Skip to main content
SpringerLink
Log in

Adaptive Multiscale Time-Frequency Analysis

  • Chapter
Springer Handbook of Bio-/Neuroinformatics

Part of the book series: Springer Handbooks ((SHB))

Abstract

Time-frequency analysis techniques are now adopted as standard in many applied fields, such as bio-informatics and bioengineering, to reveal frequency-specific and time-locked event-related information of input data. Most standard time-frequency techniques, however, adopt fixed basis functions to represent the input data and are thus suboptimal. To this cause, an empirical mode decomposition (EMD) algorithm has shown considerable prowess in the analysis of nonstationary data as it offers a fully data-driven approach to signal processing. Recent multivariate extensions of the EMD algorithm, aimed at extending the framework for signals containing multiple channels, are even more pertinent in many real world scenarios where multichannel signals are commonly obtained, e.g., electroencephalogram (EEG) recordings. In this chapter, the multivariate extensions of EMD are reviewed and it is shown how these extensions can be used to alleviate the long-standing problems associated with the standard (univariate) EMD algorithm. The ability of the multivariate extensions of EMD as a powerful real world data analysis tool is demonstrated via simulations on biomedical signals.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 269.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 349.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Abbreviations

2-D:

two-dimensional

3-D:

three-dimensional

BCI:

brain-computer interface

BEMD:

bivariate EMD

CEMD:

complex EMD

CSP:

common spatial pattern

DFT:

discrete Fourier transform

EEG:

electroencephalography

EEMD:

extended empirical mode decomposition

EMD:

empirical mode decomposition

ERS:

event-related synchronization

FGN:

fractional Gaussian noise

IMF:

intrinsic mode function

IV:

intravenous

MEG:

magnetoencephalography

MEMD-CSP:

multivariate EMD-common spatial pattern

MEMD:

multivariate EMD

NA-MEMD:

noise-assisted MEMD

PCV:

phase coherence value

RI-EMD:

rotation-invariant EMD

SMR:

sensorimotor rhythm

SSVEP:

steady state visual evoked potential

STFT:

short-time Fourier transform

TEMD:

trivariate EMD

WGN:

white Gaussian noise

References

  1. N.E. Huang, Z. Shen, S. Long, M. Wu, H. Shih, Q. Zheng, N. Yen, C. Tung, H. Liu: The empirical mode decomposition and Hilbert spectrum for non-linear and non-stationary time series analysis, Proc. R. Soc. A 454, 903–995 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  2. N.E. Huang, Z. Wu: A review on Hilbert-Huang transform: Method and its applications to geophysical studies, Rev. Geophys. 46, RG2006 (2008)

    Article  Google Scholar 

  3. D. Looney, C. Park, P. Kidmose, M. Ungstrup, D.P. Mandic: Measuring phase synchrony using complex extensions of EMD, Proc. IEEE Stat. Signal Process. Symp. (2009) pp. 49–52

    Google Scholar 

  4. G. Rilling, P. Flandrin, P. Goncalves, J.M. Lilly: Bivariate empirical mode decomposition, IEEE Signal Process. Lett. 14, 936–939 (2007)

    Article  Google Scholar 

  5. N. Rehman, D.P. Mandic: Empirical mode decomposition for trivariate signals, IEEE Trans. Signal Process. 58, 1059–1068 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. N. Rehman, D.P. Mandic: Multivariate empirical mode decomposition, Proc. R. Soc. A 466, 1291–1302 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  7. N. Rehman, D.P. Mandic: Filterbank property of multivariate empirical mode decomposition, IEEE Trans. Signal Process. 59, 2421–2426 (2011)

    Article  MathSciNet  Google Scholar 

  8. N.E. Huang, M. Wu, S. Long, S. Shen, W. Qu, P. Gloersen, K. Fan: A confidence limit for the empirical mode decomposition and Hilbert spectral analysis, Proc. R. Soc. A 459, 2317–2345 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  9. N.E. Huang, Z. Wu, S.R. Long, K.C. Arnold, K. Blank, T.W. Liu: On instantaneous frequency, Adv. Adapt. Data Anal. 1, 177–229 (2009)

    Article  MathSciNet  Google Scholar 

  10. D.P. Mandic, V.S.L. Goh: Complex Valued Non-linear Adaptive Filters: Noncircularity, Widely Linear Neural Models (Wiley, New York 2009)

    Book  Google Scholar 

  11. T. Tanaka, D.P. Mandic: Complex empirical mode decomposition, IEEE Signal Process. Lett. 14(2), 101–104 (2006)

    Article  Google Scholar 

  12. M.U. Altaf, T. Gautama, T. Tanaka, D.P. Mandic: Rotation invariant complex empirical mode decomposition, Proc. IEEE Int. Conf. Acoust. (2007), Speech, Signal Process.

