Extracting oscillating components from nonstationary time series: A wavelet-induced method

This paper consists in the description and application of a method called wavelet-induced mode extraction (WIME) in the context of time-frequency analysis. WIME aims to extract the oscillating components that build amplitude modulated-frequency modulated signals. The essence of this technique relies on the successive extractions of the dominant ridges of wavelet-based time-frequency representations of the signal under consideration. Our tests on simulated examples indicate strong decomposition and reconstruction skills, trouble-free handling of crossing trajectories in the time-frequency plane, sharp performances in frequency detection in the case of mode-mixing problems, and a natural tolerance to noise. These results are compared with those obtained with empirical mode decomposition. We also show that WIME still gives meaningful results with real-life data, namely, the Oceanic Niño Index