Statistical Identification of Kernels of Discrete Nonlinear Systems

Abstract

A method for identification of discrete nonlinear systems in terms of the Volterra-Wiener series is presented. It is shown that use of a special, composite-frequency input signal as approximation to Gaussian noise provides a computational efficiency of this method, especially for high order kernels. Orthogonal functionals and consistent estimations for Wiener kernels in the frequency domains are derived for this class of noise input. A basis of the proposed computational procedure for practical identification is the fast Fourier transform (FFT) algorithm which is used both for a generating of system stimuluses and for an analysis of system reactions.