We propose a novel interpretation of single channel Electroencephalogram (EEG) traces based on the transient nature of encoded processes in the brain. In particular, the proposed framework models EEG as the output of the noisy addition of temporal, reoccurring, transient patterns known as phasic events. This is not only neurophysiologically sound, but it also provides additional information that classical EEG analysis often disregards. Furthermore, by utilizing sparse decomposition techniques, it is possible to obtain amplitude and timing that is further modeled using estimation and fitting techniques. We model Brain-Computer Interfaces (BCI) competition data features as Gaussian Mixture Model (GMM) samples in order to show the potential of working in the joint space of the parameters. The results not only preserve the topographic discriminant behavior but also expand the realm of possible EEG analysis.