66 C H A P T E R 1: Continuous-Time Signals
One more realization could be that the processing of signals requires us to consider systems. In our
example, one could think of the human vocal system and of a microphone as a system that converts
differences in air pressure into a voltage signal. Signals and systems go together. We will consider the
interaction of signals and systems in the next chapter.
Specifically in this chapter we will discuss the following issues:n The mathematical representation of signals—Generally, how to think of a signal as a function of
either time (e.g., music and voice signals), space (e.g., images), or of time and space (e.g., videos).
In this book we will concentrate on time-dependent signals.
n Classification of signals—Using practical characteristics of signals we offer a classification of signals
indicating the way a signal is stored, processed, or both. As indicated, this second part of the book
will concentrate on the representation and analysis of continuous-time signals and systems, while
the next part will discuss the representation and analysis of discrete-time signals and systems.
n Signal manipulation—What it means to delay or advance a signal, to reflect it, or to find its odd
or even components. These are signal operations that will help us in their representation and
processing.
n Basic signal representation—We show that any signal can be represented using basic signals. This
will permit us to highlight certain characteristics of the signal and to simplify finding the cor-
responding outputs of systems. In particular, the representation in terms of sinusoids is of great
interest as it allows the development of the so-called Fourier representation, which is essential in
the development of the theory of linear systems.1.2 Classification of Time-Dependent Signals...............................................
Considering signals as functions of time-carrying information, there are many ways in which they
can be classified:(a) According to the predictability of their behavior, signals can berandomordeterministic. While
a deterministic signal can be represented by a formula or a table of values, random signals can
only be approached probabilistically. In this book we will only consider deterministic signals.
(b) According to the variation of their time variable and their amplitude, signals can be either
continuous-timeordiscrete-time,analogordiscreteamplitude, ordigital. This classification relates
to the way signals are either processed, stored, or both.
(c) According to their energy content, signals can be characterized asfinite- orinfinite-energysignals.
(d) According to whether the signals exhibit repetitive behavior or not asperiodicoraperiodicsignals.
(e) According to the symmetry with respect to the time origin, signals can beevenorodd.
(f) According to the dimension of their support, signals can be offiniteor ofinfinitesupport. Sup-
port can be understood as the time interval of the signal outside of which the signal is always
zero.