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Window Design Techniques 327
of attenuation. These window functions bear the names of the people
who first proposed them. Although these window functions can also be
analyzed similar to the rectangular window, we present only their results.
7.3.2 BARTLETT WINDOW
Since the Gibbs phenomenon results from the fact that the rectangular
window has a sudden transition from 0 to 1 (or 1 to 0), Bartlett suggested
a more gradual transition in the form of a triangular window, which is
given by
⎧
2n
M − 1 , 0 ≤ n ≤ M − 1
2
⎪⎨
w(n) =
2 − 2n
M − 1 , M − 1
(7.25)
≤ n ≤ M − 1
2
⎪⎩
0, otherwise
This window and its frequency-domain responses are shown in Figure 7.11.
Bartlett Window : M=45
Amplitude Response in dB
1
0
w(n)
Decibels
27
0
0 22 45
n
Amplitude Response
60
1 0 1
frequency in π units
Accumulated Amplitude Response
22
0
Width=(6.1)*pi/M
Wr
Decibels
26
0
−1 0 1
frequency in π units
60
−1 1
frequency in π units
FIGURE 7.11 Bartlett window: M =45
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