Page 324 - Schaum's Outline of Theory and Problems of Signals and Systems

CHAP. 61 FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS

6.5. Consider a sequence

Sketch x[n].
Find the Fourier coefficients c, of x[n].
The sequence x[n] is sketched in Fig. 6-9(a). It is seen that x[n] is the periodic extension
of the sequence {1,0,0, O} with period No = 4.

(b)
Fig. 6-9

From Eqs. (6.7) and (6.8) and Fig. 6-9(a) we have

and

since x[l] = x[2] = x[3] = 0. The Fourier coefficients of x[n] are sketched in Fig. 6-9(b).

6.6. Determine the discrete Fourier series representation for each of the following se-
quences:
7T
(a) x[nl = cos-n
4
7T T
(b) x[n]=cos-n+sin-n
3 4