ABSTRACT
The study of detection and estimation can be enhanced by using an approach based on a series representation. There are many ways to describe a given function, one particularly useful one is the series representation. A series representation refers to the use of a set of basic functions and a set of corresponding expansion coefficients to represent a particular function. The number of basic functions may be finite or countable. The chapter introduces some concepts that are essential in solving the problem of detecting signals embedded in colored Gaussian noise. It reviews Mercer’s theorem and the Karhunen-Loeve expansion, which are needed in the derivation of the detector. The bilateral Laplace transform is reviewed and the integral equation for the leucogenic noise case is converted into a differential equation, which then can be solved.
