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Module « scipy.signal »

Fonction cheby2 - module scipy.signal

Signature de la fonction cheby2

def cheby2(N, rs, Wn, btype='low', analog=False, output='ba', fs=None) 

Description

help(scipy.signal.cheby2)

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` 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.

    .. versionadded:: 1.2.0

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
--------
Design an analog filter and plot its frequency response, showing the
critical points:

>>> from scipy import signal
>>> import matplotlib.pyplot as plt
>>> import numpy as np

>>> 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 [rad/s]')
>>> 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()

Generate a signal made up of 10 Hz and 20 Hz, sampled at 1 kHz

>>> t = np.linspace(0, 1, 1000, False)  # 1 second
>>> sig = np.sin(2*np.pi*10*t) + np.sin(2*np.pi*20*t)
>>> fig, (ax1, ax2) = plt.subplots(2, 1, sharex=True)
>>> ax1.plot(t, sig)
>>> ax1.set_title('10 Hz and 20 Hz sinusoids')
>>> ax1.axis([0, 1, -2, 2])

Design a digital high-pass filter at 17 Hz to remove the 10 Hz tone, and
apply it to the signal. (It's recommended to use second-order sections
format when filtering, to avoid numerical error with transfer function
(``ba``) format):

>>> sos = signal.cheby2(12, 20, 17, 'hp', fs=1000, output='sos')
>>> filtered = signal.sosfilt(sos, sig)
>>> ax2.plot(t, filtered)
>>> ax2.set_title('After 17 Hz high-pass filter')
>>> ax2.axis([0, 1, -2, 2])
>>> ax2.set_xlabel('Time [s]')
>>> plt.show()

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