Chebyshev type II digital and analog filter design.
Design an Nth order digital or analog Chebyshev type II filter and return the filter coefficients in (B,A) or (Z,P,K) form.
Parameters: | N : int
rs : float
Wn : array_like
btype : {‘lowpass’, ‘highpass’, ‘bandpass’, ‘bandstop’}, optional
analog : bool, optional
output : {‘ba’, ‘zpk’}, optional
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Returns: | b, a : ndarray, ndarray
z, p, k : ndarray, ndarray, float
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See also
Notes
The Chebyshev type II filter maximizes the rate of cutoff between the frequency response’s passband and stopband, at the expense of ripple in the stopband and increased ringing in the step response.
Type II filters do not roll off as fast as Type I (cheby1).
Examples
Plot the filter’s frequency response, showing the critical points:
>>> from scipy import signal
>>> import matplotlib.pyplot as plt
>>> b, a = signal.cheby2(4, 40, 100, 'low', analog=True)
>>> w, h = signal.freqs(b, a)
>>> plt.plot(w, 20 * np.log10(abs(h)))
>>> plt.xscale('log')
>>> plt.title('Chebyshev Type II frequency response (rs=40)')
>>> plt.xlabel('Frequency [radians / second]')
>>> plt.ylabel('Amplitude [dB]')
>>> plt.margins(0, 0.1)
>>> plt.grid(which='both', axis='both')
>>> plt.axvline(100, color='green') # cutoff frequency
>>> plt.axhline(-40, color='green') # rs
>>> plt.show()