A sampling theorem for EEG electrode configuration

An analytical tool to help in selecting the number of electrodes required for recording electroencephalogram (EEG) signals is presented. The main assumption made is that the scalp can be modeled as a hemispherical surface. The number of sensors required to sample a surface is derived by using a mean square error (MSE) measure to approximate the continuous potential functions on the hemispherical surface. An algorithm for selecting the number of electrodes for arbitrary head geometries is also proposed. A sampling theorem is then derived with conditions on the sampling points for electrode placement.