RECENT MATHEMATICAL DEVELOPMENTS ON EMPIRICAL MODE DECOMPOSITION

被引：13
|
作者：
Xu, Yuesheng [1 ,2 ]
Zhang, Haizhang [3 ]
机构：
[1] Syracuse Univ, Dept Math, Syracuse, NY 13244 USA
[2] Sun Yat Sen Univ, Sch Math & Computat Sci, Guangzhou 510275, Guangdong, Peoples R China
[3] Univ Michigan, Ann Arbor, MI 48109 USA
来源：
ADVANCES IN DATA SCIENCE AND ADAPTIVE ANALYSIS | 2009年 / 1卷 / 04期
基金：
美国国家科学基金会;
关键词：
Empirical mode decomposition; the Hilbert-Huang transform; intrinsic mode functions; mathematical foundation; spectral sequences; orthonormal bases; nonlinear phases; the Bedrosian identity;
D O I：
10.1142/S1793536909000242
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Building the mathematical foundation for the empirical mode decomposition is an important issue in adaptive data analysis. The task of building such a foundation consists of two stages. The first is to construct a large bank of basis functions for the time-frequency analysis of nonlinear and nonstationary signals. The second is to establish a fast adaptive decomposition algorithm. We survey recent mathematical progress on these two stages. Related results on piecewise linear spectral sequences and the Bedrosian identity are also reviewed.
引用
收藏
页码：681 / 702
页数：22
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