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The N-Dimensional Uncertainty Principle for the Free Metaplectic Transformation

Author

Listed:
  • Rui Jing

    (College of Science, Tianjin University of Technology, Tianjin 300384, China)

  • Bei Liu

    (College of Science, Tianjin University of Technology, Tianjin 300384, China)

  • Rui Li

    (College of Science, Tianjin University of Technology, Tianjin 300384, China)

  • Rui Liu

    (School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071, China)

Abstract

The free metaplectic transformation is an N-dimensional linear canonical transformation. This transformation operator is useful, especially for signal processing applications. In this paper, in order to characterize simultaneously local analysis of a function (or signal) and its free metaplectic transformation, we extend some different uncertainty principles (UP) from quantum mechanics including Classical Heisenberg’s uncertainty principle, Nazarov’s UP, Donoho and Stark’s UP, Hardy’s UP, Beurling’s UP, Logarithmic UP, and Entropic UP, which have already been well studied in the Fourier transform domain.

Suggested Citation

  • Rui Jing & Bei Liu & Rui Li & Rui Liu, 2020. "The N-Dimensional Uncertainty Principle for the Free Metaplectic Transformation," Mathematics, MDPI, vol. 8(10), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:10:p:1685-:d:422644
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    References listed on IDEAS

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    1. Yong-Gang Li & Bing-Zhao Li & Hua-Fei Sun, 2014. "Uncertainty Principles for Wigner-Ville Distribution Associated with the Linear Canonical Transforms," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, May.
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