Bartlett (Triangular'') Window

The Bartlett window (or simply triangular window) may be defined by (4.31)

and the corresponding transform is (4.32)

The following properties are immediate:

• Convolution of two length rectangular windows
• Main lobe twice as wide as that of a rectangular window of length • First side lobe twice as far down as rectangular case (-26 dB)
• Often applied implicitly to sample correlations of finite data
• Also called the tent function''
• Can replace by to avoid including endpoint zeros

Matlab for the Bartlett Window:

In matlab, a length Bartlett window is designed by the statement

w = bartlett(M);
This is equivalent, for odd , to
w = 2*(0:(M-1)/2)/(M-1);
w = [w w((M-1)/2:-1:1)]';
Note that, in contrast to the hanning function, but like the hann function, bartlett explicitly includes zeros at its endpoints:
>> bartlett(3)
ans =
0
1
0
The triang function in Matlab implements the triangular window corresponding to the hanning case:
>> triang(3)
ans =
0.5000
1.0000
0.5000

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Poisson Window
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