Mean level signal crossing rate for an arbitrary stochastic process

摘要

The issue of the mean signal level crossing rate for various probability density functions with primary relevancenfor optics is discussed based on a new analytical method. This method relies on a unique transformationnthat transforms the probability distribution under investigation into a normal probability distribution, fornwhich the distribution of mean level crossings is known. In general, the analytical results for the mean levelncrossing rate are supported and confirmed by numerical simulations. In particular, we illustrate the presentnmethod by presenting analytic expressions for the mean level crossing rate for various probability distributions,nincluding ones that previously were unavailable, such as the uniform, the so-called gamma-gamma, andnthe Rice–Nakagami distribution. However, in a limited number of cases the present results differ somewhatnfrom the result reported in the literature. At present, this discrepancy remains unexplained and is laid open fornfuture discussion. © 2010 Optical Society of America