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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)

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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


 

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