Page 109 - Schaum's Outline of Theory and Problems of Signals and Systems

LINEAR TIME-INVARIANT SYSTEMS [CHAP. 2

Since the system is linear and time-invariant and by the definition of the impulse response, we
see that the output y[n] is given by
y[n] =h[n -21 -h[n -41
which is sketched in Fig. 2-27.

Fig. 2-27

2.35. A discrete-time system is causal if for every choice of no the value of the output
sequence y[n] at n =no depends on only the values of the input sequence x[n] for
n I no (see Sec. 1.5D). From this definition derive the causality condition (2.44) for a
discrete-time LTI system, that is,

From Eq. (2.39) we have
ffi
Y[.] = C h[klx[n -kl
k= -=

Note that the first summation represents a weighted sum of future values of x[n]. Thus, if the
system is causal, then