Central Limit Theorems for Conditionally Linear Random Processes

Abstract

A random process is called a linear process if it is an infinite sum of statistically independent component random processes. A particular example of a linear process is the output of a filter driven by a sequence of impulses whose times of occurrence are the times of a Poisson process. If the filter responses are also random and the responses to impulses applied at different times are statistically independent, the filter output is still a linear process. If, however, either the impulses do not occur according to a Poisson process or the filter responses are not independent, the process is called conditionally linear. The latter situation can be used to describe the radar echoes from randomly dispersed scatterers which, however, exhibit some phase coupling.It has been shown in many special cases that when a linear process is passed through a low-pass filter, the output is approximately Gaussian. These are the well-known central limit theorems for linear processes. This paper presents a very general and w...