Implementation issues for V-vector algebra

The linearity of Volterra filters with respect to the filter coefficients permits the derivation of efficient adaptation algorithms by extending the well-known algorithms used for linear filters. To actually solve the problems inherent in such an approach, a novel algebra called V-vector algebra has been recently introduced. However, since the principal elements of the V-vector algebra, i.e. V-vectors and V-matrices, are non-rectangular arrays, the operations between them are not easily represented. In this paper we discuss the problem of the actual implementation of the operations between V-vectors and V-matrices. It is shown how a suitable mapping between V-vectors (V-matrices) and vectors (matrices) of the standard algebra makes it possible to implement very efficiently the operations of the V-vector algebra.