Digital Signal Processing Reference
In-Depth Information
1
0
-1
0
2
4
6
8
10
12
14
16
1
0.5
0
0
2
4
6
8
10
12
14
16
1
0
-1
0
2
4
6
8
10
12
14
16
Time index n
FIGURE 4.16
Illustration of the window operation.
xð2Þ¼1 and wð2Þ¼0:2265
•
xð5Þ¼0:7071 and wð5Þ¼0:7008
calculate the windowed sequence data points x
w
ð2Þ and x
w
ð5Þ.
Solution:
Applying the window function operation leads to
x
w
ð2Þ¼xð2Þwð2Þ¼1 0:2265 ¼ 0:2265 and
x
w
ð5Þ¼xð5Þwð5Þ¼0:7071 0:7008 ¼0:4956
which agree with the values shown in the bottom plot in
Figure 4.16
.
Using the window function shown in Example 4.9, the spectral plot is reproduced. As a result, the
spectral leakage is greatly reduced, as shown in
Figure 4.17
.
The common window functions are listed as follows.
The rectangular window (no window function):
w
R
ðnÞ¼
1
;
0
n N
1
(4.29)
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