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A new kind of convolution, correlation and product theorems related to quaternion linear canonical transform

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Abstract

The quaternion linear canonical transform (QLCT) has been investigated and used for many years by various research communities; it has been shown to be a powerful tool for signal processing. In this paper, a novel canonical convolution operator and a related correlation operator for QLCT are proposed. Moreover, based on the proposed operators, the corresponding generalized convolution, correlation and product theorems are studied.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No. 61671063) and the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (No. 61421001).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Beijing Institute of Technology, Beijing, 100081, China

    Zhen-Wei Li, Wen-Biao Gao & Bing-Zhao Li

  2. Beijing Key Laboratory on MCAACI, Beijing Institute of Technology, Beijing, 100081, China

    Zhen-Wei Li, Wen-Biao Gao & Bing-Zhao Li

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  1. Zhen-Wei Li
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  2. Wen-Biao Gao
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  3. Bing-Zhao Li
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Correspondence to Bing-Zhao Li.

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Li, ZW., Gao, WB. & Li, BZ. A new kind of convolution, correlation and product theorems related to quaternion linear canonical transform. SIViP 15, 103–110 (2021). https://doi.org/10.1007/s11760-020-01728-x

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  • DOI: https://doi.org/10.1007/s11760-020-01728-x

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