DISCRETE ORTHONORMAL STOCKWELL TRANSFORMS (Multidimensional Stockwell transform and timefrequency analysis)

Abstract

Since its appearing in 1996, the Stockwell transform (Stransform) has been used as a tool in medical imaging, geophysics and signal processing in general. In [2] Riba and Wong gave a definition of a multidimensional version of the Stockwell transform highlighting a link among the Stockwell transform, the Gabor transform and the Wavelet transform. In [1] Battisti and Riba studied in details the discrete counterpart of the Stockwell transform proving that the system of functions known in the literature as DOST basis is indeed an orthonormal basis of L² ([0, 1)).In this paper, we present a summary of the results obtained in [1] in order to provide a O(N log N)-fast algorithm to compute the DOST-coefficients.