Ef ® cient implementation of the Volterra ® lter

An ef®cient implementation of the Volterra ®lter is presented which uses a frequency domain representation to reduce the number of computations. The multidimensional convolution of the Volterra ®lter 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 ®lter and the frequency domain representation are exploited to increase the ef®ciency 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.