cheb2ord(wp, ws, gpass, gstop, analog=False)¶
Chebyshev type II filter order selection.
Return the order of the lowest order digital or analog Chebyshev Type II filter that loses no more than gpass dB in the passband and has at least gstop dB attenuation in the stopband.
wp, ws : float
Passband and stopband edge frequencies. For digital filters, these are normalized from 0 to 1, where 1 is the Nyquist frequency, pi radians/sample. (wp and ws are thus in half-cycles / sample.) For example:
- Lowpass: wp = 0.2, ws = 0.3
- Highpass: wp = 0.3, ws = 0.2
- Bandpass: wp = [0.2, 0.5], ws = [0.1, 0.6]
- Bandstop: wp = [0.1, 0.6], ws = [0.2, 0.5]
For analog filters, wp and ws are angular frequencies (e.g. rad/s).
gpass : float
The maximum loss in the passband (dB).
gstop : float
The minimum attenuation in the stopband (dB).
analog : bool, optional
When True, return an analog filter, otherwise a digital filter is returned.
ord : int
The lowest order for a Chebyshev type II filter that meets specs.
wn : ndarray or float
The Chebyshev natural frequency (the “3dB frequency”) for use with
cheby2to give filter results.
- Filter design using order and critical points
- Find order and critical points from passband and stopband spec
Design a digital bandstop filter which rejects -60 dB from 0.2*(fs/2) to 0.5*(fs/2), while staying within 3 dB below 0.1*(fs/2) or above 0.6*(fs/2). Plot its frequency response, showing the passband and stopband constraints in gray.
>>> from scipy import signal >>> import matplotlib.pyplot as plt
>>> N, Wn = signal.cheb2ord([0.1, 0.6], [0.2, 0.5], 3, 60) >>> b, a = signal.cheby2(N, 60, Wn, 'stop') >>> w, h = signal.freqz(b, a) >>> plt.semilogx(w / np.pi, 20 * np.log10(abs(h))) >>> plt.title('Chebyshev II bandstop filter fit to constraints') >>> plt.xlabel('Normalized frequency') >>> plt.ylabel('Amplitude [dB]') >>> plt.grid(which='both', axis='both') >>> plt.fill([.01, .1, .1, .01], [-3, -3, -99, -99], '0.9', lw=0) # stop >>> plt.fill([.2, .2, .5, .5], [ 9, -60, -60, 9], '0.9', lw=0) # pass >>> plt.fill([.6, .6, 2, 2], [-99, -3, -3, -99], '0.9', lw=0) # stop >>> plt.axis([0.06, 1, -80, 3]) >>> plt.show()