Digital Signal Processing Reference
In-Depth Information
13.10.
(a)
x
1
[n + 1] =
1
1 - a
2
x
1
[n] + au[n]
y[n] =
1
1 - a
2
x
1
[n] + au[n]
az
(b)
H
1
z
2
=
z -
1
1 - a
2
0.8
0
1
3.2
B
R
B
R
13.12.
(a)
x
[n + 1] =
x
[n] +
u[n]
6.08
0.9
y[n] = [0
1.9]
x
[n]
0
0.8
n
(b)
£[n] =
C
S
6.08[0.9
n
- 0.8
n
]
0.9
n
0.8
n
62.8(0.9)
n
B
R
(c)
x
[n] =
- 60.8(0.8)
n
n
n
, n Ú 0
y[n] = 119.3
1
0.9
2
- 115.5
1
0.8
2
n
n
,
n Ú 0
(d)
(e)
(f)
y[n] = 638.4 + 577.6
1
0.8
2
- 1216
1
0.9
2
n
n
, n Ú 0
y[n] = 638.5 + 577.7
1
0.8
2
- 1216.2
1
0.9
2
n
n
n Ú 0
y[n] = 638.5 + 462.2
1
0.8
2
- 1096.9
1
0.9
2
13.19.
(a)
not stable
(b)
(c)
a = [1.9
0.8;
-1 0];
eig
n
,
n
1
1.27
2
1
0.63
2
1
a
2
