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 ...

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