Continuous quaternion Stockwell transform and Uncertainty principle

Brahim Kamel; Emna Tefjeni

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arXiv · 1912.11404

Continuous quaternion Stockwell transform and Uncertainty principle

Brahim Kamel·Emna Tefjeni

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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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Brahim Kamel, Emna Tefjeni. 2019-12-17. Continuous quaternion Stockwell transform and Uncertainty principle. https://arxiv.org/abs/1912.11404

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