UREM-ULB :
Unité de Recherche sur l’Enseignement des Mathématiques

International Francqui Chair 2009-2010 : Prof. Ingrid Daubechies (Princeton University)

Synchrosqueezed Wavelet Transforms : a Tool for Empirical Mode Decomposition

April 23th 2010, 16h00.

Université Libre de Bruxelles, Campus Plaine, Forum D.

Conférence destinée à des mathématiciens et des scientifiques à partir de BA1.

The EMD algorithm, first proposed by Norden Huang, made more robust as well as more versatile by Huang and Zhaohua Wu, 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. This decomposition has shown its usefulness in a wide range of applications including meteorology, structural stability analysis and medical studies. On the other hand, the EMD algorithm contains heuristic and ad-hoc elements that make it hard to analyze mathematically. The talk will describe a method that captures the flavor and philosophy of the EMD approach, albeit using a different approach in constructing the components. We shall define 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 the new method does indeed succeed in decomposing arbitrary functions in this class. We provide several examples, for simulated as well as real data.