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Uncertainty Inequalities for the Linear Canonical Hilbert Transform

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Abstract

The Heisenberg uncertainty principle plays an important role in signal processing, applied mathematical and physics community. The extensions of the traditional uncertainty principle to the novel transforms have received considerable attention recently. In this paper, the uncertainty inequalities under the linear canonical Hilbert transform (LCHT) are considered. First, the uncertainty principle for the complex signals associated with the one-dimensional LCHT is investigated. Subsequently, the uncertainty inequality for the complex signals derived by the two-dimensional LCHT is proposed. It is shown that the uncertainty bounds for the complex signals derived by LCHT are different from the general complex signals in the LCT domain. In addition, the example and potential applications are also presented to show the correctness and useful of the derived results. Therefore, the uncertainty principles presented here not only can enrich the ensemble of the classical uncertainty principle, but can have many real applications too.

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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 (61374135, 61633005, 61673076, 51637004), the National Key Research and Development Plan: Important Scientific Instruments and Equipment Development (2016YFF0102200) and Central Military Equipment Development Department pre Research Project (41402040301).

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Authors and Affiliations

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

    Shuiqing Xu

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

    Shuiqing Xu, Yi Chai, Youqiang Hu, Li Feng & Lei Huang

  3. School of Computer Science and Technology, Huaiyin Normal University, Huaian, 223300, China

    Lei Huang

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  1. Shuiqing Xu
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  2. Yi Chai
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  4. Li Feng
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Correspondence to Yi Chai.

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Xu, S., Chai, Y., Hu, Y. et al. Uncertainty Inequalities for the Linear Canonical Hilbert Transform. Circuits Syst Signal Process 37, 4584–4598 (2018). https://doi.org/10.1007/s00034-018-0780-1

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