Representing and decomposing neural potential signals

This paper reviews methodologies for analyzing neural potentials via frequency, time-frequency, or wavelet representations, and adaptive models that estimate the signal's spatial or temporal structure. The fundamental assumptions of each method are discussed. In particular, the Fourier transform is contrasted with overcomplete representations, which are able to precisely delineate the timing and/or frequency of neural events. Finally, a novel approach that combines overcomplete representations with adaptive signal models is presented. This approach describes a continuous signal as a linear combination of reoccurring waveforms, referred to as phasic events, which are often associated with neural processing. The new methodology automatically learns the reoccurring waveforms and quantifies the neural potentials by the set of amplitudes and timings.