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arXiv · 1902.08461

The Continuous quaternion Algebra-Valued Wavelet Transform and the Associated Uncertainty Principle

Youssef El Haoui·Said Fahlaoui
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Abstract

The purpose of this article is to extend the wavelet transform to quaternion algebra using the kernel of the two-sided quaternion Fourier transform (QFT). We study some fundamental properties of this extension such as scaling, translation, rotation, Parseval's identity, inversion theorem, and a reproducing kernel, then we derive the associated Heisenberg-Pauli-Weyl uncertainty principle UP. Finally, using the quaternion Fourier representation of the CQWT we generalize the logarithmic UP and Hardy's UP to the CQWT domain.

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BibTeXRIS

Youssef El Haoui, Said Fahlaoui. 2019-02-22. The Continuous quaternion Algebra-Valued Wavelet Transform and the Associated Uncertainty Principle. https://arxiv.org/abs/1902.08461

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