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Fonction iirfilter - module scipy.signal

Signature de la fonction iirfilter

def iirfilter(N, Wn, rp=None, rs=None, btype='band', analog=False, ftype='butter', output='ba', fs=None) 

Description

iirfilter.__doc__

    IIR digital and analog filter design given order and critical points.

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

    Parameters
    ----------
    N : int
        The order of the filter.
    Wn : array_like
        A scalar or length-2 sequence giving the critical frequencies.

        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).
    rp : float, optional
        For Chebyshev and elliptic filters, provides the maximum ripple
        in the passband. (dB)
    rs : float, optional
        For Chebyshev and elliptic filters, provides the minimum attenuation
        in the stop band. (dB)
    btype : {'bandpass', 'lowpass', 'highpass', 'bandstop'}, optional
        The type of filter.  Default is 'bandpass'.
    analog : bool, optional
        When True, return an analog filter, otherwise a digital filter is
        returned.
    ftype : str, optional
        The type of IIR filter to design:

            - Butterworth   : 'butter'
            - Chebyshev I   : 'cheby1'
            - Chebyshev II  : 'cheby2'
            - Cauer/elliptic: 'ellip'
            - Bessel/Thomson: 'bessel'

    output : {'ba', 'zpk', 'sos'}, optional
        Filter form of the output:

            - second-order sections (recommended): 'sos'
            - numerator/denominator (default)    : 'ba'
            - pole-zero                          : 'zpk'

        In general the second-order sections ('sos') form  is
        recommended because inferring the coefficients for the
        numerator/denominator form ('ba') suffers from numerical
        instabilities. For reasons of backward compatibility the default
        form is the numerator/denominator form ('ba'), where the 'b'
        and the 'a' in 'ba' refer to the commonly used names of the
        coefficients used.

        Note: Using the second-order sections form ('sos') is sometimes
        associated with additional computational costs: for
        data-intense use cases it is therefore recommended to also
        investigate the numerator/denominator form ('ba').

    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
    --------
    butter : Filter design using order and critical points
    cheby1, cheby2, ellip, bessel
    buttord : Find order and critical points from passband and stopband spec
    cheb1ord, cheb2ord, ellipord
    iirdesign : General filter design using passband and stopband spec

    Notes
    -----
    The ``'sos'`` output parameter was added in 0.16.0.

    Examples
    --------
    Generate a 17th-order Chebyshev II analog bandpass filter from 50 Hz to
    200 Hz and plot the frequency response:

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

    >>> b, a = signal.iirfilter(17, [2*np.pi*50, 2*np.pi*200], rs=60,
    ...                         btype='band', analog=True, ftype='cheby2')
    >>> w, h = signal.freqs(b, a, 1000)
    >>> fig = plt.figure()
    >>> ax = fig.add_subplot(1, 1, 1)
    >>> ax.semilogx(w / (2*np.pi), 20 * np.log10(np.maximum(abs(h), 1e-5)))
    >>> ax.set_title('Chebyshev Type II bandpass frequency response')
    >>> ax.set_xlabel('Frequency [Hz]')
    >>> ax.set_ylabel('Amplitude [dB]')
    >>> ax.axis((10, 1000, -100, 10))
    >>> ax.grid(which='both', axis='both')
    >>> plt.show()

    Create a digital filter with the same properties, in a system with
    sampling rate of 2000 Hz, and plot the frequency response. (Second-order
    sections implementation is required to ensure stability of a filter of
    this order):

    >>> sos = signal.iirfilter(17, [50, 200], rs=60, btype='band',
    ...                        analog=False, ftype='cheby2', fs=2000,
    ...                        output='sos')
    >>> w, h = signal.sosfreqz(sos, 2000, fs=2000)
    >>> fig = plt.figure()
    >>> ax = fig.add_subplot(1, 1, 1)
    >>> ax.semilogx(w, 20 * np.log10(np.maximum(abs(h), 1e-5)))
    >>> ax.set_title('Chebyshev Type II bandpass frequency response')
    >>> ax.set_xlabel('Frequency [Hz]')
    >>> ax.set_ylabel('Amplitude [dB]')
    >>> ax.axis((10, 1000, -100, 10))
    >>> ax.grid(which='both', axis='both')
    >>> plt.show()