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28 March 2024 New convolution and correlation theorems for the linear canonical wavelet transform
Hui Zhao, Bing-Zhao Li
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Proceedings Volume 13091, Fifteenth International Conference on Signal Processing Systems (ICSPS 2023); 1309102 (2024) https://doi.org/10.1117/12.3023199
Event: Fifteenth International Conference on Signal Processing Systems (ICSPS 2023), 2023, Xi’an, China
Abstract
The linear canonical wavelet transform (LCWT) is the generalization of the classical wavelet transform (WT) and the linear canonical transform (LCT). It has been proven to be a powerful mathematical tool and is widely used in signal processing, image processing, optics, and other fields. However, some basic results of this transform are not yet mature, such as convolution and correlation theorems. Therefore, this paper discusses the convolution and correlation theorems of the LCWT. Firstly, we review the basic theory of the WT, the LCT, and the LCWT. Secondly, we define the new convolution and correlation operators, and deduce the convolution and correlation theorems of the LCWT. The results show that they are similar in other joint space/spatial-frequency or time/frequency representations. Finally, we give the filter design method of the proposed convolution theorem in the LCWT domain, which provides us with more possibilities to consider performing spatially varying filtering operations in the LCWT domain.
(2024) Published by SPIE. Downloading of the abstract is permitted for personal use only.
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Hui Zhao and Bing-Zhao Li "New convolution and correlation theorems for the linear canonical wavelet transform", Proc. SPIE 13091, Fifteenth International Conference on Signal Processing Systems (ICSPS 2023), 1309102 (28 March 2024); https://doi.org/10.1117/12.3023199
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KEYWORDS
Convolution
Signal processing
Wavelet transforms
Time-frequency analysis
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