`scipy.signal._signaltools:sosfilt`

source: /scipy/signal/_signaltools.py :4957

Signature

def sosfilt ( sos , x , axis = -1 , zi = None )

Summary

Filter data along one dimension using cascaded second-order sections.

Extended Summary

Filter a data sequence, x, using a digital IIR filter defined by sos.

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: An N-dimensional 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 with x.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 by lfiltic or lfilter_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.

Notes

The filter function is implemented as a series of second-order filters with direct-form II transposed structure. It is designed to minimize numerical precision errors for high-order filters.

Array API Standard Support

sosfilt has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ⛔                   
JAX                   ✅                     ⛔                   
Dask                  ⚠️ computes graph     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

Plot a 13th-order filter's impulse response using both `lfilter` and `sosfilt`, showing the instability that results from trying to do a 13th-order 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()

✓

Aliases

scipy.signal.sosfilt