Page 245 - Schaum's Outline of Theory and Problems of Signals and Systems

FOURIER ANALYSIS OF TIME SIGNALS AND SYSTEMS [CHAP. 5

Thus, the complex Fourier coefficients for cos(2t + 7r/4) are

(d) By the result from Prob. 1.14 the fundamental period To of x(t) is 7r and w,, = 21r/T, = 2.
Thus,

Again using Euler's formula, we have

Thus, the complex Fourier coefficients for cos 4t + sin 6t are

and all other c, = 0.
(e) From Prob. 1.16(e) the fundamental period To of x(t) is rr and w, = 2rr/T,, = 2. Thus,

Again using Euler's formula, we get

Thus, the complex Fourier coefficients for sin2 t are

- I
Cpl - -- c0=$ c,=-$
4
and all other c, = 0.

5.5. Consider the periodic square wave x(t) shown in Fig. 5-8.

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