Digital Signal Processing Reference
In-Depth Information
+ 8e
-t
u
7.24.
(a)
(b)
(c)
(d)
(a)
f
1
t
2
=-9u
1
-t
2
1
-t
2
- 8e
-t
u
f
1
t
2
= 9u
1
t
2
1
t
2
- 8e
-t
u
f
1
t
2
=-9u
1
-t
2
1
t
2
f(
q
) = 0;
f(
q
) = 9;
f(
q
) = 0
(b)
(c)
7.26.
(a)
Re(a) 7 0
and
Re(b) 7 0
(b)
Either
Re
1
a
2
7 0
and
Re
1
b
2
6 0
or
Re
1
a
2
6 0
and
Re
1
b
2
7 0
(c)
Re
1
a
2
6 0
and
Re
1
b
2
6 0
3
2
e
-4t
u
1
2
e
-2t
u
7.27.
1
t
2
+
1
-t
2
7.28.
The poles at
-10
and
-5
come from right-sided time functions, and the
pole at
3
comes from a left-sided time function.
CHAPTER 8
x
1
= i,
v
i
= u,
y = v
R
8.1.
(a)
R
L
x +
1
L
u
#
x =-
y = Rx
x = y,
x
#
8.3.
(b)
= 2x + 4u
0
1
0
1
x
#
8.4.
(d-b)
=
B
R
x
+
B
R
u
-1
-3
y = [0
50]
x
$
+ 3y
#
+ y = 50u
#
(d-c)
x
#
8.6.
(a)
=-3x + 6u
y = 4x
24
s + 3
(b)
H
1
s
2
=
2s
2
+ 7s + 1
8.10.
(b)
H
1
s
2
=
s
2
+ 3s - 4
R
L
x +
1
L
u
x
#
8.12.
(a)
=-
y = Rx
R
L
(b)
H
1
s
2
=
R
L
s +
R
L
(c)
V
R
1
s
2
=
V
i
1
s
2
R
L
s +
