Digital Signal and Image Processing using MATLAB, Volume 1: Fundamentals, 2nd Edition

Chapter 1

Signal Fundamentals

Although this work is mainly focused on discrete-time signals, a discussion of continuous-time signals cannot be avoided, for at least two reasons:

– the first reason is that the quantities we will be using – taken from numeric sequences – are taken from continuous-time signal sampling. What is meant is that the numeric value of a signal, such as speech, or an electroencephalogram reading, etc., is measured at regular intervals;

– the second reason is that for some developments, we will have to use mathematical tools such as Fourier series or Fourier transforms of continuous-time signals.

The objective is not an extensive display of the knowledge needed in the field of deterministic signal processing. Many other books have already done that quite well. We will merely give the main definitions and properties useful to further developments. We will also take the opportunity to mention systems in a somewhat restricted meaning, this word referring to what are called filters.

1.1 The concept of signal

A deterministic continuous-time signal is defined as a function of the real time variable t:

The space made up of these functions is completed by the Dirac pulse distribution, or δ(t) function. Actually a distribution (a linear functional), this object can be handled just like a function without any particular problems in the exercises we will be dealing ...