@inproceedings{5ea4e2fb304e4c22b5673907964b54ef,
title = "New Convolution and Correlation Theorems for the Linear Canonical Wavelet Transform",
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.",
keywords = "Convolution theorem, Correlation theorem, Linear canonical wavelet transform, Wavelet transform",
author = "Hui Zhao and Li, {Bing Zhao}",
note = "Publisher Copyright: {\textcopyright} 2024 SPIE.; 15th International Conference on Signal Processing Systems, ICSPS 2023 ; Conference date: 17-11-2023 Through 19-11-2023",
year = "2024",
doi = "10.1117/12.3023199",
language = "English",
series = "Proceedings of SPIE - The International Society for Optical Engineering",
publisher = "SPIE",
editor = "Zhenkai Zhang and Cheng Li",
booktitle = "Fifteenth International Conference on Signal Processing Systems, ICSPS 2023",
address = "United States",
}