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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

help(scipy.signal.butter)

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. For 'bandpass' and 'bandstop' filters,
    the resulting order of the final second-order sections ('sos')
    matrix is ``2*N``, with `N` the number of biquad sections
    of the desired system.
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, if `fs` is not specified, `Wn` units are
    normalized from 0 to 1, where 1 is the Nyquist frequency (`Wn` is
    thus in half cycles / sample and defined as 2*critical frequencies
    / `fs`). If `fs` is specified, `Wn` is in the same units as `fs`.

    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.

.. warning::
    Designing high-order and narrowband IIR filters in TF form can
    result in unstable or incorrect filtering due to floating point
    numerical precision issues. Consider inspecting output filter
    characteristics `freqz` or designing the filters with second-order
    sections via ``output='sos'``.

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.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 [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.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 [s]')
>>> plt.tight_layout()
>>> plt.show()

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