scipy.signal.

sosfilt_zi#

scipy.signal.sosfilt_zi(sos)[source]#

Construct initial conditions for sosfilt for step response steady-state.

Compute an initial state zi for the sosfilt function that corresponds to the steady state of the step response.

A typical use of this function is to set the initial state so that the output of the filter starts at the same value as the first element of the signal to be filtered.

Parameters:

sosarray_like: Array of second-order filter coefficients, must have shape (n_sections, 6). See sosfilt for the SOS filter format specification.

Returns:

zindarray: Initial conditions suitable for use with sosfilt, shape (n_sections, 2).

See also

sosfilt, zpk2sos

Notes

Added in version 0.16.0.

Array API Standard Support

sosfilt_zi 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 Support for the array API standard for more information.

Examples

Filter a rectangular pulse that begins at time 0, with and without the use of the zi argument of scipy.signal.sosfilt.

>>> import numpy as np
>>> from scipy import signal
>>> import matplotlib.pyplot as plt

>>> sos = signal.butter(9, 0.125, output='sos')
>>> zi = signal.sosfilt_zi(sos)
>>> x = (np.arange(250) < 100).astype(int)
>>> f1 = signal.sosfilt(sos, x)
>>> f2, zo = signal.sosfilt(sos, x, zi=zi)

>>> plt.plot(x, 'k--', label='x')
>>> plt.plot(f1, 'b', alpha=0.5, linewidth=2, label='filtered')
>>> plt.plot(f2, 'g', alpha=0.25, linewidth=4, label='filtered with zi')
>>> plt.legend(loc='best')
>>> plt.show()

../../_images/scipy-signal-sosfilt_zi-1.png