线性正则变换域的Hilbert变换

Hilbert Transform Associated with the Linear Canonical Transform

Hilbert变换(HT)是信号处理中的一个重要的变换关系式,它被广泛应用于调制理论、边缘检测以及滤波器设计等方面,通过HT可以把一个信号与它的解析信号联系在一起;而线性正则变换(LCT)是Fourier变换(FT)、分数阶Fourier变换(FRFT)的进一步推广,是更一般形式的变换。给出LCT域中HT的定义,并指出这种LCT域中HT与传统的FT域的HT有类似的性质。

Hilbert transform（HT） is an important signal processing tool that is used in many applications such as modulations, edge detection and filter design in signal processing. An analytic signal and its original signal are connected by the HT. At the same time, the linear canonical transform （LCT） is the generalized form of Fourier transform and the fractional Fourier transform, it can be considered as a general linear transform. The definition and properties of Hilbert transform in linear canonical transform domain were proposed. Some important properties of this kind of Hilbert transform were given, and it is shown that the newly defined Hilbert transform has some similar properties with the Hilbert transform in the traditional Fourier transform domain.