基于FRFT的Hilbert变换  

The Hilbert Transform Based on the FRFT

作　　者：李雪梅[1,2] 陶然[1] 李炳照[1] 

机构地区：[1]北京理工大学信息与电子学院,北京100081 [2]北京电子科技学院电子信息工程系,北京100070

出　　处：《兵工学报》2009年第2期221-225,共5页Acta Armamentarii

基　　金：国家自然科学基金资助项目(60572094);国家自然基金重点项目(60232010);国家杰出青年科学基金项目(60625104)

摘　　要：解析信号的一个重要性质是从正频谱中恢复实信号,现有的基于分数阶Fourier变换(FRFT)的Hilber变换(HT)理论尚未解决这一问题。本文从分数阶乘积-卷积理论出发,研究了基于FRFT的HT理论与解析信号的定义和性质,给出了理论分析和推导,证明了通过解析信号在分数阶Fourier域的正频率谱能够恢复实信号。仿真结果表明,本文提出的方法可以增强单边带通信系统的保密性,并具有较高的图像加密效果。本文研究是对基于FRFT的HT理论的丰富和完善。One of the important properties of the analytic signal is to reconstruct the real signal from its analytic version,which is an unresolved problem in the published papers about the Hilbert transform（HT） based on the fractional Fourier transform（FRFT）.The definition and properties of a HT and analytic signal based on the FRFT were proposed,which are connected with the convolution and product theorem for the FRFT,the theoretic analysis and deducing were given.The analytic version contains no negative spectrum while maintaining the essential information of the real signal.The simulated result shows that the theory can enhance the security of the single-sideb and communication（SSB） system and improve the encryption for the real image.The theory is the generalization of the HT based on the FRFT.

关 键 词：信息处理技术 HILBERT变换 分数阶FOURIER变换 单边带通信 图像加密 

分 类 号：TN911.7[电子电信—通信与信息系统]