of fragmentary decomposition

A recently developed fragmentary decomposition method is employed to analyse single-trial event-related potentials (ERPs), thereby extending the traditional method of averaging. Using a conventional auditory oddball paradigm with 40 target stimuli, single-trial ERPs in 40 normal subjects were analysed for midline scalp (Fz, Cz and Pz) recording sites. The normalization e€ect, reported in our previous study of eye blink EMGs and proposed to be a characteristic property of a wide class of non-stationary physiological processes, was found to apply to these single-trial ERPs. Fragmentary decomposition of single-trial ERPs may be regarded as re-statement of the normalization e€ect. This allows both pre-stimulus EEGs and post-stimulus ERPs to be regarded as overlapping generic mass potentials (GMPs), with a characteristic Gaussian amplitude spectrum. On theoretical and empirical grounds we uniquely deduce a model GMP using an introduced``bud'' function, and physically support it by the resting and transient conditions. The model takes into account the shape of the component, which suggests a simple relationship between the peak latency and the time of the component onset. Given that GMPs may be manipulated and sorted out, we present principles of the fragmentary synthesis, i.e. probabilistic ERP reconstructions on the basis of individual and ensemble properties of its identi®ed components. Summarizing the component quanti®cation in the form of the dynamic model provides for the ®rst time the opportunity to quantify all signi®cant components in single-trial ERPs. This method of single-trial analysis opens up new possibilities of exploring the dynamical ERP changes within a recording trial, particularly in late component``cognitive'' paradigms.