Transform-domain and time- domain characterization of nonlinear systems with Volterra series

Nonlinear systems representable by differential equations with polynomial type nonlinear elements are considered. The Volterra series method is used to equivalently represent such systems by their Volterra kernel functions for analysis purposes. A method based on applying multidimensional transforms directly to a sequence of nonlinear differential equations with successively increasing dimensionality is developed to solve for the transform-domain description of the kernels. A systematic method of determining the time-domain kernel functions is also developed. Simple recursive relationships for the convergence of the series are derived. A brief comparison with two other analytical methods of nonlinear system analysis is also presented.