freqz_sos#
- scipy.signal.freqz_sos(sos, worN=512, whole=False, fs=6.283185307179586)[source]#
- Compute the frequency response of a digital filter in SOS format. - Given 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. - Parameters:
- sosarray_like
- 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.
- worN{None, int, array_like}, optional
- 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 fs. 
- wholebool, 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. 
- fsfloat, optional
- The sampling frequency of the digital system. Defaults to 2*pi radians/sample (so w is from 0 to pi). - Added in version 1.2.0. 
 
- Returns:
- wndarray
- 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). 
- hndarray
- The frequency response, as complex numbers. 
 
 - Notes - This function used to be called - sosfreqzin older versions (≥ 0.19.0)- Added in version 1.15.0. - Examples - Design a 15th-order bandpass filter in SOS format. - >>> from scipy import signal >>> import numpy as np >>> 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.freqz_sos(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() 