Showing papers on "Volterra series published in 1968"

Analysis of a class of nonlinear discrete systems using multidimensional modified z transforms

Abstract: This paper presents an analysis procedure for determining the continuous output of a pulsed continuous-time system with small nonlinearities. The analysis technique uses Volterra series representation and higher-dimensional modified z transforms. The method is compared and contrasted with the linear transform theory. Like the latter, it has certain advantages in treating cascaded and feedback systems, but the technique is more involved than in the linear method.

Volterra kernels—A generalization of the convolution integral for solving nonlinear systems

Abstract: THE APPEARANCE of nonlinear differential equations as a means of describing the behavior and dynamics of nonlinear phenomena is a common occurrence in analysis of physical systems such as occur in problems in radiative energy transfer, astronomy, physics and engineering. Unlike the analysis of linear systems, nothing comparable exists, like the convolution integral, for obtaining explicit solutions. Indeed, for a vast variety of problems no analytic technique existed to even approximate solutions, that had some modicum of generality. More work and useful results have occurred in the last decade in the direction of obtaining general solutions for a broad class of problems than at any other period in time. WOLF ¢1-4) and Ku and WOLF ¢5) developed with Dietz the Partition theory of nonlinear systems and the Taylor-Cauchy transform useful in the solution of a certain class of systems that are nonlinear. WENER c6~ gave a method for determining the response of a nonlinear system to random noise by utilizing the Volterra kernels as a means of characterizing the system. Further work along this line was done by GEORGE, (7) VAN TREES, (s) BARRETT (9) and FLAKE. (l°) KU and WOLF H x) in a recent paper gave the answers to certain questions dealing with the convergence of Volterra series and gave the recursion formula for obtaining the Volterra kernels as a function of the linear weighting or impulse response function. The purpose of this paper is to develop the heuristic aspects of the Volterra kernel characterization of nonlinear systems as a natural outgrowth of linear systems theory and to show that the response of a class of nonlinear systems is representable as a linear combination of responses of the proper separable nonlinear systems defined below.