Efficient implementation of the Volterra filter

An efficient implementation of the Volterra filter is presented which uses a frequency domain representation to reduce the number of computations. The multidimensional convolution of the Volterra filter is transformed to the frequency domain giving a transformed input matrix which is sparse and obtained directly from a one-dimensional Fourier transform. In addition to the sparse nature of the transformed input matrix, symmetries in both the Volterra filter and the frequency domain representation are exploited to increase the efficiency of the algorithm. The computational saving is demonstrated by comparing it with the direct implementation of the time domain representation and another technique which uses a frequency domain representation but does not utilise symmetry.