Estimation and detection of variable latency signals via unwrapped phase averaging

Averaging an ensemble of measurements is often useful in estimating or detecting a waveform buried in noise. However, the effectiveness of simple epoch averaging depends on having the signal at the same position in each measurement. Traditional techniques for the jitter problem include the use of adaptive crosscorrelation to align measurements before averaging, or deconvolution to recover the signal from the blurred average. The relation between time delay and Fourier phase suggests an alternative approach. We report empirical evidence indicating the possibility of using unwrapped phase averaging. The key to this technique is the scaling of the phase average by a factor related to the signal-to-noise ratio. Simulations are presented to demonstrate waveform estimation and detection under poor signal-to-noise conditions where the obscuring noise has a spectrum similar to that of the signal.