Graph theory in the analysis of nonlinear systems

Graph techniques together with the nonharmonic series representation of stationary Gaussian signals can be used in the analysis of a wide class of nonlinear systems. This point is illustrated by the derivation of the moments of a nenlinear functional of a Gaussian signal. A graphical method is developed for the derivation of the time average of products of functions of a stationary Gaussian signal without resort to any probability theory considerations. Consequently, the derivation of the moments of the functional reduces to a graph enumeration procedure and the computation of a finite number of integrals.