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Signal, Image and Video Processing

, Volume 8, Issue 1, pp 85–93 | Cite as

On uncertainty principles for linear canonical transform of complex signals via operator methods

  • Jun ShiEmail author
  • Xiaoping Liu
  • Naitong Zhang
Original Paper

Abstract

The linear canonical transform (LCT) has been shown to be a useful and powerful analyzing tool in optics and signal processing. Many results of this transform are already known, including its uncertainty principles (UPs). The existing UPs of the LCT for complex signals can only provide sharp bounds with LCT parameters satisfying \(a_1/b_1\ne a_2/b_2\). However, in most cases, we strive to find a lower bound, but not a sharper bound, since a lower bound often leads to optimization problems in signal processing applications. In this paper, we first present a much briefer and more transparent derivation to obtain a general uncertainty principle of the LCT for arbitrary signals via operator methods. Then, we derive lower bounds of three UPs of the LCT for complex signals, which are tighter lower bounds than the existing ones. We also prove that the derived results hold for arbitrary LCT parameters.

Keywords

Linear canonical transform Complex signal Hermitian operator Time-frequency analysis Uncertainty principle 

Notes

Acknowledgments

This work was completed in parts while Shi J. was visiting the Department of Electrical and Computer Engineering, University of Delaware, Newark, DE 19716 USA. The work was supported in part by the National Basic Research Program of China (Grant No. 2013CB329003), the National Natural Science Foundation of China (Grant No. 61171110), and the Short-Term Overseas Visiting Scholar Program of Harbin Institute of Technology.

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Copyright information

© Springer-Verlag London 2013

Authors and Affiliations

  1. 1.Communication Research CenterHarbin Institute of TechnologyHarbinChina
  2. 2.Shenzhen Graduate SchoolHarbin Institute of TechnologyShenzhenChina

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