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

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 0The 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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