TABLE OF CONTENTS Signal transmission is a process whereby a message (or information-bearing) signal is transmitted over a communication channel. Signal filtering purposefully alters the spectral content of the signal so that a better transmission and reception can be achieved. Many communication channels, as well as filters can be modeled as a linear time-invariant system. In this chapter we review the basics of a linear time-invariant system in frequency domain.
A system is a mathematical model of a physical process that relates the input signal (source or excition signal) to the output signal (response signal).
Let x( t) and y( t) be the input and output signals, respectively, of a system. Then the system is viewed as a mapping of x( t) into y( t). Symbolically, this is expressed as
Where 
is the operator that produces output y( t) from input x( t), as illustrated in Fig. 2-1.
If the system satisfies the following two conditions, then the system is called a linear system.
for all input signals x 1( t) and x 2( t).
for all input signal x( t) and scalar a.
Condition (2.2) is the additivity property and condition (2.3) is the homogeneity property.
If the system satisfies the following condition, then the system is called...
