cupyx.scipy.signal.cheby1(N, rp, Wn, btype='low', analog=False, output='ba', fs=None)[source]#

Chebyshev type I digital and analog filter design.

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

  • N (int) – The order of the filter.

  • rp (float) – The maximum ripple allowed below unity gain in the passband. Specified in decibels, as a positive number.

  • Wn (array_like) –

    A scalar or length-2 sequence giving the critical frequencies. For Type I filters, this is the point in the transition band at which the gain first drops below -rp.

    For digital filters, Wn are in the same units as fs. By default, fs is 2 half-cycles/sample, so these are normalized from 0 to 1, where 1 is the Nyquist frequency. (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’ for backwards compatibility, but ‘sos’ should be used for general-purpose filtering.

  • fs (float, optional) – The sampling frequency of the digital system.


  • 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'.


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.