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Analysis of intrinsic mode functions: A PDE approach

Analyse des modes empiriques : une approche EDP

Type
Articles dans des revues avec comité de lecture
Author
DIOP, El Hadji
13094 Institut de Recherche de l'Ecole Navale [IRENAV]
ALEXANDRE, Radjesvarane
13094 Institut de Recherche de l'Ecole Navale [IRENAV]
BOUDRAA, Abdel-Ouahab
13094 Institut de Recherche de l'Ecole Navale [IRENAV]

URI
http://hdl.handle.net/10985/8986
DOI
10.1109/LSP.2009.2038770
Date
2010
Journal
IEEE Signal Processing Letters

Abstract

The empirical mode decomposition is a powerful tool for signal processing. Because of its original algorithmic, recent works have contributed to its theoretical framework. Following these works, some mathematical contributions on its comprehension and formalism are provided. In this paper, the so called local mean is computed in such a way that it allows the use of differential calculus on envelopes. This new formulation makes us prove that iterations of the sifting process are well approximated by the resolution of partial differential equations (PDE). Intrinsic mode functions are originally defined in a intuitive way. Herein, a mathematical characterization of modes is given with the proposed PDE based approach.

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