One or Two Frequencies? The Empirical Mode Decomposition Answers

• Published in: IEEE transactions on signal processing 2008-01, Vol.56 (1), p.85-95
• Main Authors: Rilling, G., Flandrin, P.
• Format: Article
• Language: English
• Subjects: Amplitude estimation; Amplitude modulation; Amplitudes; Applied sciences; Decomposition; Ear; Empirical analysis; Empirical mode decomposition (EMD); Exact sciences and technology; Frequency estimation; Humans; Information, signal and communications theory; Mathematical models; Nonlinearity; Physics; resolution; Signal analysis; Signal and communications theory; Signal processing; Signal representation. Spectral analysis; Signal resolution; Signal, noise; Spectral analysis; Telecommunications and information theory; time frequency; Time frequency analysis; Unity; Waveforms
• ISSN: 1053-587X; 1941-0476
• DOI: 10.1109/TSP.2007.906771

This paper investigates how the empirical mode decomposition (EMD), a fully data-driven technique recently introduced for decomposing any oscillatory waveform into zero-mean components, behaves in the case of a composite two-tones signal. Essentially two regimes are shown to exist, depending on whether the amplitude ratio of the tones is greater or smaller than unity, and the corresponding resolution properties of the EMD turn out to be in good agreement with intuition and physical interpretation. A refined analysis is provided for quantifying the observed behaviors and theoretical claims are supported by numerical experiments. The analysis is then extended to a nonlinear model where the same two regimes are shown to exist and the resolution properties of the EMD are assessed.