Convolution Theorem Associated with the QWFRFT

作     者：MEI Yinyin FENG Qiang GAO Xiuxiu ZHAO Yanbo MEI Yinyin;FENG Qiang;GAO Xiuxiu;ZHAO Yanbo

作者机构：School of Mathematics and Computer Science Yan'an University 

出 版 物：《Chinese Journal of Electronics》 (电子学报(英文))

年 卷 期：2023年第32卷第3期

页      面：485-492页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by the National Natural Science Foundation of China (61861044, 11961072, 62001193) the Natural Science Foundation of Shaanxi Province (2022JM-400, 2020JM-547) the Graduate Education Innovation Program of Yan’an University (YCX2021047) 

主　　题：Fourier transforms Convolution Algebra Quaternions Signal processing algorithms Color Complexity theory 

摘      要：The quaternion windowed fractional Fourier transform(QWFRFT) is a generalized form of the quaternion fractional Fourier transform(QFRFT), it plays a crucial role in signal processing for the analysis of multidimensional signals. In this paper, we first give the definition of the two-sided QWFRFT and some fundamental properties. Then, the quaternion convolution is proposed, and the relation between the quaternion convolution and the classical convolution is also given. Based on the quaternion convolution of the QWFRFT, relevant convolution theorems for the QWFRFT are ***, the fast algorithm for QWFRFT is ***, the complexity of QWFRFT and the quaternion windowed fractional convolution are given.