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

When many correlative random physical proccesses are passed through nonlinear circuit elements such as detectors or rectifiers and the output random fluctuations are considered, the probability variables defined over positive region are fundamental quantities of engineering interest. First, a general expression of multi-dimensional probability density function in the form of orthogonal series such as statistical Hermite expansion is introduced. This probability expression is more general than the well-known expansion expression due to Gram Charlier, because it includes the latter. Then, as the special case of interest when many correlative physical quantities fluctuating only in positive region are treated, an explicit representation of joint probability density function in the form of statistical Laguerre expansion series is also -presented. Further, it has been pointed out that the latter method using a statistical Laguerre expansion is closely related with the statistical Hermite expansion method under a quadratic nonlinear transformation. We must call our attention to the fact that the statistical meaning 0. e., the random property) is reflected in each expansion coefficient. Finally, the detailed experimental considerations enough to corroborate the above 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.