Solution 2.9.2.10
f(t) = e
;3t
[1(t); 1(t;T
1
)]+ e
;3T
1
[1(t; T
1
);1(t ;T
2
)]
+C [1(t; T
2
);1(t ;T
3
)]
Then
F(s) = Lfe
;3t
1(t)g;Lfe
;3T
1
e
;3(t;T
1
)
1(t; T
1
)g
+Lfe
;3T
1
1(t ;T
1
)g;Lfe
3
T
1
1(t;T
2
)g
+LfC1(t ;T
2
)g;LfC1(t;T
3
)g
=
1
s +3
;
e
;3T
1
e
;T
1
s
s +3
+
e
;3T
1
e
;T
1
s
s
;
e
;3T
1
e
;T
2
s
s
+
Ce
;T
2
s
s
;
Ce
;T
3
s
s
=
1;e
;3T
1
e
;T
1
s
s +3
+
e
;3T
1
(e
;T
1
s
; e
;T
2
s
)+C(e
;T
2
s
; e
;T
3
s
)
s
1