scipy.signal.cheb1ord(wp, ws, gpass, gstop, analog=False, fs=None)[source]

Chebyshev type I filter order selection.

Return the order of the lowest order digital or analog Chebyshev Type I 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 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. (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.

fs : float, optional

The sampling frequency of the digital system.

New in version 1.2.0.

ord : int

The lowest order for a Chebyshev type I filter that meets specs.

wn : ndarray or float

The Chebyshev natural frequency (the “3dB frequency”) for use with cheby1 to give filter results. If fs is specified, this is in the same units, and fs must also be passed to cheby1.

See also

Filter design using order and critical points
Find order and critical points from passband and stopband spec

cheb2ord, ellipord

General filter design using order and critical frequencies
General filter design using passband and stopband spec


Design a digital lowpass filter such that the passband is within 3 dB up to 0.2*(fs/2), while rejecting at least -40 dB above 0.3*(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.cheb1ord(0.2, 0.3, 3, 40)
>>> b, a = signal.cheby1(N, 3, Wn, 'low')
>>> w, h = signal.freqz(b, a)
>>> plt.semilogx(w / np.pi, 20 * np.log10(abs(h)))
>>> plt.title('Chebyshev I lowpass filter fit to constraints')
>>> plt.xlabel('Normalized frequency')
>>> plt.ylabel('Amplitude [dB]')
>>> plt.grid(which='both', axis='both')
>>> plt.fill([.01, 0.2, 0.2, .01], [-3, -3, -99, -99], '0.9', lw=0) # stop
>>> plt.fill([0.3, 0.3,   2,   2], [ 9, -40, -40,  9], '0.9', lw=0) # pass
>>> plt.axis([0.08, 1, -60, 3])

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