Multi-channel Fourier packet transform of EEG: optimal representation and time-varying coherence

Multi-channel recording of electroencephalogram (EEG) provides a measure of spatial-temporal pattern of cognitive processes. When oscillatory activities are going to be studied, the time-domain EEG signal can be analyzed via Fourier or wavelet transform. However the loss of temporal information after Fourier transform and the unavailability of phase information in wavelet transform limit their applicability in EEG analysis. In this paper, multi-channel Fourier packet transform is introduced. The algorithm resembles the wavelet packet transform by its binary tree search for an optimal selection of orthogonal basis, but extends the application to the multi-channel scenario. It aims to provide a sparse signal representation to localize features in the spatial-spectral-temporal domain. Since the decomposed atoms are spatially coherent components, analysis of time-varying synchrony across scalp locations is then possible.