Uncertainty principle for measurable sets and signal recovery in quaternion domains |
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| Authors: | Kit Ian Kou Yan Yang Cuiming Zou |
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| Institution: | 1. Department of Mathematics, Faculty of Science and Technology, University of Macau, Taipa, Macao, China;2. School of Mathematics (Zhuhai), Sun Yat‐Sen University, Zhuhai, China |
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| Abstract: | The classical uncertainty principle of harmonic analysis states that a nontrivial function and its Fourier transform cannot both be sharply localized. It plays an important role in signal processing and physics. This paper generalizes the uncertainty principle for measurable sets from complex domain to hypercomplex domain using quaternion algebras, associated with the quaternion Fourier transform. The performance is then evaluated in signal recovery problems where there is an interplay of missing and time‐limiting data. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | signal recovery uncertainty principle quaternion Fourier transform |
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