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.


sos : array_like

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


zi : ndarray

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

See also

sosfilt, zpk2sos


New in version 0.16.0.


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

>>> 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')