Digital Signal Processing - Spectral Analysis: Parametric and Non-Parametric Digital Methods - page 23

Chapter 2

Digital Signal Processing

2.1. Introduction

A continuous time deterministic signal x ( t ), ∈ℜ t is by definition a function of ℜ

in C :

x : ℜ→

6

C

()

t xt

where the variable t is the time. In short, we often talk about a continuous signal,
even if the considered signal is not continuous in the usual mathematical sense. For
example, we can state displacement, speed and acceleration signals in mechanics,
voltage and current signals in electricity, biomedical signals (electrocardiogram,
electroencephalogram, electromyogram, etc.), temperature signals, etc.

A discrete time deterministic signal x ( k ) , k ∈ Z is, by definition, a series of
complex numbers:

( ) kZ

()

xxk ∈ =

In short, we often refer to discrete signals. As an example of a discrete time
signal, we can state the sunset time according to the day. Generally, the considered
signals, whether they are continuous or discrete, have real values, but the
generalization given here of complex signals poses no theoretical problem.