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希尔伯特-黄变换中的一种新包络线算法
引用本文:钟佑明,金涛,秦树人.希尔伯特-黄变换中的一种新包络线算法[J].数据采集与处理,2005,20(1):13-17.
作者姓名:钟佑明  金涛  秦树人
作者单位:重庆大学机械工程学院测试中心,重庆,400030
基金项目:国家自然科学基金 ( 5 0 1 3 5 0 5 0 )资助项目,国家自然科学基金 ( 5 0 2 75 1 5 4)资助项目
摘    要:先介绍希尔伯特一黄变换(Hilbert Huang transform,HHT)中的包络线算法,分析了两种具代表性的算法——三次样条插值法和Akima插值法存在的问题;然后在抛物线参数样条插值法原理的启发下证明了分段光滑定理,依据该定理并结合直观的几何意义提出了一种新包络线算法——分段幂函数法。算例表明,在某些情况下新算法比三次样条插值法具有更好的“柔性”,比Akima插值法具有更好的“光滑性”,用其进行HHT分析时出现虚假频率的概率更小。

关 键 词:变换  希尔伯特  定理  光滑性  新算法  幂函数  插值法  三次样条插值  包络线  算例
文章编号:1004-9037(2005)01-0013-05
修稿时间:2003年7月30日

New Envelope Algorithm for Hilbert-Huang Transform
ZHONG You-ming,Jin Tao,QIN Shu-ren.New Envelope Algorithm for Hilbert-Huang Transform[J].Journal of Data Acquisition & Processing,2005,20(1):13-17.
Authors:ZHONG You-ming  Jin Tao  QIN Shu-ren
Abstract:Hilbert-Huang transform (HHT) is a new method for signal analysis developed by Norden.E.Huang et al in 1998. The key problem is the envelope (-fitting) algorithm, however, the existing algorithms are still not very perfect. This paper first introduces the problem of envelope algorithm of HHT and analyzes the shortages of two shorts of classical envelope algorithms, i.e. cubic spline interpolation algorithm and Akima interpolation algorithm. According to the principle of the parabola parameter spline interpolation algorithm, an important conclusion, called section slide theorem is proved with eyeable geometry meaning and a new envelope algorithm-subsection power function method is presented. The new envelope algorithm is worthy of being referred and applied since some examples have shown that the new envelope algorithm sometimes is softer than cubic spline interpolation algorithm and slider than Akima interpolation algorithm, and it brings less persuade frequency in HHT analysis.
Keywords:signal analysis  algorithm  Hilbert-Huang transform  envelope  subsection power function method
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