Detection of event related potentials

A statistical approach is presented which provides efficient procedures to detect both Event Related Potential (ERP) and its spectral structure. Situations where undesirable signal or "artifact" is present, are considered. In these cases, a "noise" sample can be used which complements the insufficient knowledge given for the sample where we expect to detect the ERP. In this approach, Hotelling's T2 statistic for one and two samples arises as a natural detector of ERPs. Under the assumption of stationarity these statistics are calculated by approximate expressions in the frequency domain. For Brainstem Auditory Evoked Potentials, ROC curves confirm that the T2 statistic has higher detection rates than various indices proposed in the literature. A frequency decomposition of the T2 statistic yields a succession of complex versions of Student's t statistic that characterize the spectral structure of the ERP. Different assumptions about the recordings of ERP are discussed and several generalizations are suggested.