## Chapter 4. Mathematical Modeling of Noise

### 4.1. Introduction

The mathematical modeling of observation noise relies heavily on random process theory. The reader is referred to [Kay 2006] for much of the required background. Some of the important concepts and formulas are summarized in Appendix 4A for general random processes and in Appendix 4B for Gaussian random processes. The latter is the principal model employed in practice for noise modeling, and is therefore highlighted in this chapter.

As mentioned in Chapter 3 the models to be described can also be used for some signals. This is the case when the mathematical form of the signal is unknown and so a statistical model is the only one available. An example is for speech in which the autoregressive ...