Simulation and extraction of single-trial evoked potentials

Evoked potentials are defined as potentials that result from electrical activity in the central nervous system after a stimulation. In analysis of evoked potentials the main problem is to extract the waveform from measurements that also contain on-going background electroencephalographic (EEG) activity. The conventional tool for the analysis of evoked potentials has been averaging of the measurements over an ensemble of trials. This is the optimal way to improve the signal-to-noise ratio when the evoked potential is a deterministic signal in independent and additive background noise of zero mean. However, it is evident that the evoked potential varies with repetitions of the stimuli. There are two aims of this paper. The first is to develop a simulation method for evoked potentials with slow variations among different trials. The second aim is to develop a method to extract time variations occurring in a number of time-aligned trials to estimate the single-trial evoked potentials.