分数阶Fourier域的二维广义Hilbert变换及Bedrosian定理  

2D Hilbert Transform and Bedrosian's Principle Associated with Fractional Fourier Transform

作　　者：徐冠雷[1,2] 王孝通[1,2] 徐晓刚[3,2] 

机构地区：[1]海军大连舰艇学院航海系,辽宁大连116018 [2]海军大连舰艇学院光电技术研究所,辽宁大连116018 [3]海军大连舰艇学院自动化系,辽宁大连116018

出　　处：《数学物理学报（A辑）》2011年第3期814-828,共15页Acta Mathematica Scientia

基　　金：国家自然科学基金(60473141);辽宁省自然科学基金(20062191)资助

摘　　要：多维解析信号分析和Hilbert变换在现代信号处理理论和工程应用中有着重要的意义.该文根据解析信号在广义频域内的能量分布,提出了二维信号的方向广义Hilbert变换、全向广义Hilbert变换以及单象广义Hilbert变换等定义,并证明了时域和分数阶Fourier域内它们之间的对应关系以及推导出类似于传统Hilbert变换中的性质.同时,给出了解析信号中具有重要意义的二维广义Bedrosian定理和相应的理论证明.Hilbert transform （HT） plays an important role in signal processing. From the energy distributing of analytic signals in the FRFT domain and a few classical 2D elementary Hilbert transform, the definitions of half-platted Hilbert transform, cross-orthant Hilbert transform and single-orthant Hilbert transform are yielded. Meanwhile, the expressions and the mapping in the time domain and the transformed domain are discussed. Moreover, some important properties and conclusions are obtained as well. Finally, we define and derive 2D Bedrosian＇s principle in the FRFT domain, an important property of Hilbert transform.

关 键 词：分数阶FOURIER变换 广义Hilbert变换 解析信号 Bedrosian定理 

分 类 号：O174.2[理学—数学]