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

页码：681 / 702

页数：22

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