Digital Signal Processing Reference
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(c)
Compute the eight-point DFT of the sequence shown in Figure P12.2(b)
(d)
Use MATLAB to confirm the results of part (c).
12.15.
The signal
x(t) = 5 cos(8pt)
is sampled eight times starting at
t = 0
with
T = 0.1 s.
(a)
Compute the DFT of this sequence.
(b)
Use MATLAB to confirm the results of part (a).
(c)
Determine the Fourier transform of
x(t)
and compare it with the results of part (a)
and (b). Explain the differences.
12.16.
Repeat Problem 12.15(a) and (b) after multiplying the sequence by an eight-point
Hanning window. Discuss the differences between this DFT and that found in Problem
12.15.
x[n]
12.17.
Find
N- 1
2ppn
N
2pkn
N
B
R
B
R
A[k] =
a
cos
cos
,
n= 0
for k = 0, 1, Á , N - 1 and p H [0, N - 1].
DFT A
DFT B
1
1
0.8
0.8
0.6
0.6
0.4
0.4
0.2
0.2
0
0
0
2
4
6
0
1
2
3
4
5
6
7
1
3
5
7
k
k
DFT C
DFT D
20
1
1
16
0.8
0.6
10
0.4
5
0.2
0
0
0
1
2
3
4
5
6
7
0
1
2
3
4
5
6
7
k
k
Figure P12.19
