scipy.signal.sosfilt¶

scipy.signal.
sosfilt
(sos, x, axis=1, zi=None)[source]¶ Filter data along one dimension using cascaded secondorder sections.
Filter a data sequence, x, using a digital IIR filter defined by sos. This is implemented by performing
lfilter
for each secondorder section. Seelfilter
for details.Parameters:  sos : array_like
Array of secondorder filter coefficients, must have shape
(n_sections, 6)
. Each row corresponds to a secondorder section, with the first three columns providing the numerator coefficients and the last three providing the denominator coefficients. x : array_like
An Ndimensional input array.
 axis : int, optional
The axis of the input data array along which to apply the linear filter. The filter is applied to each subarray along this axis. Default is 1.
 zi : array_like, optional
Initial conditions for the cascaded filter delays. It is a (at least 2D) vector of shape
(n_sections, ..., 2, ...)
, where..., 2, ...
denotes the shape of x, but withx.shape[axis]
replaced by 2. If zi is None or is not given then initial rest (i.e. all zeros) is assumed. Note that these initial conditions are not the same as the initial conditions given bylfiltic
orlfilter_zi
.
Returns:  y : ndarray
The output of the digital filter.
 zf : ndarray, optional
If zi is None, this is not returned, otherwise, zf holds the final filter delay values.
See also
Notes
The filter function is implemented as a series of secondorder filters with directform II transposed structure. It is designed to minimize numerical precision errors for highorder filters.
New in version 0.16.0.
Examples
Plot a 13thorder filter’s impulse response using both
lfilter
andsosfilt
, showing the instability that results from trying to do a 13thorder filter in a single stage (the numerical error pushes some poles outside of the unit circle):>>> import matplotlib.pyplot as plt >>> from scipy import signal >>> b, a = signal.ellip(13, 0.009, 80, 0.05, output='ba') >>> sos = signal.ellip(13, 0.009, 80, 0.05, output='sos') >>> x = signal.unit_impulse(700) >>> y_tf = signal.lfilter(b, a, x) >>> y_sos = signal.sosfilt(sos, x) >>> plt.plot(y_tf, 'r', label='TF') >>> plt.plot(y_sos, 'k', label='SOS') >>> plt.legend(loc='best') >>> plt.show()