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Gaussian Window and Transform

Figure 3.36 shows an example length $ M=21$ Gaussian window and its transform. The sigma parameter was set to $ M/8$ so that simple truncation of the Gaussian yields a side-lobe level better than $ -80$ dB. Also overlaid on the window transform is a parabola; we see that the main lobe is well fit by the parabola until the side lobes begin. Since the transform of a Gaussian is a Gaussian (exactly), the side lobes are entirely caused by truncating the window.

Figure 3.36: Gaussian window and transform.
\includegraphics[width=\twidth]{eps/gaussianWindow}

More properties and applications of the Gaussian function can be found in Appendix D.


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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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