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Uncertainty Principles for the Offset Linear Canonical Transform

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Abstract

The offset linear canonical transform (OLCT) provides a more general framework for a number of well-known linear integral transforms in signal processing and optics, such as Fourier transform, fractional Fourier transform, linear canonical transform. In this paper, to characterize simultaneous localization of a signal and its OLCT, we extend some different uncertainty principles (UPs), including Nazarov’s UP, Hardy’s UP, Beurling’s UP, logarithmic UP and entropic UP, which have already been well studied in the Fourier transform domain over the last few decades, to the OLCT domain in a broader sense.

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Acknowledgements

The author thanks the referees very much for carefully reading the paper and for elaborate and valuable suggestions.

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Authors and Affiliations

  1. Department of Mathematics, School of Science, Nanchang University, Nanchang, 330031, Jiangxi, China

    Haiye Huo

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  1. Haiye Huo
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Correspondence to Haiye Huo.

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Huo, H. Uncertainty Principles for the Offset Linear Canonical Transform. Circuits Syst Signal Process 38, 395–406 (2019). https://doi.org/10.1007/s00034-018-0863-z

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  • DOI: https://doi.org/10.1007/s00034-018-0863-z

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