线性正则正余弦变换卷积及其性质  

Convolution theorems for the linear canonical sine and cosine transform and its properties

作　　者：王小霞[1] 冯强[1] WANG Xiaoxia;FENG Qiang(College of Mathematics and Computer Science,Yan’an University,Yan’an 716000,China)

机构地区：[1]延安大学数学与计算机科学学院,陕西延安716000

出　　处：《延安大学学报（自然科学版）》2023年第4期94-98,共5页Journal of Yan'an University：Natural Science Edition

基　　金：国家自然科学基金项目(62261055,61861044);陕西省自然科学基金项目(2022JM-400)。

摘　　要：卷积是一种重要的积分变换,它在信号处理领域有着非常重要的作用。基于线性正则正余弦变换,定义了两类新的线性正则正余弦变换的卷积运算,给出了线性正则正余弦变换卷积与已有卷积之间的关系,并推导出线性正则正余弦卷积定理。研究结果是经典傅里叶正余弦卷积理论在线性正则域内的进一步拓展。Convolution theorem is a basic property of linear canonical transform,which plays an important role in signal processing.In this paper,two new convolution operations of linear canonical sine and cosine transform are presented,and the relationship between the convolution of linear canonical sine and cosine transform and the exist⁃ing convolution are definded.Thus we inferred the linear sine canonical transform convolution theorem and the weighted linear canonical cosine transform convolution theorem.

关 键 词：线性正则变换 线性正则正余弦变换 卷积定理 卷积运算 

分 类 号：O174.2[理学—数学]