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Window-dependent bases for efficient representations of the Stockwell transform.
- Source :
-
Applied & Computational Harmonic Analysis . Mar2016, Vol. 40 Issue 2, p292-320. 29p. - Publication Year :
- 2016
-
Abstract
- Since its appearing in 1996, the Stockwell transform (S-transform) has been applied to medical imaging, geophysics and signal processing in general. In this paper, we prove that the system of functions (so-called DOST basis) is indeed an orthonormal basis of L 2 ( [ 0 , 1 ] ) , which is time–frequency localized, in the sense of Donoho–Stark Theorem (1989) [11] . Our approach provides a unified setting in which to study the Stockwell transform (associated with different admissible windows) and its orthogonal decomposition. Finally, we introduce a fast – O ( N log N ) – algorithm to compute the Stockwell coefficients for an admissible window. Our algorithm extends the one proposed by Y. Wang and J. Orchard (2009) [33] . [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 10635203
- Volume :
- 40
- Issue :
- 2
- Database :
- Academic Search Index
- Journal :
- Applied & Computational Harmonic Analysis
- Publication Type :
- Academic Journal
- Accession number :
- 112177640
- Full Text :
- https://doi.org/10.1016/j.acha.2015.02.002