Coherent (signal) averaging
The foundational technique for recovering an evoked response buried in noise. If a stimulus-locked signal is approximately identical across trials while the background EEG is zero-mean and uncorrelated with the trigger, averaging N time-aligned epochs preserves the signal but averages down the noise: the noise standard deviation falls as 1/sqrt(N), so the amplitude signal-to-noise ratio grows as sqrt(N). Quadrupling the trial count halves the residual noise — the sqrt(N) law that sets how many repetitions an ERP or a P300 speller selection needs.
The assumptions are strong and their violations are the method's failure modes: latency jitter across trials low-pass filters and attenuates the average (fixes: latency correction, Woody filtering); trial-to-trial amplitude variability and habituation break the identical-signal assumption; and any artifact time-locked to the stimulus (the reason evoked ocular artifact is dangerous) averages up with the signal instead of down. Averaging also discards the single-trial information that modern single-trial decoders try to keep.
A P300 speller averages roughly 10 to 15 flashes per symbol so the target P300 clears the noise floor enough to classify; more repetitions raise accuracy but lower the information transfer rate.
The sqrt(N) law forces a tradeoff between accuracy and speed.