基于LCT域乘积-卷积理论的Hilbert变换及广义Bedrosian定理  

Hilbert transform based on product-convolution theory in LCT domain and generalized Bedrosian theorem

作　　者：张小燕[1] 宋玉娥[1,2] 王承国[3] 王晓燕[4] 

机构地区：[1]北京工业职业技术学院信息工程系,北京100042 [2]北京理工大学信息与电子学院,北京100081 [3]中国农业大学烟台研究院,山东烟台264670 [4]装甲兵工程学院基础部,北京100072

出　　处：《兰州理工大学学报》2015年第1期149-153,共5页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11201482);北京市教委人才强教深化计划(PXM2014_014225_000020)

摘　　要：研究基于线性正则变换(linear canonical transform,LCT)域乘积-卷积理论的Hilbert变换,给出基于LCT的Hilbert变换定义,并推导出这种定义下解析信号的几个重要的性质与特点;同时研究LCT域的广义Hilbert变换对,得到LCT域广义Hilbert变换对的表达形式;给出LCT域Bedrosian定理及其证明过程.According to the product-convolution theory in the linear canonical transform（LCT）domain,the Hilbert transform is studied and its definition is given out.Some most important properties and features of the analytic signal are derived with this definition.Meantime the generalized Hilbert pairs in the LCT domain are studied and their expressions are obtained.The Bedrosian theorem in the LCT domain and its proof are given out,also.

关 键 词：HILBERT变换 线性正则变换 解析信号 乘积-卷积理论 Hilbert变换对 Bedrosian定理 

分 类 号：O174.2[理学—数学]