Page 336 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 61 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS 323

By the time-shifting property Eq. (6.43)

Thus, we have
m
x,[k] e-jnkX2(fl)
.F{xl[n] * x2[n 1) =
k= -m

6.25. Using the convolution theorem (6.58), find the inverse Fourier transform x[n] of

From Eq. (6.37) we have
1
anu[nI cr - ae-jn la1 < 1

Now

Thus, by the convolution theorem Eq. (6.58) we get

Hence,

6.26. Verify the multiplication property (6.59), that is,

Let x[n] = xl[n]x2[n]. Then by definition (6.27)

By Eq. (6.28)