scipy.signal.

cheb2ap

scipy.signal.cheb2ap(N, rs, *, xp=None, device=None)

Return (z,p,k) for Nth-order Chebyshev type II analog lowpass filter.

The returned filter prototype has attenuation of at least rs decibels in the stopband.

The filter’s angular (e.g. rad/s) cutoff frequency is normalized to 1, defined as the point at which the attenuation first reaches rs.

Parameters:

Nint

The order of the filter

rsfloat

The attenuation in the stopband

xparray_namespace, optional

Optional array namespace. Should be compatible with the array API standard, or supported by array-api-compat. Default: numpy

deviceany

optional device specification for output. Should match one of the supported device specification in xp.

Returns:

zndarray[complex128]

Zeros of the transfer function.

pndarray[complex128]

Poles of the transfer function.

kfloat

Gain of the transfer function.

See also

cheby2

Filter design function using this prototype

Notes

Array API Standard Support

cheb2ap has support for Python Array API Standard compatible backends in addition to NumPy. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	✅
JAX	✅	✅
Dask	✅	n/a

See Support for the array API standard for more information.

Examples

Try it in your browser!

The following plot depicts the frequency response of a 3rd-order prototype with a stopband attenuation of 40 dB:

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> from scipy.signal import freqs_zpk, cheb2ap
...
>>> z, p, k = cheb2ap(3, rs=40)
...
>>> f = np.geomspace(1e-1, 1e1, 200)
>>> _, h = freqs_zpk(z, p, k, worN=f)
>>> h_db, h_ph = 20 * np.log10(np.abs(h)), np.unwrap(np.angle(h))
...
>>> _, (ax0, ax1) = plt.subplots(2, 1, sharex='all', constrained_layout=True,
...                              figsize=(6, 4))
>>> ax0.set(title='3rd-order Chebyshev type II prototype', ylim=(-60, 3),
...         ylabel='Magnitude in dB', yticks=[-60, -40, -20, 0])
>>> ax0.fill((1, 1, 10, 10), (-40, -60, -60, -40), 'C4', alpha=.3,
...          label="-40 dB stopband")
>>> ax0.semilogx(f, h_db, 'C0', label='Magnitude')
>>> ax1.set(ylabel="Phase in radians", xlabel="Frequency in rad/s",
...         yticks=np.pi*np.arange(-1.5, 0.5, 0.5), ylim=(-1.5*np.pi, 0),
...         yticklabels=[r'-3$\pi$/2', r'-$\pi$', r'-$\pi$/2', '0'],
...         xlim=(f[0], f[-1]))
>>> ax1.semilogx(f, h_ph, 'C1', label='Phase')
>>> for ax_ in (ax0, ax1):
...     ax_.axvline(1.0, color='C5', ls='--', alpha=.5, label='Cutoff frequency')
...     ax_.grid(True, which='both')
...     ax_.legend()
>>> plt.show()

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