A fast method of discrete third-order Volterra filtering

The objective of this paper is to present a fast algorithm to compute the time-domain output of a third-order Volterra filter using fewer computational operations than the conventional time-domain multidimensional convolution approach. The approach rests upon the following : I) exploiting the relatively simple frequency-domain relationship between the input and output of such higher order filters 2) the technique of sectioning the input and output sequences in order to ensure the time-domain output corresponds to linear (as opposed to circular) convolution 3) the 1-D, rather than a multidimensional, FFT algorithm. In order to demonstrate the effectiveness of the algorithm, we compare the computational complexity of the proposed algorithm with that of the conventional time-domain multidimensional convolution approach.