1. Bivariate Empirical Mode Decomposition
- Author
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Patrick Flandrin, P. Gonalves, Jonathan M. Lilly, Gabriel Rilling, Laboratoire de Physique de l'ENS Lyon (Phys-ENS), École normale supérieure de Lyon (ENS de Lyon)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon-Centre National de la Recherche Scientifique (CNRS), Laboratoire de l'Informatique du Parallélisme (LIP), Université de Lyon-Université de Lyon-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS), Earth and Space Research Institute [Seattle] (ESR), École normale supérieure - Lyon (ENS Lyon)-Centre National de la Recherche Scientifique (CNRS)-Université Claude Bernard Lyon 1 (UCBL), Université de Lyon-Université de Lyon, École normale supérieure - Lyon (ENS Lyon)-Université Claude Bernard Lyon 1 (UCBL), Flandrin, Patrick, and Gonçalves, Paulo
- Subjects
Bivariate time series ,Mathematical optimization ,[INFO.INFO-TS] Computer Science [cs]/Signal and Image Processing ,02 engineering and technology ,Bivariate analysis ,Hilbert–Huang transform ,[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing ,0202 electrical engineering, electronic engineering, information engineering ,Applied mathematics ,Electrical and Electronic Engineering ,MATLAB ,ComputingMilieux_MISCELLANEOUS ,[SPI.SIGNAL] Engineering Sciences [physics]/Signal and Image processing ,Mathematics ,computer.programming_language ,Signal processing ,Complex-valued signals ,Series (mathematics) ,Applied Mathematics ,SIGNAL (programming language) ,020206 networking & telecommunications ,Extension (predicate logic) ,Nonlinear system ,Signal Processing ,Empirical Mode Decomposition ,020201 artificial intelligence & image processing ,[SPI.SIGNAL]Engineering Sciences [physics]/Signal and Image processing ,computer - Abstract
10 pages, 3 figures. Submitted to Signal Processing Letters, IEEE. Matlab/C codes and additional material are downloadable from http://perso.ens-lyon.fr/patrick.flandrin; The Empirical Mode Decomposition (EMD) has been introduced quite recently to adaptively decompose nonstationary and/or nonlinear time series. The method being initially limited to real-valued time series, we propose here an extension to bivariate (or complex-valued) time series which generalizes the rationale underlying the EMD to the bivariate framework. Where the EMD extracts zero-mean oscillating components, the proposed bivariate extension is designed to extract zero-mean rotating components. The method is illustrated on a real-world signal and properties of the output components are discussed. Free Matlab/C codes are available at http://perso.ens-lyon.fr/patrick.flandrin.
- Published
- 2007
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