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bundles / scipy latest / scipy / signal / _signaltools / sosfiltfilt

function

scipy.signal._signaltools:sosfiltfilt

source: /scipy/signal/_signaltools.py :5078

Signature

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

Summary

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

Extended Summary

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.

Notes

Array API Standard Support

sosfiltfilt 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                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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()
✓
fig-81f675f0062797ab.png

See also

filtfilt
freqz_sos
sosfilt
sosfilt_zi

Aliases

  • scipy.signal.sosfiltfilt

Referenced by

This package