Signal delay and waveform estimation using unwrapped phase averaging

Detection and estimation under poor signal-to-noise conditions may require the averaging of an ensemble of time-locked measurements. However, when there is a variation in signal delay, it is necessary to adjust the alignment of the measurements in order for averaging to produce an undistorted estimate of the signal waveform. We describe a technique where alignment is, in effect, replaced by averaging the unwrapped Fourier phases of the measurements. The overall procedure yields an estimate of the signal at its mean delay. Simulations are presented to demonstrate the applicability of the technique to the estimation of delay in visual evoked potentials.