Fast estimation of Wiener kernels of nonlinear systems in the frequency domain

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 an approximation to Gaussian noise provides the computational efficiency of this method especially for high order kernels. Orthogonal functionals and consistent estimates for Wiener kernels in the frequency domain are derived for this class of noise input. The basis of the proposed computational procedure for practical identification is the fast Fourier transform (FFT) algorithm which is used both for generation of actions and for analysis of system reactions.