NON-LINEAR SYSTEMS-ANALYSIS WITH NON-GAUSSIAN WHITE STIMULI - GENERAL BASIS FUNCTIONALS AND KERNELS

The Wiener-Lee-Schetzen scheme of using Gaussian white noise to test a nonlinear dynamical system is extended in two ways. 1) An arbitrary non-Gaussian white noise stationary signal can be used as the test stimulus. 2) An arbitrary function of this stimulus can then be used as the analyzing function for cross correlating with the response to obtain the kernels characterizing the system. Closed form expressions are given for the generalized orthogonal basis functions. The generalized kernels are expanded in terms of Volterra kernels and Wiener kernels. The expansion coefficients are closely related to the cumulants of the stimulus probability distribution. These results are applied to the special case of a Gaussian stimulus and a three-level analysis function. For this case a detailed analysis is made of the magnitude of the deviation of the kernels obtained with the ternary truncation as compared to the Wiener kernels obtained by cross correlating with the same Gaussian as was used for the stimulus. The deviations are found to be quite small. © 1979 IEEE