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Extrapolation Theorem for Bandlimited Signals Associated with the Offset Linear Canonical Transform

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Abstract

The offset linear canonical transform (OLCT) is a novel and effective method in signal processing and optics. Many important properties and results of the OLCT have been well studied and published. However, the extrapolation theorem of the OLCT bandlimited signals still remains unknown. In this short paper, by using the generalized prolate spheroidal wave functions (GPSWFs), the extrapolation theorem for the OLCT bandlimited signals has been provided. Firstly, the concept of the GPSWFs in the OLCT domain has been proposed. Subsequently, the dual orthogonality and completeness of the GPSWFs associated with the OLCT have been derived based on the definition. In addition, the extrapolation theorem of the OLCT bandlimited signals has been obtained by using the orthogonality and completeness properties of the GPSWFs. Finally, the simulation results are presented to show the usefulness and effectiveness of the derived theorems.

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Acknowledgements

The authors would like to thank the editor and the anonymous referee for their valuable comments and suggestions. This work was supported by the National Natural Science Foundation of China (61803140, 61803055, 51577046, 51637004), the Fundamental Research Funds for the Central Universities JZ2019HGTB0090 and JZ2019HGTB0073, the Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN201800), the National Key Research and Development Plan: Important Scientific Instruments and Equipment Development (2016YFF0102200) and Equipment research project in advance (41402040301).

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Authors and Affiliations

  1. College of Electrical Engineering and Automation, Hefei University of Technology, Hefei, 230009, China

    Shuiqing Xu, Bingbing Dong, Yingying Zhang & Yigang He

  2. College of Electrical Engineering and Automation, Wuhan University, Wuhan, 430072, China

    Shuiqing Xu & Yigang He

  3. College of Traffic and Transportation, Chongqing Jiaotong University, Chongqing, 400074, China

    Li Feng

  4. College of Automation, Chongqing University, Chongqing, 400044, China

    Li Feng & Yi Chai

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  1. Shuiqing Xu
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  2. Li Feng
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  3. Yi Chai
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  4. Bingbing Dong
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Correspondence to Li Feng or Yigang He.

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Xu, S., Feng, L., Chai, Y. et al. Extrapolation Theorem for Bandlimited Signals Associated with the Offset Linear Canonical Transform. Circuits Syst Signal Process 39, 1699–1712 (2020). https://doi.org/10.1007/s00034-019-01217-8

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  • DOI: https://doi.org/10.1007/s00034-019-01217-8

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