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Bartlett (``Triangular'') Window

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

$\displaystyle w(n) = w_R(n)\left[1 - \frac{\vert n\vert}{\frac{M-1}{2}}\right], \quad n\in\left[-\frac{M-1}{2},\frac{M-1}{2}\right]$ (4.31)

and the corresponding transform is

$\displaystyle W(\omega) = \left(\frac{M-1}{2}\right)^2\hbox{asinc}_{\frac{M-1}{2}}^2(\omega)$ (4.32)

The following properties are immediate:



Subsections
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``Spectral Audio Signal Processing'', by Julius O. Smith III, W3K Publishing, 2011, ISBN 978-0-9745607-3-1.
Copyright © 2014-06-03 by Julius O. Smith III
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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