Download PDF
Methods Inf Med 2013; 52(04): 279-296
DOI: 10.3414/ME12-01-0083
Original Articles
Schattauer GmbH

Time-frequency Techniques in Biomedical Signal Analysis[*]

A Tutorial Review of Similarities and Differences
M. Wacker
1   Bernstein Group for Computational Neuroscience Jena, Institute of Medical Statistics, Computer Sciences and Documentation, Jena University Hospital, Friedrich Schiller University Jena, Germany
,
H. Witte
1   Bernstein Group for Computational Neuroscience Jena, Institute of Medical Statistics, Computer Sciences and Documentation, Jena University Hospital, Friedrich Schiller University Jena, Germany
› Author Affiliations
Further Information

Publication History

received: 07 September 2012

accepted: 16 May 2012

Publication Date:
20 January 2018 (online)

    Permissions and Reprints

Summary

Objectives: This review outlines the method -ological fundamentals of the most frequently used non-parametric time-frequency analysis techniques in biomedicine and their main properties, as well as providing decision aids concerning their applications.

Methods: The short-term Fourier transform (STFT), the Gabor transform (GT), the S-transform (ST), the continuous Morlet wavelet transform (CMWT), and the Hilbert transform (HT) are introduced as linear transforms by using a unified concept of the time-frequency representation which is based on a standardized analytic signal. The Wigner-Ville dis -tribution (WVD) serves as an example of the ‘quadratic transforms’ class. The combination of WVD and GT with the matching pursuit (MP) decomposition and that of the HT with the empirical mode decomposition (EMD) are explained; these belong to the class of signal-adaptive approaches.

Results: Similarities between linear transforms are demonstrated and differences with regard to the time-frequency resolution and interference (cross) terms are presented in detail. By means of simulated signals the effects of different time-frequency resolutions of the GT, CMWT, and WVD as well as the resolution-related properties of the inter -ference (cross) terms are shown. The method-inherent drawbacks and their consequences for the application of the time-frequency techniques are demonstrated by instantaneous amplitude, frequency and phase measures and related time-frequency representations (spectrogram, scalogram, time-frequency distribution, phase-locking maps) of measured magnetoencephalographic (MEG) signals.

Conclusions: The appropriate selection of a method and its parameter settings will ensure readability of the time-frequency representations and reliability of results. When the time-frequency characteristics of a signal strongly correspond with the time-frequency resolution of the analysis then a method may be considered ‘optimal’. The MP-based signal-adaptive approaches are preferred as these provide an appropriate time-frequency resolution for all frequencies while simultaneously reducing interference (cross) terms.

Keywords

Gabor transform - Morlet wavelet transform - Wigner-Ville distribution - matching pursuit - Hilbert-Huang transform

* Supplementary material published on our website www.methods-online.com


 

