Digital Signal Processing Reference
In-Depth Information
MATLAB Problems
3.52
Compute the 16-point and 32-point DFTs of the 4-point sequence
x(n)
=
{
10
.
50
−
0
.
5
}
. Plot their magnitudes and compare them.
3.53
Compute the 24-point DFT of the sequence in Problem 3.52, plot the
magnitude of this DFT. Now compute 24-point IDFT of this DFT and
compare it with
x(n)
given above.
3.54
Plot the magnitude of the following transfer functions:
1
.
2
z
−
1
0
.
5
+
X
1
(z)
=
1
+
0
.
2
z
−
1
+
0
.
4
z
−
2
z
−
3
z
−
4
+
0
.
06
z
−
5
+
−
z
−
3
−
0
.
8
z
−
5
z
−
1
+
−
6
X
2
(z)
=
1
+
z
−
1
+
0
.
8
z
−
2
−
0
.
4
z
−
3
−
0
.
3
z
−
4
+
z
−
5
+
0
.
05
z
−
6
z
2
)
(
1
−
0
.
3
z)(
1
+
0
.
2
z
+
X
3
(z)
=
(z
2
+
1
.
0
)(z
2
+
0
.
2
z
−
0
.
1
z
+
0
.
05
)(z
−
0
.
3
)
z
z
+
0
.
5
0
.
8
z
X
4
(z)
=
0
.
4
−
0
.
1
)
2
+
z
+
(z
+
3.55
Plot the magnitude and phase responses of the following functions:
0
.
2
e
jω
0
.
9
e
j
2
ω
+
H
1
(e
jω
)
=
1
−
0
.
6
e
jω
+
0
.
6
e
j
2
ω
−
0
.
5
e
j
3
ω
e
j
4
ω
+
1
+
0
.
4
e
−
jω
H
2
(e
jω
)
=
1
+
0
.
5
e
−
jω
−
0
.
4
e
−
j
2
ω
+
e
−
j
3
ω
+
0
.
3
e
−
j
4
ω
+
0
.
1
e
−
j
5
ω
H
3
(e
jω
)
H
1
(e
jω
)H
2
(e
jω
)
=
3.56
Evaluate the magnitude response of the transfer function
H(z)
at
ω
=
0
.
365
π
and at
ω
=
0
.
635
π
:
z
−
1
0
.
25
+
H(z)
=
1
−
0
.
8
z
−
1
+
0
.
4
z
−
2
−
0
.
05
z
−
3
3.57
From the real sequence
x(n)
={
1
−
12
.
50
−
12
}
, show
that the DFT of [
x
e
(n)
]
=
Re
X(k)
where the even part
x
e
(n)
=
[
x(n)
+
n))
N
]
/
2.
3.58
From the real sequence in Problem 3.57, obtain its odd part and show that
its DFT
x((
−
=
j
Im
X(k)
.
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