Digital Signal Processing Using Matlab

4.1. Theoretical background

In everyday life, we are involved in different situations and we have to make decisions in order to act, react or interact with the real world. These decisions are generally subjective. Thus, for a simple task like crossing the street, the decision is always individual and depends on the culture (driving on the right side in France and driving on the left side in Great Britain), the age or on many other elements (street type, number of cars and speed, traffic light state, etc.).

Probability theory can help us to make these decisions more objective. It is suitable for the study of any partially or completely unpredictable process and forms the basis of different applications: quantum mechanics, reliability, meteorological predictions, radar, sonar, telecommunications, electronic warfare, noise filtering, games of chance, etc. Statistical methods are generally considered to be the most appropriate tools to exploit probabilistic concepts for real world applications. These methods can be found in an increasing number of modern world applications, such as information theory, industry, agriculture, science, politics, etc.

The distribution of an observed random variable is very often unknown in practical situations. Several probability density function estimates are proposed in the literature. However, most of them are not easy to implement and are timeconsuming. On the other hand, many recent algorithms do not use variable distributions directly, but other ...