Wiley signals and systems e book TLFe BO 503

Auueridix A. Solufions to thtx Exercises

488

Sorrnulizirig to 1 V, Imh, lms gives the vdues R = 1:C

+

102 1
N ( s )= ICls~ 0.1s + 1

+

h) N ( s ) = 1

+

-k 0.1
0.01s 4- 0.1

52

I

s2

-0.01s

92

100; I, = 0. I .

:

+ 0.01 s + 0.1

+

-0.0 1s
- 1+ ~
(s 01)2 A U$

+

0

h(t) = a ( t ) -- O.O1e(t)e-mlf c o s d l t
with

01

= 0 . 0 0 5 : d ~=

fi33iiF

A0
and A = -0.01; B = -.L

M

xI

1.58.1P

w'l

or

h ( t )= S ( l )

+ e - " l ~ ( f ) AI c o ~ ( w l+t pi)

with Al

0.01 ancl

M

(PI

x -89"

c) KCIC{/I} : R P { R>
} - U ] . Right-sided since h ( f )is the impulse rcsponstb of
a real system a d must therefore be cmzsal.

1

d) Tlic system iesponsc ? ( t )convcrgcs if ROC{l(s) contains the. iinagmary
axis. Since ROC{ I ( s ) ) =KOC{N(s))nROe{vcs)}, ROC(Lr(s)}mist also
' 0 and WO can be trcely chosen. The

coritaiii the imaginary axis. So crg >
input signal can B;LTIC
any amplitmk, but mist d e t q 01 er Iiine.