Advances in Applied Clifford Algebras

, Volume 26, Issue 1, pp 479–497 | Cite as

Tighter Uncertainty Principles Based on Quaternion Fourier Transform

  • Yan Yang
  • Pei Dang
  • Tao Qian


The quaternion Fourier transform (QFT) and its properties are reviewed in this paper. Under the polar coordinate form for quaternion-valued signals, we strengthen the stronger uncertainty principles in terms of covariance for quaternion-valued signals based on the right-sided quaternion Fourier transform in both the directional and the spatial cases. We also obtain the conditions that give rise to the equal relations of two uncertainty principles. Examples are given to verify the results.

Mathematics Subject Classification

46F10 30G35 94A12 


Uncertainty principle Quaternion Fourier transform Covariance 


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Copyright information

© Springer Basel 2015

Authors and Affiliations

  1. 1.School of Mathematics and Computational ScienceSun Yat-Sen UniversityGuangzhouChina
  2. 2.Faculty of Information TechnologyMacau University of Science and TechnologyMacaoChina
  3. 3.Department of MathematicsUniversity of MacauMacaoChina

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