TABLE OF CONTENTS This chapter is a concise review of time-domain and transform-domain representations of single-rate discrete-time signals and systems. We consider first the time-domain representation of discrete-time signals and systems. The representation in transform domain comprises the discrete-time Fourier transform (DTFT), the discrete Fourier transform (DFT), and the z-transform. The basic realization structures for FIR and IIR systems are briefly described. Finally, the relations between continuous and discrete signals are given.
A signal is a function of at least one independent variable. In this book, we assume that the independent variable is time even in cases where the independent variable is a quantity other than time.
We define a continuous-time signal, x c( t), as a signal that exists at every instant of time t. A continuous-time signal with a continuous amplitude is also called an analog signal. The independent variable t is a continuous variable and x c( t) can assume any value over a continuous range of numbers.
A discrete-time signal is a sequence of numbers denoted as { x[ n]}, where n is said to be the time index, and x[ n] denotes the value of the n th element in the sequence. A discrete-time signal is called a discrete signal. The quantity x[ n] is also called the sample value, and its time index n is called the sample index. The quantity x