  • References

  • 1 Witte H, Ungureanu M, Ligges C, Hemmelmann D, Wustenberg T, Reichenbach J. et al Signal informatics as an advanced integrative concept in the framework of medical informatics: New trends demonstrated by examples derived from neuroscience. Methods Inf Med 2009; 48 (01) 18-28.
    Thieme ConnectPubMedSearch in Google Scholar
  • 2 Lachaux JP, Rodriguez E, Martinerie J, Varela FJ. Measuring phase synchrony in brain signals. Hum Brain Mapp 1999; 8 (04) 194-208.
    CrossrefPubMedSearch in Google Scholar
  • 3 Bruns A. Fourier-, Hilbert- and wavelet-based signal analysis: are they really different approaches?. J Neurosci Meth 2004; 137 (02) 321-332.
    CrossrefPubMedSearch in Google Scholar
  • 4 Lehmann TM, Aach T, Witte H. Sensor, signal and image informatics - State of the art and current topics. Methods Inf Med 2006; 45: 57-67.
    PubMedSearch in Google Scholar
  • 5 Boashash B. Time-frequency signal analysis. Methods and applications. Melbourne: Longman Cheshire. 1992.
    Search in Google Scholar
  • 6 Hlawatsch F, Boudreaux-Bartels GF. Linear and quadratic time-frequency signal representations. Ieee Signal Proc Mag 1992; 9 (02) 21-67.
    CrossrefPubMedSearch in Google Scholar
  • 7 Schwab K, Ligges C, Jungmann T, Hilgenfeld B, Haueisen J, Witte H. Alpha entrainment in human electroencephalogram and magnetoencephalogram recordings. Neuroreport 2006; 17 (17) 1829-1833.
    CrossrefPubMedSearch in Google Scholar
  • 8 Harris FJ. Use of windows for harmonic-analysis with discrete Fourier-transform. P Ieee 1978; 66 (01) 51-83.
    CrossrefPubMedSearch in Google Scholar
  • 9 Witte H, Putsche P, Hemmelmann C, Schelenz C, Leistritz L. Analysis and modeling of time-variant amplitude-frequency couplings of and between oscillations of EEG bursts. Biol Cybern 2008; 99 (02) 139-157.
    CrossrefPubMedSearch in Google Scholar
  • 10 Auger F, Flandrin P, Goncalves P, Lemoine O. Time-frequency toolbox. For use with MATLAB. http://wwwnongnuorg/tftb/tutorialpdf. 1995.
    Search in Google Scholar
  • 11 Mallat SG, Zhang ZF. Matching pursuits with time-frequency dictionaries. Ieee T Signal Proces 1993; 41 (12) 3397-3415.
    CrossrefPubMedSearch in Google Scholar
  • 12 Wacker M, Witte H. Adaptive phase extraction: Incorporating the Gabor transform in the matching pursuit algorithm. Ieee T Bio-Med Eng 2011; 58 (10) 2844-2851.
    CrossrefPubMedSearch in Google Scholar
  • 13 Huang NE, Shen Z, Long SR, Wu MLC, Shih HH, Zheng QN. et al The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis. P Roy Soc Lond a Mat 1998; 454 1971 903-995.
    CrossrefPubMedSearch in Google Scholar
  • 14 Stockwell RG, Mansinha L, Lowe RP. Localization of the complex spectrum: The S transform. Ieee T Signal Proces 1996; 44 (04) 998-1001.
    CrossrefPubMedSearch in Google Scholar
  • 15 Carmona R, Hwang WL, Torresani B. Practical time-frequency analysis. San Diego: Academic Press; 1998.
    Search in Google Scholar
  • 16 Mertins A. Signal analysis. John Wiley Sons Ltd; 1999.
    Search in Google Scholar
  • 17 Mattat SG. A wavelet tour of signal processing. The sparse way. 3rd ed. Elsevier: 2009.
    Search in Google Scholar
  • 18 Claasen TACM, Mecklenbräuker WFG. The Wigner distribution - a tool for time-frequency signal analysis. Part II: Discrete-time signals. Philips Journal of Research 1980; 35: 276-300.
    PubMedSearch in Google Scholar
  • 19 Claasen TACM, Mecklenbräuker WFG. The Wigner distribution - a tool for time-frequency signal analysis. Part III: Relations with other time-frequency transformations Philips Journal of Research 1980; 35: 372-389.
    PubMedSearch in Google Scholar
  • 20 Jones DL, Parks TW. A resolution comparison of several time-frequency representations. Ieee T Signal Proces 1992; 40 (02) 413-420.
    CrossrefPubMedSearch in Google Scholar
