Generalized Hilbert transform and its properties in 2D LCT domain
Generalized Hilbert transform and its properties in 2D LCT domain
复制标题
DOI：
10.1016/j.sigpro.2009.01.009
复制
发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Guanlei Xu;Xiaotong Wang;Xiaogang Xu
中科院分区：
文献类型：
--
作者：
Guanlei Xu;Xiaotong Wang;Xiaogang Xu
希尔伯特变换在信号处理中起着重要作用。随着新变换的发展，一维（1D）希尔伯特变换已扩展到分数阶傅里叶变换域。然而，由于二维信号的复杂性和LCT参数较多的原因，线性正则变换(LCT)域中的二维(2D)希尔伯特变换的研究变得复杂，目前还处于起步阶段。本文给出了LCT域中半平面Hilbert变换、互正交Hilbert变换和单正交Hilbert变换的定义。此外，还讨论了时域和变换域之间的关系。此外，还获得了一些重要的性质和结论。最后，我们定义并推导了LCT域中的2D Bedrosian原理。
Hilbert transform plays an important role in signal processing. With the development of new transforms, one-dimensional (1D) Hilbert transform has been extended into fractional Fourier transform domain. However, the researches of two-dimensional (2D) Hilbert transform in linear canonical transform (LCT) domain become complicated for the reasons of the complexity of 2D signals and more parameters in LCT, and now they are in the infancy. In this paper, the definitions of half-planed Hilbert transform, cross-orthant Hilbert transform and single-orthant Hilbert transform are yielded in LCT domain. In addition, the relation between time domain and transformed domain are discussed. Moreover, some important properties and conclusions are obtained as well. Finally, we defined and derived 2D Bedrosian's principle in LCT domain.