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Sampling formulas for non-bandlimited quaternionic signals

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Abstract

In this paper, sampling theorems for certain types of non-bandlimited quaternionic signals are proposed. We show that the non-bandlimited quaternionic signal can be reconstructed from its samples as well as the samples of its generalized Hilbert transforms associated with quaternion Fourier and linear canonical transform. Some simulations are provided to show how the sampling formulas can be used in applications.

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Acknowledgements

The authors highly appreciate Dr Dong CHENG’s insightful and helpful suggestions on our manuscript. Xiaoxiao Hu was supported by the Research Development Foundation of Wenzhou Medical University (QTJ18012), Wenzhou Science and Technology Bureau (G2020031) and Scientific Research Task of Department of Education of Zhejiang Province ( Y202147071). Kit Ian Kou was supported by The Science and Technology Development Fund, Macau SAR (No. FDCT/085/2018/A2) and University of Macau (File no. MYRG2019-00039-FST). This work was supported by the Guangdong Basic and Applied Basic Research Foundation (No. 2019A1515111185).

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  1. The First Affiliated Hospital of Wenzhou Medical University, Wenzhou Medical University, Zhejiang, 325000, China

    Xiaoxiao Hu

  2. Department of Mathematics, University of Macau, Taipa, Macau, China

    Kit Ian Kou

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  1. Xiaoxiao Hu
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  2. Kit Ian Kou
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Correspondence to Xiaoxiao Hu.

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Hu, X., Kou, K.I. Sampling formulas for non-bandlimited quaternionic signals. SIViP 16, 1559–1567 (2022). https://doi.org/10.1007/s11760-021-02110-1

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  • DOI: https://doi.org/10.1007/s11760-021-02110-1

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