Signals and Systems - Electrical Engineering

CHAPTER 0 From the Ground Up!.............................................................................

In theory there is no difference

between theory and practice.

In practice there is.

Lawrence “Yogi” Berra, 1925

New York Yankees baseball player

This chapter provides an overview of the material in the book and highlights the mathematical back-
ground needed to understand the analysis of signals and systems. We consider a signal a function of
time (or space if it is an image, or of time and space if it is a video signal), just like the voltages or
currents encountered in circuits. A system is any device described by a mathematical model, just like
the differential equations obtained for a circuit composed of resistors, capacitors, and inductors.

By means of practical applications, we illustrate in this chapter the importance of the theory of signals
and systems and then proceed to connect some of the concepts of integro-differential Calculus with
more concrete mathematics (from the computational point of view, i.e., using computers). A brief
review of complex variables and their connection with the dynamics of systems follows. We end this
chapter with a soft introduction to MATLAB, a widely used high-level computational tool for analysis
and design.

Significantly, we have called this Chapter 0, because it is the ground floor for the rest of the material
in the book. Not everything in this chapter has to be understood in a first reading, but we hope that
as you go through the rest of the chapters in the book you will get to appreciate that the material in
this chapter is the foundation of the book, and as such you should revisit it as often as needed.

0.1 Signals and Systems and Digital Technologies

In our modern world, signals of all kinds emanate from different types of devices—radios and TVs,
cell phones, global positioning systems (GPSs), radars, and sonars. These systems allow us to com-
municate messages, to control processes, and to sense or measure signals. In the last 60 years, with
the advent of the transistor, the digital computer, and the theoretical fundamentals of digital signal

Signals and Systems Using MATLAB®. DOI: 10.1016/B978-0-12-374716-7.00002-
©c2011, Elsevier Inc. All rights reserved. 3