Continuous quaternion Stockwell transform and Uncertainty principle

2019/12/17 by Kamel, Brahim, Emna Tefjeni, Tefjeni, Emna · 1 citation
Mathematics · Physics and Astronomy · #Mathematical Analysis and Transform Methods #Advanced Differential Geometry Research #Algebraic and Geometric Analysis

paper · pdf · doi:10.48550/arxiv.1912.11404

Abstract

In this paper we propose a novel transform called continuous quaternionic stockwell transform. We express the admissibility condition in term of the (two-sided) quaternion Fourier transform . We show that its fundamental properties, such as Plancherel, Parseval and inversion formula, can be established whenever the continuous quaternion stockwell satisfy a particular admissibility condition. We present several examples of the continuous quaternion stockwell transform. We apply the continuous quaternion stockwell transform properties and the two sided quaternion Fourier transform to establish a number of uncertainty principle for these extended Stockwell .

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