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In the present article, we propose a directionally tuned variant of the continuous Stockwell transform in the context of multi-dimensional signal analysis. Owing to the directional selectivity coupled with a frequency adaptable window, the proposed transform serves as a bridge between the directional short-time Fourier and wavelet transforms. Besides the formulation of all the fundamental results, including the orthogonality relation and reconstruction formula, we also obtain several uncertainty inequalities associated with the directional Stockwell transform.

Directional Stockwell transform in L 2 (ℝ n )