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Fonction filtfilt - module scipy.signal

Signature de la fonction filtfilt

def filtfilt(b, a, x, axis=-1, padtype='odd', padlen=None, method='pad', irlen=None) 

Description

filtfilt.__doc__

    Apply a digital filter forward and backward to a signal.

    This function applies a linear digital filter twice, once forward and
    once backwards.  The combined filter has zero phase and a filter order
    twice that of the original.

    The function provides options for handling the edges of the signal.

    The function `sosfiltfilt` (and filter design using ``output='sos'``)
    should be preferred over `filtfilt` for most filtering tasks, as
    second-order sections have fewer numerical problems.

    Parameters
    ----------
    b : (N,) array_like
        The numerator coefficient vector of the filter.
    a : (N,) array_like
        The denominator coefficient vector of the filter.  If ``a[0]``
        is not 1, then both `a` and `b` are normalized by ``a[0]``.
    x : array_like
        The array of data to be filtered.
    axis : int, optional
        The axis of `x` to which the filter is applied.
        Default is -1.
    padtype : str or None, optional
        Must be 'odd', 'even', 'constant', or None.  This determines the
        type of extension to use for the padded signal to which the filter
        is applied.  If `padtype` is None, no padding is used.  The default
        is 'odd'.
    padlen : int or None, optional
        The number of elements by which to extend `x` at both ends of
        `axis` before applying the filter.  This value must be less than
        ``x.shape[axis] - 1``.  ``padlen=0`` implies no padding.
        The default value is ``3 * max(len(a), len(b))``.
    method : str, optional
        Determines the method for handling the edges of the signal, either
        "pad" or "gust".  When `method` is "pad", the signal is padded; the
        type of padding is determined by `padtype` and `padlen`, and `irlen`
        is ignored.  When `method` is "gust", Gustafsson's method is used,
        and `padtype` and `padlen` are ignored.
    irlen : int or None, optional
        When `method` is "gust", `irlen` specifies the length of the
        impulse response of the filter.  If `irlen` is None, no part
        of the impulse response is ignored.  For a long signal, specifying
        `irlen` can significantly improve the performance of the filter.

    Returns
    -------
    y : ndarray
        The filtered output with the same shape as `x`.

    See Also
    --------
    sosfiltfilt, lfilter_zi, lfilter, lfiltic, savgol_filter, sosfilt

    Notes
    -----
    When `method` is "pad", the function pads the data along the given axis
    in one of three ways: odd, even or constant.  The odd and even extensions
    have the corresponding symmetry about the end point of the data.  The
    constant extension extends the data with the values at the end points. On
    both the forward and backward passes, the initial condition of the
    filter is found by using `lfilter_zi` and scaling it by the end point of
    the extended data.

    When `method` is "gust", Gustafsson's method [1]_ is used.  Initial
    conditions are chosen for the forward and backward passes so that the
    forward-backward filter gives the same result as the backward-forward
    filter.

    The option to use Gustaffson's method was added in scipy version 0.16.0.

    References
    ----------
    .. [1] F. Gustaffson, "Determining the initial states in forward-backward
           filtering", Transactions on Signal Processing, Vol. 46, pp. 988-992,
           1996.

    Examples
    --------
    The examples will use several functions from `scipy.signal`.

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

    First we create a one second signal that is the sum of two pure sine
    waves, with frequencies 5 Hz and 250 Hz, sampled at 2000 Hz.

    >>> t = np.linspace(0, 1.0, 2001)
    >>> xlow = np.sin(2 * np.pi * 5 * t)
    >>> xhigh = np.sin(2 * np.pi * 250 * t)
    >>> x = xlow + xhigh

    Now create a lowpass Butterworth filter with a cutoff of 0.125 times
    the Nyquist frequency, or 125 Hz, and apply it to ``x`` with `filtfilt`.
    The result should be approximately ``xlow``, with no phase shift.

    >>> b, a = signal.butter(8, 0.125)
    >>> y = signal.filtfilt(b, a, x, padlen=150)
    >>> np.abs(y - xlow).max()
    9.1086182074789912e-06

    We get a fairly clean result for this artificial example because
    the odd extension is exact, and with the moderately long padding,
    the filter's transients have dissipated by the time the actual data
    is reached.  In general, transient effects at the edges are
    unavoidable.

    The following example demonstrates the option ``method="gust"``.

    First, create a filter.

    >>> b, a = signal.ellip(4, 0.01, 120, 0.125)  # Filter to be applied.

    `sig` is a random input signal to be filtered.

    >>> rng = np.random.default_rng()
    >>> n = 60
    >>> sig = rng.standard_normal(n)**3 + 3*rng.standard_normal(n).cumsum()

    Apply `filtfilt` to `sig`, once using the Gustafsson method, and
    once using padding, and plot the results for comparison.

    >>> fgust = signal.filtfilt(b, a, sig, method="gust")
    >>> fpad = signal.filtfilt(b, a, sig, padlen=50)
    >>> plt.plot(sig, 'k-', label='input')
    >>> plt.plot(fgust, 'b-', linewidth=4, label='gust')
    >>> plt.plot(fpad, 'c-', linewidth=1.5, label='pad')
    >>> plt.legend(loc='best')
    >>> plt.show()

    The `irlen` argument can be used to improve the performance
    of Gustafsson's method.

    Estimate the impulse response length of the filter.

    >>> z, p, k = signal.tf2zpk(b, a)
    >>> eps = 1e-9
    >>> r = np.max(np.abs(p))
    >>> approx_impulse_len = int(np.ceil(np.log(eps) / np.log(r)))
    >>> approx_impulse_len
    137

    Apply the filter to a longer signal, with and without the `irlen`
    argument.  The difference between `y1` and `y2` is small.  For long
    signals, using `irlen` gives a significant performance improvement.

    >>> x = rng.standard_normal(5000)
    >>> y1 = signal.filtfilt(b, a, x, method='gust')
    >>> y2 = signal.filtfilt(b, a, x, method='gust', irlen=approx_impulse_len)
    >>> print(np.max(np.abs(y1 - y2)))
    1.80056858312e-10