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Generalized uncertainty principles associated with Hilbert transform

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Abstract

This correspondence investigates the Heisenberg’s uncertainty principle and windowed uncertainty principle associated with 1D fractional Hilbert transform (FRHT) and the Heisenberg’s uncertainty principle associated with two types of 2D FRHT for the first time. These uncertainty bounds are related with the transform parameters of the fractional transform. In addition, we show that the certainty bounds for the complex signals derived by FRHT are different with that of the general complex signals in most cases. The special cases of these principles in traditional domains are provided as well. These new derived uncertainty principles will enrich the ensemble of the uncertainty principle as well as providing new physical interpretation.

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Acknowledgments

This work is supported by the NSFs of China (Grant Nos. 60975016 and 61002052).

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Authors and Affiliations

  1. Department of Oceanography, Dalian Naval Academy, Dalian, 116018, China

    Xu Guanlei, Wang Longtao, Liu Bo & Su Shipeng

  2. Department of Navigation, Dalian Naval Academy, Dalian, 116018, China

    Wang Xiaotong & Xu Xiaogang

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  1. Xu Guanlei
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  2. Wang Xiaotong
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  3. Wang Longtao
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  4. Liu Bo
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  5. Su Shipeng
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  6. Xu Xiaogang
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Correspondence to Xu Guanlei.

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Guanlei, X., Xiaotong, W., Longtao, W. et al. Generalized uncertainty principles associated with Hilbert transform. SIViP 8, 279–285 (2014). https://doi.org/10.1007/s11760-013-0547-x

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  • DOI: https://doi.org/10.1007/s11760-013-0547-x

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