Window-Dependent Bases for Efficient Representations of the Stockwell Transform

By U. Battisti, L. Riba. 2014

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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).

Subfields: Applied Mathematics, Computer Vision and Pattern Recognition, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/f841bef35c8783558d658c31bb7a4334d512efb3