Theory of separable processes with applications to the identification of nonlinear systems

By considering the class of separable random processes, a generalised Wiener-Hopf equation is derived for systems under Gaussian excitation that can be described by a model consisting of a linear system in cascade with a static nonlinear element, followed by another linear system. This result, together with a similar relationship for the 2nd-order crosscorrelation function, is used to formulate an identification and structure testing algorithm for this class of nonlinear system. The results of a simulation study are included to illustrate the validity of the algorithm.