Fundamentals of Statistical Signal Processing, Volume III

Chapter 8. Optimal Approaches Using the Big Theorems

8.1. Introduction

In this chapter we summarize the main theorems of mathematical statistics that are used to derive optimal statistical signal processing algorithms. They will be referred to in subsequent chapters as the theoretical underpinnings of the algorithms to be described. These theorems all rely on knowledge of the probability density function (PDF) of the data. As an example, for a signal in noise problem, such as encountered in the estimation of the amplitude of a signal embedded in noise, we will need to explicitly write down the PDF. To do so we will need to choose a model for the signal, as discussed in Chapter 3, as well as a model for the noise, as discussed in Chapter 4. For ...