- scipy.signal.lfilter(b, a, x, axis=-1, zi=None)¶
Filter data along one-dimension with an IIR or FIR filter.
Filter a data sequence, x, using a digital filter. This works for many fundamental data types (including Object type). The filter is a direct form II transposed implementation of the standard difference equation (see Notes).
b : array_like
The numerator coefficient vector in a 1-D sequence.
a : array_like
The denominator coefficient vector in a 1-D sequence. If a is not 1, then both a and b are normalized by a.
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 filter delays. It is a vector (or array of vectors for an N-dimensional input) of length max(len(a),len(b))-1. If zi is None or is not given then initial rest is assumed. See lfiltic for more information.
y : array
The output of the digital filter.
zf : array, optional
If zi is None, this is not returned, otherwise, zf holds the final filter delay values.
The filter function is implemented as a direct II transposed structure. This means that the filter implements:
a*y[n] = b*x[n] + b*x[n-1] + ... + b[nb]*x[n-nb] - a*y[n-1] - ... - a[na]*y[n-na]
using the following difference equations:
y[m] = b*x[m] + z[0,m-1] z[0,m] = b*x[m] + z[1,m-1] - a*y[m] ... z[n-3,m] = b[n-2]*x[m] + z[n-2,m-1] - a[n-2]*y[m] z[n-2,m] = b[n-1]*x[m] - a[n-1]*y[m]
where m is the output sample number and n=max(len(a),len(b)) is the model order.
The rational transfer function describing this filter in the z-transform domain is:
-1 -nb b + bz + ... + b[nb] z Y(z) = ---------------------------------- X(z) -1 -na a + az + ... + a[na] z