Signals and Systems - Electrical Engineering

CHAPTER 2 Continuous-Time Systems.......................................................................

Things should be made as simple as possible,

but not any simpler.

Albert Einstein (1879–1955)

physicist

2.1 Introduction

In this chapter we will consider the following topics:

n Systems and their classification—The concept ofsystemis useful in dealing with actual devices or
processes for purposes of analysis and synthesis. A transmission line, for instance, carrying infor-
mation from one point to another is a system, even though physically it is just wires connecting
two terminals. Voltages and currents in this system are not just functions of time but also of
space. It takes time for a voltage signal to “travel” from one point to another separated by miles—
Kirchhoff’s laws do not apply. Resistance, capacitance, and inductance of the line are distributed
over the length of the line—that is, the line is modeled as a concatenation of circuits charac-
terized by values of resistance, capacitance, and inductance per unit length. A less complicated
system could be one consisting of resistors, capacitors, and inductors where ideal models are
used to represent these elements and to perform analysis and synthesis. The word “ideal” indi-
cates that the models only approximate the real behavior of resistors, capacitors, and inductors. A
more realistic model for a resistor would need to consider possible changes in the resistance due
to temperature, and perhaps other marginal effects present in the resistor. Although this would
result in a better model, for most practical applications it would be unnecessarily complicated.
n Linear time-invariant systems—We initiate the characterization of systems, and propose the linear
time-invariant (LTI) model as a mathematical idealization of the behavior of systems—a good
starting point. It will be seen that most practical systems deviate from it, but despite that, the
behavior of many devices is approximated as linear and time invariant. A transistor, which is a
nonlinear device, is analyzed using linear models around an operating point. Although the vocal
system is hardly time invariant or linear, or even represented by a differential equation, in speech

Signals and Systems Using MATLAB®. DOI: 10.1016/B978-0-12-374716-7.00005-3
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