Estimation of the Volterra functional series of a nonlinear system using frequency-response data

An algorithm is presented for the estimation of the parameters of the Volterra kernels of non-linear systems using a composite-frequency input signal. Transformations are presented between the Volterra and Wiener descriptions of nonlinear systems, which, together with an aperiodic model of Gaussian white noise, reveal the uniqueness of harmonics in the response spectrum. A periodic approximation to Gaussian white noise is proposed and is used in conjunction with a parameterised version of the kernel functions, derived from the examination of general nonlinear structures, in a parameter-estimation algorithm. The results of a simulation study are summarised.