On the generation of the baseband and narrowband non-Gaussian processes

Abstract

One of the widely used classifications of random processes implies their separation from the baseband and narrowband ones. Exponent and exponentially decaying cosine waves represent the most popular approximations of the observed processes' autocovariation functions (ACF). We consider the generation of such processes with any specified marginal probability density function (PDF). The approach is based on the representation of the process considered to be a stationary solution of certain stochastic differential equations (SDE) with the white Gaussian noise in the right-hand side. It removes the known Pearson restrictions on the kind of available process' PDF and, in the part related to the generation of the processes with strictly exponential ACF, is very close to that considered by Haddad (1970). Concerning the generation of the narrowband non-Gaussian processes with the exact exponential envelope of its ACF, synthesis of the corresponding SDE may be considered to be principally novel. Several examples of nonlinear dynamical systems generating baseband and narrowband stationary continuous processes with the given PDF are considered. Some aspects of the SDE numerical simulation are presented. The generation method proposed may be useful in communication and signal processing applications where a proper interference simulation appears to be really important.