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 obta ined directly from a one-dimensional Fourier transform. In addition to the sparse nature of the transformed input matrix, symmetries in both the Volte rra filter and the frequency domain representation are exploited to increas e the efficiency of the algorithm. The computational saving is demonstrated by comparing it with the direct implementation of the time domain represen tation and another technique which uses a frequency domain representation b ut does not utilise symmetry.