ABSTRACT
Statistical models derived from Gaussian noise appear throughout the scientific literature and indeed are the subject of entire books [1]. This chapter reviews the properties of a number of processes based on Gaussian noise that are commonly encountered in modelling the statistics of scattered waves. Although these models have generally been developed with particular applications in mind, the context in which they have arisen will be covered in later chapters and here they will be discussed in abstract terms, with only their mathematical properties being presented. In anticipation of the applications of the models, general concern will be with the properties of narrowband complex processes that can be expressed in the form of Equation 1.40
E
(
t
) =
A
(
t
) exp[
i
φ
(
t
)] =
X
(
t
) +
iY
(
t
) (3.1)
There are surprisingly few results in the literature relating to the phase statistics of such processes, and most of this chapter will be devoted to the description of intensity fluctuations. However, there is one important generalization of the Gaussian process for which results for the phase properties have been worked out, and this will be considered first.
