Said Assous

Evaluation of the modified S -transform for time-frequency synchrony analysis and source localisation

This article considers the problem of phase synchrony and coherence analysis using a modified version of the S-transform, 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 non-stationary characteristics. The basic method includes a cross-spectral analysis to study the phase synchrony of non-stationary 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.

Fourier extension and hough transform for multiple component FM signal analysis

Conventional representations in the time or frequency domain are inadequate for non-stationary signals which have statistical properties varying with time. In particular the advent of pulse compression techniques and the use of time varying chirp-type signals widespread in radar, sonar and seismic technologies means there is a need for time-frequency representation. We present a technique which extends the Fourier transform to non-stationary signals. We call the technique Fourier Extension analysis. We show that the analysis extends naturally to a time-frequency representation using the Hough transform projection, and investigate the resolutions obtainable with regard to separation of chirp signals compared with the usual matched filter approach common in radar processing. A visual interpretation of the magnitude and phase of the analytic results is introduced allowing a range of transform orders to be viewed simultaneously. Using frequency modulated signals, we demonstrate significantly higher resolution both in rate and time separation. Examples are given using synthetic and real world chirp signals illustrating improvements in time-frequency resolution using the new approach compared to the commonly used quadratic transforms.

Phase synchrony and coherence analysis of bio-signals using cross-time-frequency distributions

Phase synchrony and coherence analysis of bio-signals such as EEG, HRV, Respiratory and Blood Pressure can be explored to study the phase coupling between different physiological activities for different biological mechanisms. Due to the non-stationary nature of these bio-signals, the preferred approach requires a cross time-frequency based representation to describe the phase coupling between two or more different spatially recorded entities. The selected technique for this purpose is the cross-Modified S transform (X-MST), due to some properties of the modified S transform (MST), such as phase preservation. Both simulated examples and real data demonstrate the usefulness of the technique. The performance and limitations of the X-MST method are discussed in the context of a comparison with a quadratic Time-Frequency distributions such as the cross-Wigner-Ville distribution (WVD).