Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool

The EMD algorithm is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of components, well separated in the time–frequency plane, each of which can be viewed as approximately harmonic locally, with slowly varying amplitu...

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Vydáno v:Applied and computational harmonic analysis Ročník 30; číslo 2; s. 243 - 261
Hlavní autoři: Daubechies, Ingrid, Lu, Jianfeng, Wu, Hau-Tieng
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier Inc 01.03.2011
Témata:
Algorithms
Decomposition
Empirical mode decomposition
Harmonics
Mathematical analysis
Mathematical models
Medical
Philosophy
Synchrosqueezing
Time-frequency analysis
Wavelet
Wavelet transforms
Wavelet
Time-frequency analysis
Empirical mode decomposition
Synchrosqueezing
ISSN:1063-5203, 1096-603X
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Popis
Shrnutí:The EMD algorithm is a technique that aims to decompose into their building blocks functions that are the superposition of a (reasonably) small number of components, well separated in the time–frequency plane, each of which can be viewed as approximately harmonic locally, with slowly varying amplitudes and frequencies. The EMD has already shown its usefulness in a wide range of applications including meteorology, structural stability analysis, medical studies. On the other hand, the EMD algorithm contains heuristic and ad hoc elements that make it hard to analyze mathematically. In this paper we describe a method that captures the flavor and philosophy of the EMD approach, albeit using a different approach in constructing the components. The proposed method is a combination of wavelet analysis and reallocation method. We introduce a precise mathematical definition for a class of functions that can be viewed as a superposition of a reasonably small number of approximately harmonic components, and we prove that our method does indeed succeed in decomposing arbitrary functions in this class. We provide several examples, for simulated as well as real data.
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ISSN:1063-5203
1096-603X
DOI:10.1016/j.acha.2010.08.002