scipy.signal.cheby2

scipy.signal.cheby2(N, rs, Wn, btype='low', analog=False, output='ba')

Chebyshev type II digital and analog filter design.

Design an Nth-order digital or analog Chebyshev type II filter and return the filter coefficients.

Parameters:

N : int

The order of the filter.

rs : float

The minimum attenuation required in the stop band. Specified in decibels, as a positive number.

Wn : array_like

A scalar or length-2 sequence giving the critical frequencies. For Type II filters, this is the point in the transition band at which the gain first reaches -rs. For digital filters, Wn is normalized from 0 to 1, where 1 is the Nyquist frequency, pi radians/sample. (Wn is thus in half-cycles / sample.) For analog filters, Wn is an angular frequency (e.g. rad/s).

btype : {‘lowpass’, ‘highpass’, ‘bandpass’, ‘bandstop’}, optional

The type of filter. Default is ‘lowpass’.

analog : bool, optional

When True, return an analog filter, otherwise a digital filter is returned.

output : {‘ba’, ‘zpk’, ‘sos’}, optional

Type of output: numerator/denominator (‘ba’), pole-zero (‘zpk’), or second-order sections (‘sos’). Default is ‘ba’.

Returns:

b, a : ndarray, ndarray

Numerator (b) and denominator (a) polynomials of the IIR filter. Only returned if output='ba'.

z, p, k : ndarray, ndarray, float

Zeros, poles, and system gain of the IIR filter transfer function. Only returned if output='zpk'.

sos : ndarray

Second-order sections representation of the IIR filter. Only returned if output=='sos'.

See also

cheb2ord, cheb2ap

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).

The 'sos' output parameter was added in 0.16.0.

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.semilogx(w, 20 * np.log10(abs(h)))
>>> 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()

(Source code)