Module « scipy.signal »

Fonction butter - module scipy.signal

Signature de la fonction butter

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

Description

butter.__doc__

    Butterworth digital and analog filter design.

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

    Parameters
    ----------
    N : int
        The order of the filter.
    Wn : array_like
        The critical frequency or frequencies. For lowpass and highpass
        filters, Wn is a scalar; for bandpass and bandstop filters,
        Wn is a length-2 sequence.

        For a Butterworth filter, this is the point at which the gain
        drops to 1/sqrt(2) that of the passband (the "-3 dB point").

        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
    --------
    buttord, buttap

    Notes
    -----
    The Butterworth filter has maximally flat frequency response in the
    passband.

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

    If the transfer function form ``[b, a]`` is requested, numerical
    problems can occur since the conversion between roots and
    the polynomial coefficients is a numerically sensitive operation,
    even for N >= 4. It is recommended to work with the SOS
    representation.

    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.butter(4, 100, 'low', analog=True)
    >>> w, h = signal.freqs(b, a)
    >>> plt.semilogx(w, 20 * np.log10(abs(h)))
    >>> plt.title('Butterworth filter frequency response')
    >>> 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.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 15 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.butter(10, 15, 'hp', fs=1000, output='sos')
    >>> filtered = signal.sosfilt(sos, sig)
    >>> ax2.plot(t, filtered)
    >>> ax2.set_title('After 15 Hz high-pass filter')
    >>> ax2.axis([0, 1, -2, 2])
    >>> ax2.set_xlabel('Time [seconds]')
    >>> plt.tight_layout()
    >>> plt.show()