Frequency-domain analysis of nonlinear 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 rigour had been lacking. Some of the results presented include generalisations or rigorous formalisations of wellknown special cases. Explicit and recursive formulas for obtaining n th-order transfer functions of composite nonlinear systems are presented. A recursive method for obtaining the n th-order output of a nonlinear circuit by solving a linear circuit n times is derived. Each time different input sources arc used. Recursive formulas for obtaining the n th-order transfer functions of nonlinear circuits are then generated. These results are used to obtain formulas for n th-order transfer functions of cascade systems, as well as inverse systems. Methods for synthesising 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.