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

See filtfilt for more complete information about this method.

Notes

versionadded

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 :None:None:`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 :None:None:`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 :None:None:`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.

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

Examples

>>> 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()

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.signal._signaltools.sosfilt scipy.signal._signaltools.lfilter scipy.signal._signaltools.sosfiltfilt scipy.signal._signaltools.filtfilt

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