Page 247 - Schaum's Outline of Theory and Problems of Signals and Systems

FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS [CHAP. 5

Substituting these values in Eq. (5.81, we get

1
1
- - sin w,l + -sin3wot + -sin5w0t + . ) (.5.107)
2 7r 3 5
5.6. Consider the periodic square wave x(t) shown in Fig. 5-9.

(a) Determine the complex exponential Fourier series of x(t 1.
(b) Determine the trigonometric Fourier series of x(r).

Fig. 5-9

(a) Let

Using Eq. (5.102b), we have

Thus.

Hence.
A rn A
c0 = - c,,,, = 0, m z 0 C ~ + I = (-1) (2m + I)a ( 5.108)
2