`w` is normalized to the range [0, pi) (radians/sample). h : ndarray The frequency response, as complex numbers. See Also -------- freqz, sosfilt Notes ----- .. versionadded:: 0.19.0 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() Fr–