Digital Signal Processing Reference
In-Depth Information
Fig. 4.4 Analyzed signals
(a, b) and their DFTs
(c, d) for N = 20
(a)
2
)
x
(
n
1
0
0
5
10
15
20
n
(b)
1
x
(
n
)
0
-1
n
0
5
10
15
20
(c)
20
X
(
k
)
10
0
0
5
10
15
20
k
(d)
20
)
X
(
k
10
0
0
5
10
15
20
k
Thus
X
2
ð
k
Þ¼
N
for k
¼
N
1
:
0
for other k
and finally, the sought transform is equal:
¼
N
n
2p
N
X
ð
k
Þ¼
DFT
2
½
d
ð
k
1
Þþ
d
ð
k
N
þ
1
Þ:
cos
The considered signals along with calculated DFT functions are presented in
Fig.
4.4
.
Example 4.11
Determine the inverse DFT for a signal with the following DFT:
X
ð
k
Þ¼
N
for k
¼
0
for other k
:
0
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