TABLE OF CONTENTS This chapter is devoted to discrete-time systems, and introduces the one-sided 
Transform. The definition, theorems, and properties are discussed, and the 
transforms of the most common discrete-time functions are derived. The discrete transfer function is also defined, and several examples are given to illustrate its application. The Inverse 
transform, and the methods available for finding it, are also discussed.
The 
performs the transformation from the domain of discrete-time signals, to another domain which we call z domain. It is used with discrete-time signals, [*] the same way the Laplace and Fourier transforms are used with continuous-time signals. The 
transform yields a frequency domain description for discrete-time signals, and forms the basis for the design of digital systems, such as digital filters. Like the Laplace transform, there is the one-sided, and the two-sided 
transform. We will restrict our discussion to the one-sided 
transform F(z) of a discrete-time function f[n] defined as
and the Inverse 
transform is defined as
We can obtain a discrete-time waveform from an analog (continuous or with a finite number of discontinuities) signal, by multiplying it by a train of impulses. We denote the continuous signal as f(t), and the impulses as
Multiplication of f(t) by ?[n] produces the signal g(t) defined as
These signals are shown in Figure 9.1.
Of course, after multiplication by ?[n], the only values of f(t) which are not zero,...
