二维Hilbert变换研究

Review of Bidimensional Hilbert Transform

Hilbert变换是信号处理的重要工具之一,具有许多优良性能。对二维Hilbert变换研究工作进行总结,分析传统二维Hilbert变换、分数阶变换域内的二维Hilbert变换、广义分数阶变换域内的二维Hilbert变换等各类二维Hilbert变换的优缺点,同时对与Hilbert变换密切相关的二维Bedrosian定理进行分析,指出现有研究工作中存在的问题和研究方向,以期能为Hilbert变换研究人员提供相关借鉴。

Hilbert transform is one of the useful tool in signal processing, and much effective performance have been found. In this paper, the current work of the bi-dimensional Hilbert transform is reviewed, the advantage and shortage of different kind of bi-dimensional Hilbert transform is analyzed, they are the traditional hi-dimensional Hilbert transform, bi-dimensional Hilbert transform in fractional Fourier transform domains, bi-dimensional Hilbert transform in generalized fractional Fourier transform domains, by the way, bi-Dimensional Bedrosian＇s Principle is analyzed too. At last, current questions and some useful further study work are proposed, in order to provide the relevant reference for the Hilbert transformation researchers.