Page 373 - Schaum's Outline of Theory and Problems of Signals and Systems

FOURIER ANALYSIS OF DISCRETE-TIME SIGNALS AND SYSTEMS [CHAP. 6

Supplementary Problems

6.62. Find the discrete Fourier series for each of the following periodic sequences:
(a) x[n] = cos(0,l~n)
(b) x[n] = sin(0.l.rrn)
(c) x[n] = 2cos(1.6~n) + sin(2.47rn)
~0.1~
Am. (a) x[n] = $ejnon + 1 ze ~ ~ R0 = ~ 0 ~ ,

6.63. Find the discrete Fourier series for the sequence x[n] shown in Fig. 6-40.

Fig. 6-40

6.64. Find the trigonometric form of the discrete Fourier series for the periodic sequence x[n]
shown in Fig. 6-7 in Prob. 6.3.
3 Tr Tr 1
Am. x[n] = - - cos-n - sin-n - -cos rn
2 2 2 2
6.65. Find the Fourier transform of each of the following sequences:
(a) x[nl= al"l, la1 < 1
(6) x[n] = sin(flon), IRoI < 7r
(c) x[nl= u[ -n - 11
1 -a2
Am. (a) X(fl)=
1 -2acosfl+a2