Appendix A Solutions to the Exercises -173
~ ~ l u t ~ ~ n 4.4
Eq 4.1: C { x ( t ) } = X ( S ) = x 7 .r(t)e-’t tlt
31‘
L ( A f ( t ) -I- B g ( t ) } = / [ A f ( l ) + L ? g ( t ) ] ~ - ’ ~ dt
-x
S o l ~ t i ~ n 4.5
2s + 3
a) F ( s ) = - ROC‘ : R e ( s } > -1
(s +- 2 ) ( s + 1)
(s + 3 ) ( s + 1)
3s + 1 b) G(s) = ROC : X P { S ) > -1
5 s i 11
- -
5s2 + 16s -?- 11 ( + 3)(s + a ) ( s t 1)
c) F(s) + G(s) =
( s + 2)(s + 3 )
-2
Solution 4.6
EL] 4.1: G{:r(t)} = X ( 5 ) =