Improving the ensemble average of visual evoked potentials. I. Theory of correction by spectral phase difference...

The considered causes of variability of visual evoked potentials (VEPs) are additive noise and time variability. The time variability can be modelled in three different ways: 1. time invariant VEP waveform and delay-time "jitter"; 2. time variant VEP waveform, due to 2a. jitter of individual components or 2b. constant VEP waveform and "wow", i.e. expansion or compression of the time scale. The wow model has not been considered so far in the literature. Correction of jitter and/or wow is based on a frequency domain method: the "spectral phase difference" method (SPD). When jitter is present the SPD method is applied in the frequency domain on the single responses, or on a subensemble of a small number of responses. For the wow a new method is proposed where the time scale is logarithmically compressed prior to the calculation of the spectrum. It is shown that the SPD method can also be applied then to estimate the compression factor yielding the wow. The single responses, or the averaged sub-ensembles, can subsequently be corrected by this factor and finally be averaged. Improvement of the precision and accuracy of estimates of both the peak latencies and the peak amplitudes, as well as a comparison between the results of the jitter and wow models, have been reported in a companion paper.