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A new convolution theorem associated with the linear canonical transform

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Abstract

In this paper, we first introduce a new notion of canonical convolution operator, and show that it satisfies the commutative, associative, and distributive properties, which may be quite useful in signal processing. Moreover, it is proved that the generalized convolution theorem and generalized Young’s inequality are also hold for the new canonical convolution operator associated with the LCT. Finally, we investigate the sufficient and necessary conditions for solving a class of convolution equations associated with the LCT.

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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, China

    Haiye Huo

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  1. Haiye Huo
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Correspondence to Haiye Huo.

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Huo, H. A new convolution theorem associated with the linear canonical transform. SIViP 13, 127–133 (2019). https://doi.org/10.1007/s11760-018-1337-2

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  • DOI: https://doi.org/10.1007/s11760-018-1337-2

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