Identification of nonlinear systems using random amplitude Poisson distributed input functions

Nonlinear system identification using a doubly random input function which is a Poisson train of events with random amplitudes as a system input is investigated. These doubly random input functions are useful for identifying systems that naturally require amplitude modulated point process inputs as stimuli such as the hippocampal formation in the central nervous system. This is an extension of earlier work in which a Poisson train of events with only constant amplitude was used as the input for system identification. Analogous to the Wiener theory, we have developed both continuous and discrete functionals up to second-order for this doubly random input function. Closed form solutions for the diagonal terms of the second-order kernels in both cases have been obtained and convergence properties are demonstrated. Two hypothetical discrete second-order nonlinear systems are illustrated and one of them was simulated to test the theory presented. Discrete kernels computed from the simulated data agree with the theoretical prediction.