General Statistical Treatment of Response of Nonlinear Rectifying Device to Stationary Random Input

摘要

When many correlative random physical proccesses are passed through nonlinearcircuit elements such as detectors or rectifiers and the output randomfluctuations are considered, the probability variables defined over positiveregion are fundamental quantities of engineering interest.First, a general expression of multi-dimensional probability density functionin the form of orthogonal series such as statistical Hermite expansion is introduced.This probability expression is more general than the well-known expansionexpression due to Gram Charlier, because it includes the latter. Then,as the special case of interest when many correlative physical quantities fluctuatingonly in positive region are treated, an explicit representation of jointprobability density function in the form of statistical Laguerre expansion seriesis also -presented. Further, it has been pointed out that the latter method usinga statistical Laguerre expansion is closely related with the statistical Hermiteexpansion method under a quadratic nonlinear transformation. We must callour attention to the fact that the statistical meaning (i. e., the random property)is reflected in each expansion coefficient.Finally, the detailed experimental considerations enough to corroborate theabove theories are given for the following two cases :(a) a quadratic rectifier with non-Gaussian random input,(b) a non-quadratic rectifier with Gaussian random input.