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Integral Transforms and Special Functions Volume 18, 2007 - Issue 8
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Original Articles

Continuous and discrete inversion formulas for the Stockwell transform

Jingde Du Calgary Scientific, Inc., 208-1210 20th Avenue SE, Calgary, Alberta, T2G 1M8, Canada
,
M. W. Wong Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, CanadaCorrespondence[email protected]
&
Hongmei Zhu Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, Ontario, M3J 1P3, Canada
Pages 537-543 | Received 23 Aug 2006, Published online: 13 Aug 2007
 
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Abstract

The Stockwell transform of a signal, i.e., a function in L 2(ℝ), is defined as a hybrid of the Gabor transform and the wavelet transform. The continuous and discrete reconstruction formulas for a signal from its Stockwell transform are established.

Acknowledgements

This research has been supported by grants from the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Mathematics of Information Technology and Complex Systems (MITACS).

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