  • 21 Zou HX, Lu XG, Dai QH, Li YD. Nonexistence of cross-term free time-frequency distribution with concentration of Wigner-Ville distribution. Sci China Ser F 2002; 45 (03) 174-180.
    PubMedSearch in Google Scholar
  • 22 Lin CF, Zhu JD. Hilbert-Huang transformation-based time-frequency analysis methods in biomedical signal applications. Proc IMechE Part H: Journal of Engineering in Medicine 2012; 226: 208-216.
    PubMedSearch in Google Scholar
  • 23 Laila DS, Messina AR, Pal BC. A refined Hilbert-Huang transform with applications to interarea oscillation monitoring. Ieee T Power Syst 2009; 24 (02) 610-620.
    CrossrefPubMedSearch in Google Scholar
  • 24 Li XL, Yao X, Fox J, Jefferys JG. Interaction dynamics of neuronal oscillations analysed using wavelet transforms. J Neurosci Meth 2007; 160 (01) 178-185.
    CrossrefPubMedSearch in Google Scholar
  • 25 Helbig M, Schwab K, Leistritz L, Eiselt M, Witte H. Analysis of time-variant quadratic phase couplings in the trace alternant EEG by recursive estimation of 3rd-order time-frequency distributions. J Neurosci Meth 2006; 157 (01) 168-177.
    CrossrefPubMedSearch in Google Scholar
  • 26 Auger F, Flandrin P. Improving the readability of time-frequency and time-scale representations by thereassignment method. Ieee T Signal Proces 1995; 43 (08) 2038
    PubMedSearch in Google Scholar
  • 27 Durka PJ, Ircha D, Blinowska KJ. Stochastic time-frequency dictionaries for matching pursuit. Ieee T Signal Proces 2001; 49 (03) 507-510.
    CrossrefPubMedSearch in Google Scholar
  • 28 Yang Y, Deng J, Wu C. Analysis of mode mixing phenomena in the Empirical Mode Decomposition method. 2nd International Symposium on Information Science and Engineering. 2009. doi: 10.1109/ISISE.2009.19
    Search in Google Scholar
  • 29 Wu Z, Huang NE. Ensemble empirical mode decomposition: a noise-assisted data analysis method. Advances in Adaptive Data Analysis 2008; 1 (01) 1-41.
    PubMedSearch in Google Scholar
  • 30 Flandrin P, Rilling G, Goncalves P. Empirical mode decomposition as a filter bank. Ieee Signal Proc Let 2004; 11 (02) 112-114.
    CrossrefPubMedSearch in Google Scholar
  • 31 Arnold M, Doering A, Witte H, Dorschel J, Eiselt M. Use of adaptive Hilbert transformation for EEG segmentation and calculation of instantaneous respiration rate in neonates. J Clin Monitor 1996; 12 (01) 43-60.
    PubMedSearch in Google Scholar
  • 32 Florin E, Gross J, Pfeifer J, Fink GR, Timmermann L. The effect of filtering on Granger causality based multivariate causality measures. Neuroimage 2010; 50 (02) 577-588.
    CrossrefPubMedSearch in Google Scholar
  • 33 Silchenko AN, Adamchic I, Pawelczyk N, Hauptmann C, Maarouf M, Sturm V. et al Data-driven approach to the estimation of connectivity and time delays in the coupling of interacting neuronal subsystems. J Neurosci Meth 2010; 191 (01) 32-44.
    CrossrefPubMedSearch in Google Scholar
  • 34 Assous S, Boashash B. Evaluation of the modified S-transform for time-frequency synchrony analysis and source localisation. EURASIP J Adv Signal Process. 2012.
    Search in Google Scholar
  • 35 Halbleib A, Gratkowski M, Schwab K, Ligges C, Witte H, Haueisen J. Topographic analysis of engagement and disengagement of neural oscillators in photic driving: A combined electroencephalogram/magnetoencephalogram study. J Clin Neurophysiol 2012; 29 (01) 33-41.
    CrossrefPubMedSearch in Google Scholar
  • 36 Rutkowski TM, Mandic DP, Cichocki A, Przybyszewski AW. EMD approach to multichannel EEG data - the amplitude and phase components clustering analysis. J Circuit Syst Comp 2010; 19 (01) 215-229.
    CrossrefPubMedSearch in Google Scholar
  • 37 Rehman N, Mandic DP. Multivariate empirical mode decomposition. P Roy Soc a-Math Phy 2010; 466 2117 1291-1302.
    PubMedSearch in Google Scholar