线性正则域的Hartley变换及其不确定性原理  

Hartley transform for linear canonical transformation and uncertainty principle

作　　者：李永刚 张川 Li Yonggang;Zhang Chuan(School of Science, Zhengzhou University of Aeronautics, Zhengzhou, Henan 450046, China;The 11^th Research Institute of China Electronics Technology Group Corporation, Beijing 100015, China)

机构地区：[1]郑州航空工业管理学院理学院,河南郑州450046 [2]中国电子科技集团公司第十一研究所,北京100015

出　　处：《光电工程》2018年第6期55-59,共5页Opto-Electronic Engineering

摘　　要：Hartley变换是傅里叶变换的推广,它的一个非常好的性质就是把实信号变换成实信号,从而减少计算量。近些年,随着分数阶傅里叶变换在信号处理中被广泛的应用,线性正则变换也逐渐被应用到信号处理,所以把Hartley变换推广到正则域是一个有研究价值的问题。本文首先通过变化傅里叶变换域Hartley变换的核函数,得到了一个具有共轭性的核函数,之后,通过把该核函数替换成线性正则变换的核函数,从而得到了正则域的Hartley变换,在这个定义的基础上,得到了正则域Hartley变换满足实数性质和奇偶不变性,之后再利用线性正则变换的Heisenberg不确定性原理,得到了正则域Hartley变换的Heisenberg不确定性原理。Hartley transform is a generalization of Fourier transform and it transforms the real signal into real signal thereby reducing the amount of computation. In recent years, with the wide applications of fractional Fourier transform in signal processing, linear canonical transform has gradually been applied to signal processing. Hence, it is a valuable problem to generalize Hartley transform in linear canonical transform domain. In this paper, a kernel function with conjugate property is obtained by changing kernel function of Hartley transform in Fourier transform domain. After that, we obtain Hartley transform in linear canonical transform domain by using kernel function of linear canonical transform. Then, Hartley transform in linear canonical transform domain has the properties of real number and odd-even invariance. Finally, by using Heisenberg uncertainty principle in linear canonical transform domain, we obtain Heisenberg uncertainty principle of Hartley transform in linear canonical transform domain.

关 键 词：HARTLEY变换 线性正则变换 不确定性原理 信息熵 

分 类 号：TN911.7[电子电信—通信与信息系统]