    Google Scholar 

  13. H. Niederreiter: Random number generation and quasi-Monte Carlo methods, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 63 (Society for Industrial and Applied Mathematics, Philadelphia 1992)

    Google Scholar 

  14. J. Cui, W. Freeden: Equidistribution on the sphere, Siam J. Sci. Comput. 18(2), 595–609 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  15. N. Rehman, Y. Xia, D.P. Mandic: Application of multivariate empirical mode decomposition for seizure detection in EEG signals, Proc. 32rd Annu. Int. Conf. IEEE Eng. Med. Biol. Soc. (EMBC) (2010) pp. 1650–1653

    Google Scholar 

  16. D. Looney, D.P. Mandic: Multi-scale image fusion using complex extensions of EMD, IEEE Trans. Signal Process. 57(4), 1626–1630 (2009)

    Article  MathSciNet  Google Scholar 

  17. P. Flandrin, G. Rilling, P. Goncalves: Empirical mode decomposition as a filter bank, IEEE Signal Process. Lett. 11, 112–114 (2004)

    Article  Google Scholar 

  18. K.J. Friston, K.M. Stephan, R.S.J. Frackowiak: Transient phase locking and dynamic correlations: Are they the same thing?, Human Brain Mapp. 5, 48–57 (1997)

    Article  Google Scholar 

  19. G. Tononi, M. Edelman: Consciousness and complexity, Science 282, 1846–1851 (1998)

    Article  Google Scholar 

  20. R. Srinivasan, D. Russell, G. Edelman, G. Tononi: Increased synchronization of neuromagnetic responses during conscious perception, J. Neurosci. 19(13), 5435–5448 (1999)

    Google Scholar 

  21. V. Menon, W.J. Freeman, B.A. Cutillo, J.E. Desmond, M.F. Ward, S.L. Bressler, K.D. Laxer, N. Barbaro, A.S. Gevins: Spatio-temporal correlations in human gamma band electrocorticograms, Electroencephalogr. Clin. Neurophysiol. 98(2), 89–102 (1996)

    Article  Google Scholar 

  22. R. Ferri, F. Rundo, O. Bruni, M. Terzano, C. Stam: Dynamics of the EEG slow-wave synchronization during sleep, Clin. Neurophysiol. 116(12), 2783–2795 (2005)

    Article  Google Scholar 

  23. E.R. Kandel, J.H. Schwartz: Principles of Neural Science, 3rd edn. (Appleton and Lange, Norwalk 1985)

    Google Scholar 

  24. J. Lachaux, A. Lutz, D. Rudrauf, D. Cosmelli, M. Quyen, J. Martinerie, F. Varela: Estimating the time-course of coherence between single-trial brain signals: An introduction to wavelet coherence, Clin. Neurophysiol. 32(3), 157–174 (2002)

    Article  Google Scholar 

  25. P. Tass, M.G. Rosenblum, J. Weule, J. Kurths, A. Pikovsky, J. Volkmann, A. Schnitzler, H.-J. Freund: Detection of n:m phase locking from noisy data: Application to magnetoencephalography, Phys. Rev. Lett. 81(15), 3291–3294 (1998)

    Article  Google Scholar 

  26. C.M. Sweeny-Reed, S.J. Nasuto: A novel approach to the detection of synchronisation in EEG based on empirical mode decomposition, J. Comput. Neurosci. 23(1), 79–111 (2007)

    Article  Google Scholar 

  27. A.Y. Mutlu, S. Aviyente: Multivariate empirical mode decomposition for quantifying multivariate phase synchronization, EURASIP J. Adv. Signal Process. 2011, 1–13 (2011)

    Article  Google Scholar 

  28. G. Pfurtscheller, C. Neuper, D. Flotzinger, M. Pregenzer: EEG-based discrimination between imagination of right and left hand movement, Electroencephalogr. Clin. Neurophysiol. 103(6), 642–651 (1997)

    Article  Google Scholar 

  29. G. Pfurtscheller, F.H. Lopes da Silva: Event-related EEG/MEG synchronization and desynchronization: Basic principles, Clin. Neurophysiol. 110(11), 1842–1857 (1999)

    Article  Google Scholar 

  30. B. Blankertz: BCI Competition IV (Berlin Institute of Technology), accessable online at http://www.bbci.de/competition/iv/

  31. H. Ramoser, J. Muller-Gerking, G. Pfurtscheller: Optimal spatial filtering of single trial EEG during imagined hand movement, IEEE Trans. Rehabil. Eng. 8(4), 441–446 (2000)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. COMSATS Institute of Information Technology, Park Road, Chak Shahzad, Islamabad, Pakistan

    Naveed ur Rehman

  2. Communication and Signal Processing Research Group, Department of Electrical and Electronic Engineering, Imperial College London, Exhibition Road, SW7 2BT, London, UK

    David Looney

  3. Department of BioEngineering, University California, San Diego, 9500 Gilman Drive, 92093, La Jolla, CA, USA

    Cheolsoo Park

  4. Department of Electrical and Electronic Engineering, Communication and Signal Processing Research Group, Imperial College London, Exhibition Road, SW7 2BT, London, UK

    Danilo P. Mandic

Authors
  1. Naveed ur Rehman
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. David Looney
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Cheolsoo Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Danilo P. Mandic
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Naveed ur Rehman , David Looney , Cheolsoo Park or Danilo P. Mandic .

Editor information

Editors and Affiliations

  1. KEDRI – Knowledge Engineering and Discovery Research Institute, Auckland University of Technology, 120 Mayoral Drive, 1010, Auckland, New Zealand

    Nikola Kasabov

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer-Verlag

About this chapter

Cite this chapter

Rehman, N.u., Looney, D., Park, C., Mandic, D.P. (2014). Adaptive Multiscale Time-Frequency Analysis. In: Kasabov, N. (eds) Springer Handbook of Bio-/Neuroinformatics. Springer Handbooks. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30574-0_43

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-30574-0_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30573-3

  • Online ISBN: 978-3-642-30574-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation