FREQUENCY-DOMAIN ANALYSIS OF NON-LINEAR SYSTEMS - FORMULATION OF TRANSFER-FUNCTIONS

This paper represents a sequel to an earlier paper, where a unified study of the applications of Volterra functional series to nonlinear analysis is presented. The same philosophy is followed here, giving special emphasis on frequency-domain results which either have not been published before, or where rigor had been lacking. Some of the results presented include generalizations or rigorous formalizations of well-known special cases. Explicit and recursive formulas for obtaining nth-order transfer functions of composite nonlinear systems are presented. A recursive method for obtaining the nth-order output of a nonlinear circuit by solving a linear circuit n times is derived. Each time different input sources are used. Recursive formulas for obtaining the nth-order transfer functions of nonlinear circuits are then generated. These results are used to obtain formulas for nth-order transfer functions of cascade systems, as well as inverse systems. Methods for synthesizing nonlinear circuits and inverse systems via feedback configurations are given. Finally, the general structures of transfer functions for a large class of nonlinear systems are also derived.