Sharper Hardy Uncertainty Relations on Signal Concentration in terms of Linear Canonical Transform

XU Xiaogang; XU Guanlei; WANG Xiaotong

doi:10.23919/cje.2023.00.096

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Xiaogang XU, Guanlei XU, Xiaotong WANG, “Sharper Hardy Uncertainty Relations on Signal Concentration in terms of Linear Canonical Transform,” Chinese Journal of Electronics, vol. 33, no. 4, pp. 1–10, 2024 doi: 10.23919/cje.2023.00.096

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Xiaogang XU, Guanlei XU, Xiaotong WANG, “Sharper Hardy Uncertainty Relations on Signal Concentration in terms of Linear Canonical Transform,” Chinese Journal of Electronics, vol. 33, no. 4, pp. 1–10, 2024 doi: 10.23919/cje.2023.00.096

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Sharper Hardy Uncertainty Relations on Signal Concentration in terms of Linear Canonical Transform

doi: 10.23919/cje.2023.00.096

1.
College of Computer and Information Engineering, Zhejiang Gongshang University, Hangzhou 310018, China

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Author Bio:
Xiaogang XU received his Ph. D. degree in Information and System Analysis in 1999 at Dalian Science and Technology University in Dalian. Now he is a professor and MS tutor of the Department of Arming System and Automation at Dalian Naval Academy. His main research interests are virtual reality and computer graphs. (Email: xgl_86@sohu.com)

Guanlei XU received his Ph. D. degree in Information Engineering and Control in 2009 at Dalian Naval Academy. Now he is a lecturer in the Department of Military Oceanography at Dalian Naval Academy. His main research interests are signal analyzing and image processing. (Email: xgl_86@163.com)

Xiaotong WANG received his Ph. D. degree in Information and System Analysis in 1996 from Dalian Science and Technology University in Dalian. Now he is a professor and the PhD tutor of the Department of Navigation at Dalian Naval Academy. His main research interests are signal/image processing and application in navigation. (Email: xxggll_86@163.com)
Corresponding author: Email: xgl_86@163.com
Received Date: 2023-03-28
Accepted Date: 2023-06-20

Available Online: 2023-07-21

Abstract

Abstract

Linear canonical transform is of much significance to optics and information science. Hardy uncertainty principle, like Heisenberg uncertainty principle, plays an important role in various fields. In this paper, four new sharper Hardy uncertainty relations on linear canonical transform are derived. These new derived uncertainty relations are connected with the linear canonical transform parameters and indicate new insights for signal energy concentration. Especially, for certain transform parameters, e.g. b=0, these new proposed uncertainty relations break the traditional counterparts in signal energy concentration, as will result in new physical interpretation in terms of uncertainty principle. Theoretical analysis and numerical examples are given to show the efficiency of these new relations.
- Hardy uncertainty principle,
- Linear canonical transform (LCT),
- Signal concentration

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References(35)

References

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