Response of linear systems to stationary bandlimited non-Gaussian processes

A method is developed for calculating statistics of the state of a linear system subjected to an arbitrary stationary bandlimited non-Gaussian process. The method is based on the representations of the input process obtained from a Shanon’s sampling theorem and Monte Carlo simulation. It is shown that the system output at a time t can be approximated by a finite sum of deterministic functions of t with random coefficients given by equally spaced values of the input process over a window of finite width centered on t. The number of terms in the sum depends on both input and system memory. Numerical examples show that the proposed method is simple to implement, efficient, accurate, and can also be applied to input process that are not bandlimited.