Spherical harmonic analysis of the electroencephalogram

Summary form only given. The theoretical and practical problems of performing spherical harmonic analysis (SHA) on the electroencephalogram (EEG) have been investigated. One problem considered is related to sampling theory, that is, determining the effect of sample positions and detecting the presence of spatial aliasing. Another involves constraining the solution of the spherical harmonic coefficients to prevent instabilities. It has been found that the unconstrained solution does not always provide a realistic global solution. Some of the practical problems that have been investigated are spatial bandwidth estimation and placement errors. Spatial bandwidth estimation is important for determining the minimum number of electrodes required to sample the EEG adequately and to determines the order in a SHA. The sensitivity of the results to errors in determining the electrode positions on the scalp has also been studied