Abstract

Empirical Wavelet Transform (EWT)

Jerome Gilles
University of California, Los Angeles (UCLA)
Department of Mathematics

I will present an ongoing work about the construction
of a new kind of wavelet. Contrarilly to classical wavelets which are a priori fixed the proposed ones are adaptive with regards to the signal we want to analyze. This approach combines the idea of the Empirical Mode Decomposition (EMD) and the wavelet theory.
I will present concepts taken from either the wavelet theory and the EMD which will be useful to our approach. Then I will show how to build empirical wavelets, give the condition to reach the orthonormality and give the corresponding algorithm. I will present many experiments both on simulated signals and a real Electrocardiogram (ECG) signal. In conclusion I will discuss the possible evolutions of this approach, its extension to images (and N-dimensional signals) and possible applications.