One or Two Frequencies? The Empirical Mode Decomposition Answers

By Gabriel Rilling, Patrick Flandrin. IEEE Transactions on Signal Processing, 2008

610 citations recorded by the source corpus.

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.

Subfields: Cardiology and Cardiovascular Medicine, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/ec41e2a30c0301f08802572d2bfee7ab4d75c8ef

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In Cardiology and Cardiovascular Medicine

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Citations in the corpus

Variational Mode Decomposition (2014, background): “The lack of mathematical theory and the aformentioned degrees of freedom reducing the algorithm’s robustness all leave room for theoretical development and improvement on the robustness of the decomposition [2], [3].”
Analysis of daily river flow fluctuations using Empirical Mode Decomposition and arbitrary order Hilbert spectral analysis (2009, methodology): “However, this is beyond our topic here: for more details122 about the EMD method, we refer to Huang et al. (1998, 1999); Rilling et al.123 (2003); Huang et al. (2003); Flandrin et al. (2004); Flandrin and Gonçalvès124 (2004); Huang (2005); Rilling and Flandrin (2008).125 2.2.”
A time varying filter approach for empirical mode decomposition (2017, methodology): “Firstly, we fully address the separation problem [7] as well as the intermittence problem [8].”
Empirical Mode Decomposition-Based Time-Frequency Analysis of Multivariate Signals: The Power of Adaptive Data Analysis (2013, background): “35 s) [20], despite the actual reconstruction based on (2) still being perfect.”
Multivariate empirical mode decomposition (2010, methodology): “Notice the similar separability of the tones as with standard EMD; for more detail, see Rilling & Flandrin (2008).”
Time-Frequency Reassignment and Synchrosqueezing: An Overview (2013, background): “The separation power of EMD was studied in [27] and depends on the amplitude and frequency ratio between the modes: if they are too close, EMD cannot separate them.”
The Synchrosqueezing algorithm for time-varying spectral analysis: Robustness properties and new paleoclimate applications (2011, neutral): “In general, EMD/EEMD is sensitive to amplitude changes over time that impose strong requirements on the frequency separation between the components [37], while Synchrosqueezing and the other time-frequency methods produce good results as long as the bandwidth of the mother wavelet or window is small”
The Monogenic Synchrosqueezed Wavelet Transform: A tool for the Decomposition/Demodulation of AM-FM images (2012, neutral): “MSC 2010: 65T60, 92C55, 94A08.”
Synchrosqueezed wavelet transforms: An empirical mode decomposition-like tool (2011, background): “The decomposition of signals that are superpositions of a few cosines was studied in [10], with interesting results.”
Nonlinear Chirp Mode Decomposition: A Variational Method (2017, methodology): “For instance, these EMD-based methods have poor resolution to separate close modes [13].”
Development of EMD-Based Denoising Methods Inspired by Wavelet Thresholding (2009, result): “This is in agreement with the analytically derived frequency responses of the equivalent filtering operations that correspond to EMDs with different number of sifting iterations in a two-sinusoids signal case [6].”