## 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 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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Poisson Window

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Spectrum Analysis of an Oboe Tone