Evaluation of the modified S -transform for time-frequency synchrony analysis and source localisation
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RESEARCH
Open Access
Evaluation of the modified S-transform for timefrequency synchrony analysis and source localisation Said Assous1* and Boualem Boashash2,3
Abstract This article considers the problem of phase synchrony and coherence analysis using a modified version of the Stransform, referred to here as the Modified S-transform (MST). This is a novel and important time-frequency approach to study the phase coupling between two or more different spatially recorded entities with nonstationary characteristics. The basic method includes a cross-spectral analysis to study the phase synchrony of nonstationary signals, and relies on some properties of the MST, such as phase preservation. We demonstrate the usefulness of the technique using simulated examples and real newborn EEG data. The results show the advantage of using the cross-MST in the study of the connectivity between different signals using the time-frequency coherence. The MST led to improvements in resolution of almost twofold over the standard S-Transform in the examples presented in the article. Keywords: time-frequency coherence, cross time-frequency, modified S-transform, phase synchrony, array processing, EEG signal, time-frequency signal analysis, Quadratic Time-Frequency Distributions, instantaneous frequency
1 Introduction 1.1 Time-frequency methods
Non-stationary signals have statistical properties that vary with time and hence the traditional time averaged amplitude spectrum obtained using Fourier transform is inadequate to track changes in signal magnitude, frequency or phase. In analyzing non-stationary and multicomponent signals, time-frequency-based techniques were shown to outperform classical techniques based on either time or frequency domains [1] (Chapter 1). The basic idea of time-frequency analysis is to understand and describe situations where the frequency content of a signal is changing in time. Although time-frequency analysis had its origin almost 50 years ago, significant advances have occurred in the past 20 years or so. In particular, the time-frequency representation has received considerable attention as a powerful high resolution and precision tool for analyzing a variety of biosignals and systems such as speech, ECG, EEG, PCG, EMG, as well as signals arising from other fields [2]. A * Correspondence: [email protected] 1 Weatherford, East Leake, Leicestershire LE12 6JX, UK Full list of author information is available at the end of the article
time-frequency distribution (TFD) is used to analyze and process non-stationary signals in the joint time-frequency domain. Several TFDs exist in the literature [1]. Most of them are based on the Wigner-Ville distribution (WVD) [3], as all the other TFDs can be expressed as a smoothed version of the WVD. A popular candidate of this class is the spectrogram, which is the square modulus of the short time Fourier transform (STFT). The spectrogram is the WVD smoothed in time and frequency by the ambiguity function of the window used in the STFT [4]; and all the quadratic
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