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# scipy.signal.sosfiltfilt

scipy.signal.sosfiltfilt(sos, x, axis=-1, padtype='odd', padlen=None)

  A forward-backward digital filter using cascaded second-order sections.

  See `filtfilt` for more complete information about this method.

  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 * (2 * len(sos) + 1 - min((sos[:, 2] == 0).sum(),
                                      (sos[:, 5] == 0).sum()))

      The extra subtraction at the end attempts to compensate for poles and zeros at the origin (e.g. for odd-order filters) to yield equivalent estimates of padlen to those of `filtfilt` for second-order section filters built with `scipy.signal` functions.

  Returns:
    y ndarray

      The filtered output with the same shape as x.

  See also

  `filtfilt`, `sosfilt`, `sosfilt_zi`, `sosfreqz`

  Notes

  New in version 0.18.0.

  Examples

      >>> import numpy as np
      >>> from scipy.signal import sosfiltfilt, butter
      >>> import matplotlib.pyplot as plt
      >>> rng = np.random.default_rng()

  Create an interesting signal to filter.

      >>> n = 201
      >>> t = np.linspace(0, 1, n)
      >>> x = 1 + (t < 0.5) - 0.25*t**2 + 0.05*rng.standard_normal(n)

  Create a lowpass Butterworth filter, and use it to filter x.

      >>> sos = butter(4, 0.125, output='sos')
      >>> y = sosfiltfilt(sos, x)

  For comparison, apply an 8th order filter using `sosfilt`. The filter is initialized using the mean of the first four values of x.

      >>> from scipy.signal import sosfilt, sosfilt_zi
      >>> sos8 = butter(8, 0.125, output='sos')
      >>> zi = x[:4].mean() * sosfilt_zi(sos8)
      >>> y2, zo = sosfilt(sos8, x, zi=zi)

  Plot the results. Note that the phase of y matches the input, while y2 has a significant phase delay.

      >>> plt.plot(t, x, alpha=0.5, label='x(t)')
      >>> plt.plot(t, y, label='y(t)')
      >>> plt.plot(t, y2, label='y2(t)')
      >>> plt.legend(framealpha=1, shadow=True)
      >>> plt.grid(alpha=0.25)
      >>> plt.xlabel('t')
      >>> plt.show()