On empirical mode decomposition and its algorithms
This presentation is the property of its rightful owner.
Sponsored Links
1 / 111

On Empirical Mode Decomposition and its Algorithms PowerPoint PPT Presentation


  • 110 Views
  • Uploaded on
  • Presentation posted in: General

On Empirical Mode Decomposition and its Algorithms. G. Rilling, P. Flandrin (Cnrs - Éns Lyon, France) P. Gonçalvès (Inria Rhône-Alpes, France). outline. Empirical Mode Decomposition (EMD) basics examples algorithmic issues elements of performance evaluation perspectives. basic idea.

Download Presentation

On Empirical Mode Decomposition and its Algorithms

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


On Empirical Mode Decomposition and its Algorithms

G. Rilling, P. Flandrin (Cnrs - Éns Lyon, France)

P. Gonçalvès (Inria Rhône-Alpes, France)

IEEE-EURASIP Workshop on Nonlinear Signal and Image Processing, Grado (I), June 9-11, 2003


outline

  • Empirical Mode Decomposition (EMD) basics

  • examples

  • algorithmic issues

  • elements of performance evaluation

  • perspectives


basic idea

  • « multimodal signal = fast oscillations on the top of slower oscillations »

  • Empirical Mode Decomposition (Huang)

    • identify locally the fastest oscillation

    • substract to the signal and iterate on the residual

    • data-driven method, locally adaptive and multiscale


Huang’s algorithm

  • compute lower and upper envelopes from interpolations between extrema

    • substract mean envelope from signal

    • iterate until mean envelope = 0 and #{extrema} = #{zero-crossings} ± 1

  • substract the obtained Intrinsic Mode Function (IMF) from signal and iterate on residual


how EMD works


EMD and AM-FM signals

  • quasi-monochromatic harmonic oscillations

  • self-adaptive time-variant filtering

  • example : 2 sinus FM + 1 Gaussian wave packet


EMD


time-frequency signature


time-frequency signature


time-frequency signature


time-frequency signature


nonlinear oscillations

  • IMF ≠ Fourier mode and, in nonlinear situations, 1 IMF = many Fourier modes

  • example : 1 HF triangle + 1 MF tone + 1 LF triangle


EMD


issues

  • algorithm ?

    • intuitive but ad-hoc procedure, not unique

    • several user-controlled tunings

  • performance ?

    • difficult evaluation since no analytical definition

    • numerical simulations


algorithmic issues

  • interpolation

    • type ? cubic splines

    • border effects ? mirror symmetry

  • stopping criteria

    • mean zero ? 2 thresholds

    • variation 1 : « local EMD »

  • computational burden

    • about log2 N IMF ’s for N data points

    • variation 2 : « on-line EMD »


performance evaluation

  • extensive numerical simulations

  • deterministic framework

    • importance of sampling

    • ability to resolve multicomponent signals

  • a complement to stochastic studies

    • noisy signals + fractional Gaussian noise

    • PF et al., IEEE Sig. Proc. Lett., to appear


EMD of fractional Gaussian noise


1. EMD and (tone) sampling


case 1 — oversampling


equal height maxima


constant upper envelope


equal height minima


constant lower envelope


zero mean : tone = IMF


case 2 — moderate sampling


fluctuating maxima


modulated upper envelope


fluctuating minima


modulated lower envelope


non zero mean : tone ≠ IMF


experiment 1

  • 256 points tone, with 0 ≤ f ≤1/2

  • error = normalized L2 distance comparing tone vs. IMF #1

  • minimum when 1/f even multiple of the sampling period


experiment 2

  • 256 points tones, with 0 ≤ f1 ≤1/2 and f2 ≤ f1

  • error = weighted normalized L2 distance comparing tone #1 vs. IMF #1, and tone #2 vs. max{IMF #k, k ≥ 2}


experiment 3

  • intertwining of amplitude ratio, sampling rate and frequency spacing

  • dominant effect when f1 ≤ 1/4 : constant-Q (wavelet-like) « confusion band »


concluding remarks

  • EMD is an appealing data-driven and multiscale technique

  • spontaneous dyadic filterbank structure in « stationary » situations, stochastic (fGn) or not (tones)

  • EMD defined as output of an algorithm: theoretical framework beyond numerical simulations?


(p)reprints, Matlab codes and demoswww.ens-lyon.fr/~flandrin/emd.html


  • Login