Digital Signal Processing Reference
In-Depth Information
CHAPTER 10
10.3.
(a)
(b)
(c)
(d)
y[5] = 6
y[3] = 8
n = 2,
3,
4
y[n] = 2d[n + 1] + 4d[n] + 6d[n - 1] + 8d[n - 2] + 8d[n - 3]
+ 8d[n - 4] + 6d[n - 5] + 4d[n - 6] + 2d[n - 7]
b
n+ 1
- a
n+ 1
b - a
10.4.
(a)
y[n] =
u[n]
b
4
+ ab
3
+ a
2
b
2
+ a
3
b + a
4
(b)
b
n- 2
a
a
3
b -
a
3
b
n- 3
1
2
a
1
a
3
b
2
10.9.
(a)
b
u[3 - n]
a
3
b - 1
a
n+ 1
a - b
u[-1 - n] +
ab
n
a - b
u[n]
(b)
a
1
-
a
n+ 1
1 - a
1
-
a
100
1 - a
(c)
b1
u[n] - u[n - 100]
2
+
u[n - 100]
b
n+ 1
1
a
1
b
2
1
(d)
- 1
u[n + 1] +
u[-2 - n]
b
2
b
2
- 1
c
b
n+ 1
- b
2
a
2
n- 1
1
2
(e)
d
u[n - 2]
b - a
2
(f)
51u[-n] +
1
52 - n
21
u[n - 1] - u[n - 52]
2
-n+ 1
1
ab
2
a
b
n
b
n
ab
b
n
(g)
a
b
u[1 - n] +
1 - ab
+
b
u[n - 2]
1 - ab
a
n- 3
1 -
b
-n+ 3
ca
a
b
(h)
u[3 - n] + 1u[n - 4]
d
a
b
n
u[n]
10.11.
(a)
(b)
(d)
h[n] =
1
n + 1
21
0.6
2
h[n] = d[n + 4]
h[n] = d[n] + 2d[n - 1] + 3d[n - 2] + 2d[n - 3] + d[n - 4]
10.12.
(a)
causal
(b)
stable
a
1
-
0.9
n+ 1
1 - 0.9
b
u[n]
(c)
3
2
u[n] + 3
n
u[-n - 1]
(e)
not causal, stable,
(f)
not causal, not stable
(g)
not causal, not stable
y[n] =
1
2
