Digital Signal Processing Reference
In-Depth Information
3.33.
(a)
a = 4
and
K = 14.14
3.37.
(a)
H
1
s
2
= H
1
1
s
2
H
2
1
s
2
+ H
1
1
s
2
H
3
1
s
2
H
4
1
s
2
+ H
4
1
s
2
H
5
1
s
2
CHAPTER 4
1
2j
,
-1
2j
,
1
2
,
1
2
,
1
2
,
1
2
,
4.2.
(i)
(a)
C
0
= 7, C
1
=
C
-1
=
C
2
=
C
-2
=
C
4
=
C
-4
=
C
k
= 0
for all other
k
.
(b)
C
0
= 7,
2 ƒC
1
ƒ = 1,
u
1
=-p/2,
2 ƒC
2
ƒ = 1,
u
2
= 0,
2 ƒC
4
ƒ = 1,
u
4
= 0,
all other coefficients 0.
1
2
,
C
1
=
1
4
,
C
-1
=
1
4
,
C
k
= 0
(ii) (a)
C
0
=
for all other
k
1
2
,
2 ƒC
1
ƒ =
1
2
,
u
1
= 0,
(b)
C
0
=
all other coefficients zero
1
2
,
C
-3
=
1
2
,
C
5
=
1
2j
,
C
-5
=
1
2j
,
C
k
= 0,
4.3.
(i)
(a)
yes,
(b)
C
3
=
all other
k
(iii) (a)
no, aperiodic
4.6.
(a)
(b)
(c)
0
p
p
3j
kp
a
kp
2
4.10.
(a)
C
k
=
c
1 - cos
bd
and
1
p
-
p
k
p
2
C
0
= lim
k:0
C
k
=
a
3j
a
2
sin
a
bb
-1
k
2
p
2
[e
-jkp
1
2
(c)
C
k
=
1
-jkp - 1
2
+ 1]
and
C
0
=
1
e
j
2
k
(e)
C
k
=
2
c
- jk
d
1 - k
2
p
1
-8
4.11.
(a)
C
k
=
2
,
k
odd,
C
k
= 0,
k
even
1
pk
2
4j
pk
,
k Z 0
(c)
C
0
= 0,
C
k
=
12
p
,
C
k
=
-12
(e)
C
0
=
2
,
k Z 0
4k
2
p
1
- 1
4.14.
(a)
C
k
= 10,
k
odd,
C
k
= 0,
k
even
C
k
= 5[1 - e
-jkp
]
(b)
4.17.
(a)
(c)
(e)
m = 2
m = 2
m = 1
