Using the Poly-Gaussian Models to Represent non-Gaussian Signals and Noises

Described representation non-Gaussian signals and noise through the use of poly-Gaussian models. A poly-Gaussian representation of random signals and non-Gaussian noise in discrete, continuous and discrete-continuous forms is given. It is shown that in order to use poly-Gaussian models, it is also necessary to obtain poly-Gaussian representations of arbitrary densities of the probability distribution. A description of the Gaussian spectra of non-Gaussian processes is given. The properties of poly-Gaussian random processes are described, in particular, the relationship between the parameters of the mixture and the components for the one-dimensional and finite-dimensional cases. Continuous-time poly-Gaussian processes are considered. It is shown that direct methods for finding multidimensional functions of poly-Gaussian processes are based on the use of multidimensional probability distribution densities of random processes. The results of modeling the found distribution densities are presented. It is shown that knowledge of one-dimensional distributions allows one to determine the mathematical expectation, two-dimensional - the mixed moment of the second order.