Page 246 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 51 FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS

Fig. 5-8

(a) Let

Using Eq. (5.102a), we have

since ooTo = 27r and ePik" = ( - I)&. Thus,
ck = 0 k=2m#O

Hence,

and we obtain
A A " 1
ej(2m + I)""'
x(t)=-+- C -
2 ~~,,,~-~2rn+l
(b) From Eqs. (5.1051, (5.10), and (5.12) we have