Description of non-Gaussian Random Processes, Signals and Noise Using the Statistical Linearization Method

Using stochastic differential equations to describe non-Gaussian signals and noise makes it unnecessary to determine multidimensional probability density function (PDF) of random processes. The paper describes the use of statistical linearization method to describe non-Gaussian random processes, signals and noise. In this case, if a large number of terms of the sequence are used, an acceptable error of the description can be obtained. The method involves finding the best probability approximation of an instantaneous non-linear transformation by a linear dependence. Here, the initial and approximating functions should have similar mathematical expectation and correlation functions. It is noted that there are two ways to determine the parameters of a statistically linearized dependence; one of them allows analyzing vector random processes. Connection between the cumulant method and statistical linearization is analyzed. It is shown that the method of statistical linearization is a particular case of the method of semiinvariants (cumulants). The dependences of PDFs of the steady-state non-Gaussian random process are obtained based on the criteria for determining parameters of statistical linearization. These PDFs emphasize advantages of approximation methods considered in the article.