain [dB]')
... plt.title('Frequency Response')
... plt.subplot(2, 1, 2)
... plt.plot(w/np.pi, np.angle(h))
... plt.grid(True)
... plt.yticks([-np.pi, -0.5*np.pi, 0, 0.5*np.pi, np.pi],
... [r'$-\pi$', r'$-\pi/2$', '0', r'$\pi/2$', r'$\pi$'])
... plt.ylabel('Phase [rad]')
... plt.xlabel('Normalized frequency (1.0 = Nyquist)')
... plt.show()
The following pages refer to to this document either explicitly or contain code examples using this.
scipy.signal._signaltools.sosfiltfilt
scipy.signal._filter_design.iirfilter
scipy.signal._filter_design.sosfreqz
scipy.signal._signaltools.sosfilt
scipy.signal._filter_design.freqz
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