Wiley signals and systems e book TLFe BO 540

525

Appendix A. Solulioiis to the Exercises

Solution 13.8
The locntioii of the poles is the dccidiiig factor (see Sec. 13.5).

I No poles except at iiiliiiity

+

finite,

KO(‘ : 121 < K

2 . 3 . No poles r x ( y ) t at the origin + finite, ROC . O <
22 0.5
4.I&(?) =
infinite, ROC . 1 - 1 > 0.3
#? - 0.5
2(.Z 1)
5. &(?) =
+ finite. ROC : O < 1 ~ 1

+

1 ~ 1

+

~

-

~

*
-7

Solution 13.9
Because the series a.rc infinite, the iiiverse transform

is

carried out by sp1it)ting

X,,(.)

p;i,rt,ial fractions of -:

r2[k]

=

-46[kj

-

.c

+ (4

-

GX-)(-O.~)’E[~]

Solution 13.10
R)

H , ( Z ) = ( : - ~ ) ( Z ’ ~= + 1 ) = ( : - I )

( ; :)(
~ + - + j -

; f)

-+--I-