Page 341 - Schaum's Outline of Theory and Problems of Signals and Systems

FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSI'EMS [CHAP. 6

-2-10 1 2 3 4 5 n
Fig. 6-17

Thus, the output y[nl is given by
~[nl 5 all n
=

634. Consider the discrete-time LTI system shown in Fig. 6-18.
(a) Find the frequency response H(n) of the system.
(b) Find the impulse response h[n] of the system.
(c) Sketch the magnitude response IH(n)I and the phase response NR).
(d) Find the 3-dB bandwidth of the system.
(a) From Fig. 6-18 we have
y[n] =x[n] +x[n - 11 (6.145)

Taking the Fourier transform of Eq. (6.145) and by Eq. (6.77), we have

(b) By the definition of h[nl [Eq. (2.3011 and Eq. (6.145) we obtain
h[n] = 6[n] + 6[n - 11

Osnsl
h[n] =
otherwise
(c) From Eq. (6.146)

xlnl

Fig. 6-18