On uncertainty principle for the two-sided quaternion linear canonical transform

Abstract

The quaternion linear canonical transform (QLCT), as a generalized form of the quaternion Fourier transform, is a powerful analyzing tool in image and signal processing. In this paper, we propose five different forms of uncertainty principles for the two-sided QLCT, including logarithmic uncertainty principle, Heisenberg-type uncertainty principle, local uncertainty principle, Benedicks–Amrein–Berthier uncertainty principle and entropic uncertainty principle. These consequences actually describe the quantitative relationships of a quaternion-valued signal in arbitrary two different QLCT domains, and they have great applications in signal recovery and physical quantum.

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Acknowledgements

This paper was in part supported by the Natural Science Foundation of China grant No.12071021.

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Correspondence to Shenzhou Zheng.

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Zhu, X., Zheng, S. On uncertainty principle for the two-sided quaternion linear canonical transform. J. Pseudo-Differ. Oper. Appl. 12, 3 (2021). https://doi.org/10.1007/s11868-021-00395-x

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Keywords

  • Quaternion linear canonical transform (QLCT)
  • Quaternion Fourier transform (QFT)
  • Uncertainty principle

Mathematics Subject Classification

  • 42B10
  • 30G35
  • 11R52