3.1 INTRODUCTION

Discrete-time signal is basically a sequence of numbers. Such signals arise naturally in inherently discrete-time situations such as population studies, amortization problems, national income models, and radar tracking. They may also arise as a result of sampling continuous-time signals in sampled data systems and digital filtering. Such signals can be denoted by x[ n], ?[ n], and so on, where the variable n takes integer values, and x[ n] denotes the nth number in the sequence labeled x. In this notation, the discrete-time variable n is enclosed in square brackets instead of parentheses, which we have reserved for enclosing continuous-time variable, such as t.

Systems whose inputs and outputs are discrete-time signals are called discrete-time systems. A digital computer is a familiar example of this type of system. A discrete-time signal is a sequence of numbers, and a discrete-time system processes a sequence of numbers x[ n] to yield another sequence ?[ n] as the output. ^{[ ]}

A discrete-time signal, when obtained by uniform sampling of a continuous-time signal x( t), can also be expressed as x( nT), where T is the sampling interval and n, the discrete...