# 3BACKGROUND: SIGNAL THEORY

## 3.1 INTRODUCTION

This chapter details relevant signal theory and associated results that are important for subsequent chapters. Material on orthogonality, Dirichlet theory, and the Dirac Delta provide the basis for a discussion of Fourier theory and signal power. This is followed by a discussion of the power spectral density, and autocorrelation, functions. Finally, an introduction to the Cramer representation of a signal, and the Cramer transform, is given.

## 3.2 SIGNAL ORTHOGONALITY

Orthogonality and signal decomposition underpin a significant level of modern analysis, particularly, in the communications field. The following definitions are fundamental:

Get *A Signal Theoretic Introduction to Random Processes* now with O’Reilly online learning.

O’Reilly members experience live online training, plus books, videos, and digital content from 200+ publishers.