MMD-an efficient approximation to the 2nd order Volterra filter

Nonlinear filtering based on the Volterra series expansion is very popular. A serious problem thereby is the increased filter complexity. This paper presents an efficient approximation to the 2nd order Volterra filter. The proposed filter structure is called multi memory decomposition (MMD) and is composed of 3 linear FIR filters with one multiplier. Therefore, the number of required filter operations is comparable to that of linear filters, i.e. O(N). Two algorithms for the determination of the optimal FIR coefficients of the MMD model are presented. The first one approximates the effective MMD kernel to a quadratic reference kernel. The second algorithm determines the MMD coefficients adaptively from input and output measurements. Simulations as well as real time applications show the good performance of the MMD approximation