Calculation of Parameters of Non-Gaussian Stationary Random Processes Levels Crossing for Signal Processing

摘要

Calculation technique of parameters of a given level crossing for a wide class of stationary differentiable centered non-Gaussian random processes with a known instantaneous value distribution law and a known correlation function is described. This technique is based on the non-inertia non-linear conversion of a given non-Gaussian random process in an equivalent centered Gaussian process with a different correlation function. The equivalence means that the distribution law of intervals between adjacent zeros of both input and output processes is not changed. It is shown that a distribution law of a centered non-Gaussian random process instantaneous values poorly affects the character of distribution of intervals between adjacent zeros, which mainly depends on its correlation function (or energy spectrum). Correspondingly, processes with equal zero level crossing moments have approximately equal autocorrelation functions, that poorly depend on instantaneous value distribution law.