Window-Dependent Bases for Efficient Representations of the Stockwell Transform
Functional Analysis
2015-01-05 v3
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). Our approach provides a unified setting in which to study the Stockwell transform (associated to 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).
Cite
@article{arxiv.1406.0513,
title = {Window-Dependent Bases for Efficient Representations of the Stockwell Transform},
author = {Ubertino Battisti and Luigi Riba},
journal= {arXiv preprint arXiv:1406.0513},
year = {2015}
}
Comments
27 pages, 6 figures