Digital Filters Design for Signal and Image Processing

Chapter written by Yannick BERTHOUMIEU, Eric GRIVEL and Mohamed NAJIM.
Throughout a range of fields as varied as multimedia, telecommunications, geophysics, astrophysics, acoustics and biomedicine, signals and systems play a major role. Their frequential and temporal characteristics are used to extract and analyze the information they contain. However, what importance do signals and systems really hold for these disciplines? In this chapter we will look at some of the answers to this question.
First we will discuss different types of continuous and discrete-time signals, which can be termed random or deterministic according to their nature. We will also introduce several mathematical tools to help characterize these signals. In addition, we will describe the acquisition chain and processing of signals.
Later we will define the concept of a system, emphasizing invariant discrete-time linear systems.
The function of a signal is to serve as a medium for information. It is a representation of the variations of a physical variable.
A signal can be measured by a sensor, then analyzed to describe a physical phenomenon. This is the situation of a tension taken to the limits of a resistance in order to verify the correct functioning of an electronic board, as well as, to cite one example, speech signals that describe air pressure fluctuations perceived by the human ear.
Generally, a signal is a function of time. There are two kinds of signals: continuous and discrete-time.