Page 275 - Schaum's Outline of Theory and Problems of Signals and Systems

FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS [CHAP. 5

(b) From Eq. (5.154)

Thus, by Eq. (5.66) and using the partial-fraction expansion technique, we have

1 1
+
= qw) -
2 + jw jw(2 + jw)

where we used the fact that f(w)6(w) = f(O)6(o) [Eq. (1.2511. Thus,

We observe that the Laplace transform method is easier in this case because of the
Fourier transform of dt).

5.46. Consider the LTI system in Prob. 5.45. If the input x(t) is the periodic square
waveform shown in Fig. 5-27, find the amplitude of the first and third harmonics in the
output y(t).
Note that x(t) is the same x(t) shown in Fig. 5-8 [Prob. 5.51. Thus, setting A = 10, To = 2,
and w, = 2rr/T0 = rr in Eq. (5.1061, we have

Next, from Prob. 5.45

Fig. 5-27