CHAPTER 4

RANDOM SIGNALS

4.1 CHAPTER OBJECTIVES

On completion of this chapter, the reader should be able to

1. differentiate between random and deterministic signals;

2. explain the fundamental principles of statistics, as they apply to signal processing;

3. utilize statistical distributions in understanding and analyzing signal processing problems; and

4. explain and implement histogram equalization and median filtering.

4.2 INTRODUCTION

Random noise signals may be represented mathematically using statistical methods. It is important to understand the nature of “random” systems, and that “random” does not necessarily mean “totally unpredictable.” From a signal processing perspective, if we understand the nature of random fluctuations in a signal, we are in a better position to remove, or at least to minimize, their negative effects. To this end, some practical examples in image filtering and image enhancement are included in this chapter to demonstrate some practical applications of theory.

4.3 RANDOM AND DETERMINISTIC SIGNALS

A broad but useful categorization of signal types is into two classes:

1. Random signals are those which are not precisely predictable; that is, given the past history of a signal and the amplitude values it has taken on, it is not possible to precisely predict what particular value it will take on at certain instants in the future. The value of the signal may only be predicted subject to certain (hopefully known) probabilities.

2. Deterministic signals ...