Page 372 - Schaum's Outline of Theory and Problems of Signals and Systems

FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS

From Eq. (6.241)

Thus, choosing N = 320, we obtain

Aw = 2 = =0.625 rad

Then from Eqs. (6.244), (6.249), and (1.921, we have
N- 1
X[k] = Atx(n At) e-j(2T/N'nk
n=O

which is the estimate of X(k Ao).
Setting k = 0, k = 1, and k = 10 in Eq. (6.250), we have

From Table 5-2

and

1
-
x(l0 Ao) = X(6.25) = - 0,158e-11.412
1 + j6.25
Even though x(t) is not band-limited, we see that X[kl offers a quite good approxima-
-
-.
tion to X(w) for the frequency range we specified.