希尔伯特-黄变换的端点延拓

Practical implementation of the Hilbert-Huang Transform algorithm

希尔伯特-黄变换(HHT)是近年来发展起来的一种新的时间序列信号分析方法.该文在对HHT深入研究与充分肯定的基础上,发展了信号的镜像闭合延拓和包络的极值延拓两种方法.通过几个典型的例子检验了两种方法,并与Huang等(1998,1999)进行了比较,得到了令人满意的结果.镜像闭合延拓法根据信号端点的分布特性,把镜子放在具有对称性的极值位置,通过镜像法把镜内信号映射成一个周期性的信号,不存在端点,从根本上避免了经验模态分解和希尔伯特变换的端点问题.极值延拓法简单易行,具有与镜像闭合法相当的效果,在处理非对称波形信号时更显其优越性.

Hilbert-Huang Transform (HHT)is a newly developed powerful method for nonlinear and non-stationary time series analysis. The empirical mode decomposition is the key part of HHT, while its algorithm was protected by NASA as a US patent, which limits the widely application among the scientific community. Two approaches, mirror periodic and extrema extending methods, have been developed for handling the end effects of empirical mode decomposition. The implementation of the HHT is realized in detail to widen the application. The detail comparison of results from two methods with that from Huang et al. (1998, 1999), as well as the comparison between two methods is presented. Generally, both methods reproduce faithful results as that of Huang et al. For mirror periodic method (MPM), the data is extended once forever. Ideally, it is a way for handling the end effects of the HHT, especially for the signal that has symmetric waveform. The extrema extending method(EEM) behaves as good as MPM, and it is better than MPM for the signal that has strong asymmetric waveform. However, it has to perform extrema envelope extending in every shifting process.