Skip to main content
SpringerLink
Log in

Wavelet Analysis

  • Living reference work entry
  • First Online:
Encyclopedia of Computational Neuroscience

Definition

Wavelet analysis is a powerful signal processing method that represents a signal in terms of wavelets. A wavelet or small wave is a wavelike function, upon scaled and translated, that can be used to decompose a signal into its basic constituent components at different scales. Each scale component can be converted into a frequency range. The resulting wavelet transform measures the time-frequency variations of frequency components in a nonstationary signal. Wavelet analysis is thus a natural choice for the analysis of neural data in which the nonstationarity is abundant.

Detailed Description

Techniques for wavelet analysis generally consist of continuous and discrete wavelet transforms that are below described and related to each other. Wavelet analysis is then contrasted with Fourier analysis, followed by its applications in neural data analysis.

Continuous and Discrete Wavelet Transforms

Continuous wavelet transform (CWT) is used to decompose a continuous time signal into...

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

Access this chapter

Log in via an institution

Institutional subscriptions

References

  • Bartnik EA, Blinowska KJ, Durka PJ (1992) Single evoked potential reconstruction by means of wavelet transform. Biol Cybern 67:175–181

    Article  CAS  PubMed  Google Scholar 

  • Bertrand O, Bohorquez J, Pernier J (1994) Time-frequency digital filtering based on an invertible wavelet transform: an application to evoked potentials. IEEE Trans Biomed Eng 41:77–88

    Article  CAS  PubMed  Google Scholar 

  • Blanco S, Figliola A, Quian QR, Rosso O (1998) Time-frequency analysis of electroencephalogram series (III): information transfer function and wavelets packets. Phys Rev E 57:932–940

    Article  CAS  Google Scholar 

  • Daubechies I (1992) Ten lectures on wavelets. SIAM, Philadelphia

    Book  Google Scholar 

  • Hulata E, Segev R, Shapir Y, Benveniste M, Ben-Jacob E (2000) Detection and sorting of neural spikes using wavelet packets. Phys Rev Lett 85:4637–4640

    Article  CAS  PubMed  Google Scholar 

  • Laubach M (2004) Wavelet-based processing of neuronal spike trains prior to discriminant analysis. J Neurosci Methods 134:159–168

    Article  PubMed  Google Scholar 

  • Letelier JC, Weber PP (2000) Spike sorting based on discrete wavelet transform coefficients. J Neurosci Methods 101:93–106

    Article  CAS  PubMed  Google Scholar 

  • Liang H, Bressler SL, Desimone R, Fries P (2005a) Empirical mode decomposition: a method for analyzing neural data. Neurocomputing 65:801–807

    Article  Google Scholar 

  • Liang H, Bressler SL, Buffalo EA, Desimone R, Fries P (2005b) Empirical mode decomposition of field potentials from macaque V4 in visual spatial attention. Biol Cybern 92(6):380–392

    Article  PubMed  Google Scholar 

  • Mallat S (1998) A wavelet tour of signal processing. Academic, New York

    Google Scholar 

  • Nenadic Z, Burdick JW (2005) Spike detection using the continuous wavelet transform. IEEE Trans Biomed Eng 52:74–87

    Article  PubMed  Google Scholar 

  • Quian Quiroga R, Garcia H (2003) Single-trial event-related potentials with wavelet denoising. Clin Neurophysiol 114:376–390

    Article  CAS  PubMed  Google Scholar 

  • Quian Quiroga R, Nadasdy Z, Ben-Shaul Y (2004) Unsupervised spike detection and sorting with wavelets and superparamagnetic clustering. Neural Comput 16:1661–1687

    Article  PubMed  Google Scholar 

  • Quian QR, Schürmann M (1999) Functions and sources of evoked EEG alpha oscillations studied with the wavelet transform. Clin Neurophysiol 110:643–654

    Article  Google Scholar 

  • Tallon-Baudry C, Bertrand O, Delpuech C, Pernier J (1996) Stimulus specificity of phase-locked and non-phase-locked 40 Hz visual responses in human. J Neurosci 13:4240–4249

    Google Scholar 

  • Wang Z, Maier A, Leopold DA, Logothetis NK, Liang H (2007) Single-trial evoked potential estimation using wavelets. Comput Biol Med 37:463–473

    Article  PubMed  Google Scholar 

  • Wang Z, Logothetis NK, Liang H (2009) Extraction of percept-related induced local field potential during spontaneously reversing perception. Neural Netw 22:720–727

    Article  PubMed  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Biomedical Engineering, Drexel University, 3141 Chestnut Street, 19104, Philadelphia, PA, USA

    Hualou Liang

Authors
  1. Hualou Liang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hualou Liang .

Editor information

Editors and Affiliations

  1. Atlanta, Georgia, USA

    Dieter Jaeger

  2. Department of Biomedical Engineering, Florida International University, Miami, Florida, USA

    Ranu Jung

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer Science+Business Media New York

About this entry

Cite this entry

Liang, H. (2014). Wavelet Analysis. In: Jaeger, D., Jung, R. (eds) Encyclopedia of Computational Neuroscience. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-7320-6_422-1

Download citation

  • DOI: https://doi.org/10.1007/978-1-4614-7320-6_422-1

  • Received:

  • Accepted:

  • Published:

  • Publisher Name: Springer, New York, NY

  • Online ISBN: 978-1-4614-7320-6

  • eBook Packages: Springer Reference Biomedicine and Life SciencesReference Module Biomedical and Life Sciences

Publish with us

Policies and ethics

Search

Navigation