Parallel-cascade realizations and approximations of truncated Volterra systems

This paper introduces parallel-cascade realizations of truncated Volterra systems with arbitrary, but finite order of nonlinearity. Parallel-cascade realizations implement higher-order Volterra systems using parallel and multiplicative combinations of lower-order Volterra systems. Such realizations are very modular and therefore well-suited for VLSI implementation. A systematic way of approximating higher-order Volterra systems in parallel-cascade form using a reduced number of branches and a bound on the mean-square error in the output signals caused by such approximate realizations are derived. A variation of the parallel-cascade structure in which a pth order Volterra filter is implemented as a parallel combination of linear filters whose outputs are raised to the pth power is also described.