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New Inequalities and Uncertainty Relations on Linear Canonical Transform Revisit

Abstract

The uncertainty principle plays an important role in mathematics, physics, signal processing, and so on. Firstly, based on definition of the linear canonical transform (LCT) and the traditional Pitt's inequality, one novel Pitt's inequality in the LCT domains is obtained, which is connected with the LCT parameters and Then one novel logarithmic uncertainty principle is derived from this novel Pitt's inequality in the LCT domains, which is associated with parameters of the two LCTs. Secondly, from the relation between the original function and LCT, one entropic uncertainty principle and one Heisenberg's uncertainty principle in the LCT domains are derived, which are associated with the LCT parameters and The reason why the three lower bounds are only associated with LCT parameters and and independent of and is presented. The results show it is possible that the bounds tend to zeros.

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Correspondence to Xu Guanlei.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Guanlei, X., Xiaotong, W. & Xiaogang, X. New Inequalities and Uncertainty Relations on Linear Canonical Transform Revisit. EURASIP J. Adv. Signal Process. 2009, 563265 (2009). https://doi.org/10.1155/2009/563265

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Keywords

  • Information Technology
  • Quantum Information
  • Uncertainty Relation
  • Full Article
  • Canonical Transform