Separation of overlapping waveforms having known temporal distributions

Abstract

A simple Fourier technique is described that allows isolation of component waveforms from recordings of time-shifted, overlapping, linear sums of these components. This procedure can be applied if certain assumptions are satisfied, namely, the times of occurrences of the underlying component waveforms are known, the component waveforms are time-invariant, and there are at least as many different recordings as there are underlying component waveforms. The method is a type of adaptive inverse filtering, and can be generalized to allow recovery of waveforms that have been distorted by many time-invariant linear processes in addition to time delays. An application of the technique to human scalp-recorded event-related potentials (ERPs) is discussed which allows resolution of overlapping stimulus-locked and response-locked waveform complexes. Some possible effects of violating the assumptions of the procedure are explored for this example. The method should prove of value when it is impossible to record the underlying component waveforms in isolation, and the waveshapes, rather than their times of occurrence, are important experimental dependent variables.