sosfiltfilt

def sosfiltfilt(sos, x, axis=-1, padtype='odd', padlen=None):
    """
    A forward-backward filter.

    This function applies a linear filter twice, once forward
    and once backwards.  The combined filter has linear phase.

    Before applying the filter, the function can pad 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 end points.  On both the forward and backwards passes, the
    initial condition of the filter is found by using `lfilter_zi` and
    scaling it by the end point of the extended data.

    Parameters
    ----------
    sos : array_like
        Array of second-order filter coefficients, must have shape
        ``(n_sections, 6)``. Each row corresponds to a second-order
        section, with the first three columns providing the numerator
        coefficients and the last three providing the denominator
        coefficients.
    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)).

    Returns
    -------
    y : ndarray
        The filtered output, an array of type numpy.float64 with the same
        shape as `x`.

    See Also
    --------
    soslfilter_zi, soslfilter

    Examples
    --------
    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 rate, or 125 Hz, and apply it to x with filtfilt.  The
    result should be approximately xlow, with no phase shift.

    >>> from scipy import signal
    >>> sos = signal.butter(8, 0.125, output='sos')
    >>> y = signal.sosfiltfilt(sos, 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.

    """

    if padtype not in ['even', 'odd', 'constant', None]:
        raise ValueError(("Unknown value '%s' given to padtype.  padtype must "
                         "be 'even', 'odd', 'constant', or None.") %
                         padtype)

#    b = np.atleast_1d(b)
#    a = np.atleast_1d(a)
    x = np.asarray(x)

    ntaps = sos.shape[0]*2

    if padtype is None:
        padlen = 0

    if padlen is None:
        # Original padding; preserved for backwards compatibility.
        edge = ntaps * 3
    else:
        edge = padlen

    # x's 'axis' dimension must be bigger than edge.
    if x.shape[axis] <= edge:
        raise ValueError("The length of the input vector x must be at least "
                         "padlen, which is %d." % edge)

    if padtype is not None and edge > 0:
        # Make an extension of length `edge` at each
        # end of the input array.
        if padtype == 'even':
            ext = even_ext(x, edge, axis=axis)
        elif padtype == 'odd':
            ext = odd_ext(x, edge, axis=axis)
        else:
            ext = const_ext(x, edge, axis=axis)
    else:
        ext = x

    # Get the steady state of the filter's step response.
    zi = sosfilt_zi(sos)

    # Reshape zi and create x0 so that zi*x0 broadcasts
    # to the correct value for the 'zi' keyword argument
    # to lfilter.
    zi_shape = [1] * x.ndim
    zi_shape[axis] = zi.size
    zi = np.reshape(zi, zi_shape)
    x0 = axis_slice(ext, stop=1, axis=axis)
    zix0 = zi * x0
    zix0 = reshape(zix0, (sos.shape[0], 2 ))


    # Forward filter.
    (y, zf) = sosfilt(sos, ext, axis=axis, zi=zix0)

    # Backward filter.
    # Create y0 so zi*y0 broadcasts appropriately.

    y0 = axis_slice(y, start=-1, axis=axis)
    ziy0 = zi * y0
    ziy0 = reshape(zix0, (sos.shape[0], 2 ))

    (y, zf) = sosfilt(sos, axis_reverse(y, axis=axis), axis=axis, zi=ziy0)

    # Reverse y.
    y = axis_reverse(y, axis=axis)

    if edge > 0:
        # Slice the actual signal from the extended signal.
        y = axis_slice(y, start=edge, stop=-edge, axis=axis)

    return y