A forward-backward filter.
This function applies a linear filter twice, once forward and once backwards. The combined filter has linear phase.
Before applying the filter, the function can pad the data along the given axis in one of three ways: odd, even or constant. The odd and even extensions have the corresponding symmetry about the end point of the data. The constant extension extends the data with the values at end points. On both the forward and backwards passes, the initial condition of the filter is found by using lfilter_zi and scaling it by the end point of the extended data.
b : (N,) array_like
a : (N,) array_like
x : array_like
axis : int, optional
padtype : str or None, optional
padlen : int or None, optional
y : ndarray
First we create a one second signal that is the sum of two pure sine waves, with frequencies 5 Hz and 250 Hz, sampled at 2000 Hz.
>>> t = np.linspace(0, 1.0, 2001) >>> xlow = np.sin(2 * np.pi * 5 * t) >>> xhigh = np.sin(2 * np.pi * 250 * t) >>> x = xlow + xhigh
Now create a lowpass Butterworth filter with a cutoff of 0.125 times the Nyquist rate, or 125 Hz, and apply it to x with filtfilt. The result should be approximately xlow, with no phase shift.
>>> from scipy import signal >>> b, a = signal.butter(8, 0.125) >>> y = signal.filtfilt(b, a, x, padlen=150) >>> np.abs(y - xlow).max() 9.1086182074789912e-06
We get a fairly clean result for this artificial example because the odd extension is exact, and with the moderately long padding, the filter’s transients have dissipated by the time the actual data is reached. In general, transient effects at the edges are unavoidable.