Characterization of interictal and ictal scalp EEG signals with the Hilbert transform

The present paper reports on the application of the Hilbert transform to biological time series of the brain electrical activity of epilepsy patients. The Hilbert transform will be used to estimate the instantaneous frequency, the instantaneous amplitude and the phase synchronization of scalp EEG recordings. As a fourth measure derived from the Hilbert transform we will define a measure of rhythmicity. The purpose of this paper is to combine the time evolution of these four measures to come to a characterization of the dynamics present in, and between, different EEG channels. By applying these measures to scalp EEG recordings of patients with Mesial Temporal Lobe Epilepsy we will show that they are useful for off-line analysis of large amounts of EEG data. Because all these measures are derived from the fast Hilbert transform it is also possible to use them as an analysis tool for online monitoring.