Theory of volterra processors and some applications

This paper deals with a class of nonlinear, time-invariant systems with memory - called discrete Volterra processors - based on the truncation of discrete-time Volterra series expansions of input-output relationships. These systems can be implemented by a finite-length transversal filter, a finite number of multipliers, and a summing bus, and share the interesting property of being described by a linear combination of suitable nonlinear functions of the input samples. Two examples of application are considered in some detail: (i) The design of minimum mean-square error predictors of discrete-time random processes, and (ii) The identification of discrete nonlinear systems with memory.