Time-frequency phase analysis of ictal EEG recordings with the S-transform

The calculation and visualization of temporal and phase information in the brain, such as during cognitive processes and epileptiform activity, is an important tool in EEG-based studies of physiological brain activation. To this end, we present a technique that estimates the phase and time offsets between different channels in EEG recordings of seizure activity. The offset information is visually combined with amplitude information to emphasize the most significant signal features. The estimates of phase and time offset are derived from the S-transform, a time-frequency representation that is similar to a windowed Fourier transform, but with a wavelet-like, scalable window. The phase offsets are obtained from the differences between phase spectra of S-transforms of different traces, and the time offsets are then obtained from the frequency-domain gradients of the phase offsets. This is analogous to the link between frequency "phase ramping" and time translation in ordinary Fourier analysis. In this paper, we present a synthetic example to help describe the method, and then show ictal EEG recordings from two human subjects. The differences between the recording times of spike-wave discharges at different electrodes exhibit behavior that is strongly dependent on time and frequency.