Signals and Systems

1.6 DISCRETE TIME SIGNALS

The discrete time signals are obtained at sampling instants because they are obtained by time sampling of continuous time signals. Figure 1.14(a) shows the exponential signal e^–t for – ∞ to ∞. Let us sample this exponential signal at time instants separated by period T shown in Fig.1.14(c); Fig. 1.14(b) shows the sampling instants which is a train of impulses. Usually, the sampling instants are represented by t_n = nT and hence the sampled or discrete time signal is represented by

 

 

Fig. 1.14 A discrete time signal

 

x(t_n) = x(nT)     (1.31)

 

 

If sample duration is T = 1 s, we can write

 

 

 

Figure 1.15 ...