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328 Chapter 7 FIR FILTER DESIGN
Hann Window : M=45
Amplitude Response in dB
1
0
w(n)
Decibels
32
0
0 22 45
n
Amplitude Response
60
−1 0 1
frequency in π units
Accumulated Amplitude Response
23
0
Width=(6.2)*pi/M
Wr
Decibels
44
0
−1 0 1
frequency in π units
60
−1 1
frequency in π units
FIGURE 7.12 Hann window: M =45
7.3.3 HANN WINDOW
This is a raised cosine window function given by
⎧ [ ( )]
2πn
⎪⎨ 0.5 1 − cos
M−1
, 0 ≤ n ≤ M − 1
w(n) =
⎪⎩
0, otherwise
(7.26)
This window and its frequency-domain responses are shown in Figure 7.12.
7.3.4 HAMMING WINDOW
This window is similar to the Hann window except that it has a small
amount of discontinuity and is given by
⎧
( )
⎨
2πn
0.54 − 0.46 cos
M−1
, 0 ≤ n ≤ M − 1
w(n) =
(7.27)
⎩
0, otherwise
This window and its frequency-domain responses are shown in Figure 7.13.
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