Fast Volterra Filtering

Fast algorithm for computing the response of a discrete Volterra model given a input sequence.

Implementation of the algorithm proposed in the paper:

Morhac, M., 1991 - A Fast Algorithm of Nonlinear Volterra Filtering

Basically, the output of each n-homogeneous subsystem is decomposed into a summation of convolutions. Each of these convolutions is performed in the frequency domain, which improves the efficiency of the computation.

The Volterra model must be provided to the algorithm as a structure containing the kernels in the triangular form, i.e., such that

h(t1,...,tn) ~= 0 only if t1<=t2<=...<=tn

A example is given below:

% Building the model
kernels = {k1 k2 k3 ... kP};

% Defining the memory extension of
% each kernel (in samples)
memories = [N1 N2 N3 ... NP];

% Given an input u, the output
% is computed with
y = fastVMcell(u, kernels, memories);

% y is a P x M vector where the p-th
% row is the output of the
% p-th homogeneous nonlinear system,
% i.e., the multidimensional convolution
% of the input with the kernel kp.

% To get the overall output of the
% Volterra filter, use
yP = sum(y,1);

Note: The code provided *does not* compute Volterra kernels for a model. It only computes the output of a Volterra filter, given its kernels and the input.