Digital Signal Processing Reference
In-Depth Information
x
#
8.15.
(a)
=-3x + 6u
y = 4x
= e
-3t
(b)
(c)
(d)
(f)
£
1
t
2
= 8e
-3t
,
t 7 0
y
c
1
t
2
1 - e
-3t
y
p
1
t
2
= 8
1
2
,
t 7 0
y
1
t
2
= 8,
t 7 0
2s
2
+ 7s + 1
8.21.
(a)
H
1
s
2
=
s
2
+ 3s - 4
2s
8.24.
(a)
H
1
s
2
=
s
3
- s
2
- 1
210
-2 -11
100
0
2
0
v
#
(b)
=
C
S
v +
C
S
u
y = [1
0
0]
v
8.26.
(a)
not stable
(b)
(c)
e
-4t
,
e
t
A = [-4
5;
0
1];
eig
1
A
2
CHAPTER 9
9.2.
(a) (i)
(ii)
d[n + 1] + d[n] - 2d[n - 1]
- 2d[n + 12] - 2d[n + 9] - 2d[n + 6] - 2d[n + 3]
+ d[n] + d[n - 3] + d[n - 6] + d[n - 9]
(iii)
-2d[n + 4] - 2d[n + 3] - 2d[n + 2] - 2d[n + 1] + d[n]
+ d[n - 1] + d[n - 2] + d[n - 3]
(iv)
-2d[n + 1] - 2d[n] - 2d[n - 1] - 2d[n - 2] + d[n - 3]
+ d[n - 4] + d[n - 5] + d[n - 6]
(v)
d[n] + d[n - 1] + d[n - 2] + d[n - 3] - 2d[n - 4]
- 2d[n - 5] - 2d[n - 6] - 2d[n - 7]
(vi)
-2d[n + 7] - 2d[n + 6] - 2d[n + 5] - 2d[n + 4]
+ d[n + 3] + d[n + 2] + d[n + 1] + d[n]
9.5.
9.7.
y[n] = 3
1
u[n] - u[n - 3]
2
+ 6
1
u[-n] - u[-n - 3]
2
(a)
x
e
[n] =-d[n + 2] - d[n - 2]
and
x
o
[n]
= d[n + 2] + 2d[n + 1] - 2d[n - 1] - d[n - 2]
1
2
d[n + 4] + d[n + 3] +
3
2
d[n + 2] + d[n + 1]
(b)
x
e
[n] =
3
2
d[n - 2] + d[n - 3] +
1
2
d[n - 4]
+ d[n - 1] +
1
2
d[n + 4] + d[n + 3]
and
x
o
[n] =
1
2
d[n + 2] -
1
2
d[n - 2] - d[n - 3] -
1
2
d[n - 4]
+
