Window-dependent bases for efficient representations of the Stockwell transform

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 L2([0,1])L2([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(Nlog⁡N)O(Nlog⁡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].