Signals and Systems 2
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SIGNALS We will be considering two basic types of signals: (i) Continuous-time signals and (ii) Discrete-time signals. In case of continuous-time signals the independent variable is continuous, and thus these signals are defined for continuum of values of the independent variable. On the other hand, discrete-time signals are defined only at discrete instants of times, and consequently, for these signals, the independent variable takes on only a discrete set of values. To distinguish between continuous-time and discrete-time signals, we will use the symbol t to denote continuous-time independent variable and n to denote discrete-time independent variable. Similarly (.) is used to denote continuous while [.] is used to denote discrete valued quantities. A discrete-time signal is defined only at discrete instant of time, otherwise zero. Thus independent variable has discrete values and let t = nT, n is integer (0, ± 1, ± 2, ...) and T is the sampling time. Thus a discrete time signal is defined as f [nT], and for the sake of convenience, it is denoted by f [n]. A continuous time signal f (t) and discrete time signal f [n] are shown in Fig. 2.1(a) and (b) respectively. Illustrations of continuous-time signals f (t) and discrete-time signals f [n] are being made throughout the chapter for better concept and understanding.