A Modified Volterra Series Representation for a Class of Single-Valued, Continuous Nonlinear Systems

Abstract

A modification is presented to the Volterra functional series representation of the response from a cascaded linear-nonlinear-linear system in which the nonlinear element is single-valued, separable, and continuous. The particular advantage of this approach is that the dynamic effects represented in the convolution terms are independent of the bias or mean level of the input signal to the system. The effects of bias and element gain are included in a weighting coefficient βi (m) to each term in the series, with the first term representing the small signal gain of the system. The special case of pseudo-random input signals to the nonlinear system model is also examined using the modified functional series. It is concluded that the three-level sequence is particularly useful in producing a truncation in the modified cross-correlation series representation of the system.