Multivariate spectral analysis of electroencephalography data

We propose a time-domain approach to detect cross-trial frequencies based on nonlinear correlation functions. This method is a multivariate extension of discrete Fourier transform (DFT) and can be applied to short and/or sparse time series. Cross-trial and/or cross-channel spectra (CTS) can be obtained for electroencephalography (EEG) data where multiple short data segments of the same experiment are available. There are two versions of CTS: The first one assumes some phase coherency across the trials while the second one is independent of phase coherency. We demonstrate that the phase dependent version is more consistent with traditional spectral methods as implemented in EEGLAB. This multivariate spectral analysis is a spatio-temporal extension of DFT and should not be confused with cross-spectral analysis. We applied this method to EEG data recorded while participants reached for and grasped a virtual object where we compared a cross-trial spectrogram (CTS) of data around a stimulus with traditional event related spectral perturbations (ERSP) analysis. We show that CTS can be applied to shorter data windows than ERSP by using spatio-temporal information in the EEG and therefore yields higher temporal resolution. Furthermore a CTS can be computed for each individual subject while ERSP is commonly computed on a whole population of subjects.