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 trans-form 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 func-tion 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 ca-nonical 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.
展开▼
