M Wacker1, H Witte. 1. Bernstein Group for Computational Neuroscience Jena, Institute of Medical Statistics, Computer Sciences and Documentation, Jena University Hospital, Friedrich Schiller University Jena, 07740 Jena, Germany. Matthias.Wacker@mti.uni-jena.de
Abstract
OBJECTIVES: This review outlines the methodological 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 distribution (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 interference (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.
OBJECTIVES: This review outlines the methodological 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 distribution (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 interference (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.
Authors: Ahmed Faeq Hussein; Shaiful Jahari Hashim; Ahmad Fazli Abdul Aziz; Fakhrul Zaman Rokhani; Wan Azizun Wan Adnan Journal: J Med Syst Date: 2017-11-29 Impact factor: 4.460
Authors: Umberto Melia; Montserrat Vallverdú; Xavier Borrat; Jose Fernando Valencia; Mathieu Jospin; Erik Weber Jensen; Pedro Gambus; Pere Caminal Journal: PLoS One Date: 2015-04-22 Impact factor: 3.240