Digital Signal Processing Reference
In-Depth Information
CHAPTER 7
5e
-2s
s
7.1.
(a)
5
s
e
-3s
- e
-2s
(c)
c
d
7.3.
(a)
f
1
t
2
= 5tu
1
t
2
- 5
1
t - 2
2
u
1
t - 2
2
- 15u
1
t - 2
2
+ 5u
1
t - 4
2
5
s
2
-
5
s
2
e
-2s
15
s
e
-2s
5
s
e
-4s
(b)
F
1
s
2
=
-
+
s
7.5.
(a)
F
1
s
2
=
s
2
- a
2
e
jbt
+ e
-jbt
2
e
-at
+ e
at
2
2`
`
(b)
cos
1
bt
b=aj
=
b=aj
=
= cosh
1
at
2
s
s
L
c
cos
1
bt
2d
`
b=aj
=
`
b=aj
=
s
2
+ b
2
s
2
- a
2
a
(c)
F
1
s
2
=
s
2
- a
2
sin
1
bt
2
ƒ
b=aj
= jsinh
1
at
2
-jb
a
`
j
L
c
sin
1
bt
2d
b=aj
=
b=aj
=
s
2
+ b
2
s
2
- a
2
c
e
-2s
s
e
-3s
s
7.7.
(a)
5
-
d
3
e
-2s
s
2
(b)
7.10.
(a)
2
(b)
The final value theorem gives 0 which is an error. There is no final value.
1
s
2
7.11.
(a)
1 - e
-2t
7.13.
(a)
(b)
f
1
t
2
= 2.5
1
2
u
1
t
2
1.5 - 2e
-t
+ 0.5e
-2t
f
1
t
2
=
1
2
u
1
t
2
1 - e
-3
1
t - 2
2
2
7.15.
(a)
(b)
f
1
t
2
=
1
u
1
t - 2
2
1 - e
-3t
1 - e
-3
1
t - 2
2
2
f
1
t
2
=
1
2
u
1
t
2
-
1
u
1
t - 2
2
1
s + 2
,
Re
7.21.
(a)
1
s
2
7-2
1
s - 2
,
Re
(c)
1
s
2
6 2
e
8
e
4s
s + 2
,
Re
(e)
1
s
2
7-2
