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Uncertainty Principle for the Two-Sided Quaternion Windowed Linear Canonical Transform

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Abstract

In this paper, we investigate the (two-sided) quaternion windowed linear canonical transform (QWLCT) and study the uncertainty principles associated with the QWLCT. First, several important properties of the QWLCT such as bounded, shift, modulation and orthogonality relations are presented based on the spectral representation of the quaternionic linear canonical transform (QLCT). Second, Pitt’s inequality and the Lieb inequality for the QWLCT are explored. Moreover, we study different kinds of uncertainty principles for the QWLCT, such as the logarithmic uncertainty principle, the entropic uncertainty principle, the Lieb uncertainty principle and Donoho–Stark’s uncertainty principle. Finally, we provide a numerical example and a potential application to signal recovery by using Donoho–Stark’s uncertainty principle associated with the QWLCT.

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Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

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Funding

The authors sincerely thank the editors and referees for their elaborate and valuable suggestions, which helped to improve this paper. This work is supported by the National Natural Science Foundation of China (No. 61671063).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 102488, P.R. China

    Wen-Biao Gao

  2. Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, 102488, P.R. China

    Bing-Zhao Li

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  1. Wen-Biao Gao
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Correspondence to Bing-Zhao Li.

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Gao, WB., Li, BZ. Uncertainty Principle for the Two-Sided Quaternion Windowed Linear Canonical Transform. Circuits Syst Signal Process 41, 1324–1348 (2022). https://doi.org/10.1007/s00034-021-01841-3

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  • DOI: https://doi.org/10.1007/s00034-021-01841-3

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