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Bartlett (``Triangular'') Window
The Bartlett window (or simply triangular window) may be
defined by
![$\displaystyle w(n) = w_R(n)\left[1 - \frac{\vert n\vert}{\frac{M-1}{2}}\right], \quad n\in\left[-\frac{M-1}{2},\frac{M-1}{2}\right]$](img439.png) |
(4.31) |
and the corresponding transform is
![$\displaystyle W(\omega) = \left(\frac{M-1}{2}\right)^2\hbox{asinc}_{\frac{M-1}{2}}^2(\omega)$](img440.png) |
(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
Subsections
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