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Fonction cheby2 - module scipy.signal

Signature de la fonction cheby2

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

Description

cheby2.__doc__

    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

    >>> 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()

    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 [seconds]')
    >>> plt.show()