Phase-Interpolated Averaging for Analyzing Electroencephalography and Magnetoencephalography Epochs

Stimulus-locked averages of electroencephalography (EEG) and magnetoencephalography (MEG) epochs reveal characteristic waveforms. EEG/MEG generation models to have reconstruct such waveforms have been recently proposed. These models assume that evoked, phase-modulated, and amplitude-modulated activities occur solely or simultaneously. We propose a two-stage stimulus-locked averaging method, called phase-interpolated averaging, to investigate the EEG/MEG generation process. First, virtual EEG/MEG epochs, which would be obtained as if instantaneous phases for each time sampling point were on a phase-grid, are interpolated from actually measured EEG/MEG epochs. Then, the virtual EEG/MEG epochs are discrete Fourier transformed. A simulation revealed that the zeroth Fourier term revealed the evoked activity, the first Fourier term revealed the amplitude-modulated activity, and the condition number of the interpolation reflected the phase-modulated activity. On the basis of these facts, a preliminary EEG analysis implied that the evoked activity is much smaller than what would be expected by using conventional averaging, the evoked and phase-modulated activities simultaneously occur, and the amplitude-modulated activity occasionally associates with the evoked and phase-modulated activities. To the best of our knowledge, this is the first time that these three activities have been shown to coexist by actually separating them.