分数阶希尔伯特变换的复包络分析

Analysis on Envelope of Two Complex Signals Based on Fractional Hilbert Transform

分数Hilbert变换,也即传统的Hilbert变换由整数阶向分数阶的推广,由此其应用领域也得到了扩展,譬如在通信中的单边带调制解调系统,图像的边缘提取等领域中得到广泛的应用。首先,文中回顾了利用经典希尔伯特变换的正交性把经典的Hilbert变换的定义形式进行广义化后得到的分数阶Hilbert变换,并讨论了由分数阶Hilbert变换构造的两类复信号,最后讨论了这两类复信号的包络提取并且给出了具体的实例。

Fractional Hilbert transform, that is, the traditional Hilbert fractional order has expanded i demodulation system and in image ts ed expression of Hilbert transform in application fields, such as the wide-use in ge th extraction. Firstly, fractional Hilbert e frequency domain and the effect on the transfo single transfo phase, rm from integral order to sideband modulation and rm is obtained based on the meanwhile its formulation expressed by using Hilbert transform is educed. Then the structural transformation of the fractional analysis of the signal expression by using the fractional Hilbert transform is discussed. Finally, the fractional analysis of the signal envelope extraction and concrete examples is given