Chebyshev type I digital and analog filter design.
Design an Nth order digital or analog Chebyshev type I filter and return the filter coefficients in (B,A) or (Z,P,K) form.
Parameters: | N : int
rp : 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 I filter maximizes the rate of cutoff between the frequency response’s passband and stopband, at the expense of ripple in the passband and increased ringing in the step response.
Type I filters roll off faster than Type II (cheby2), but Type II filters do not have any ripple in the passband.
The equiripple passband has N maxima or minima (for example, a 5th-order filter has 3 maxima and 2 minima). Consequently, the DC gain is unity for odd-order filters, or -rp dB for even-order filters.
Examples
Plot the filter’s frequency response, showing the critical points:
>>> from scipy import signal
>>> import matplotlib.pyplot as plt
>>> b, a = signal.cheby1(4, 5, 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 I frequency response (rp=5)')
>>> 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(-5, color='green') # rp
>>> plt.show()