Determination of optimum nonlinear systems for generalized error criteria based on the use of gate functions

A generalization of the error criteria in the analysis of optimum nonlinear systems is presented. The experimental and analytical techniques presented are based upon the expansion of the nonlinear system in the orthogonal set of gate functions that were introduced into the study of nonlinear systems by Bose in 1955. It is shown that, for various error criteria, the coefficients in the expansion can be determined independently of each other. By making use of this result, methods are developed for the determination of nonlinear systems with and without memory, for which an arbitrary weighted function of the error or the probability of an arbitrary function of the error is a minimum.