Spectral properties of signal averaging and a novel technique for improving the signal-to-noise ratio.

Averaging is one well-known method for improving the signal-to-noise (S/N) ratio of data or a time series, in which small amplitude responses to regularly occurring stimuli are contaminated by noise. We have considered the spectral properties of that process and introduce a new method which further improves the S/N ratio. We also demonstrate that the signal recovered by normal averaging is identical to that recovered by the frequency extraction technique which we propose. A formula for the sums-of-squares of the recovered signal is derived. The success of the frequency extraction technique has been demonstrated on sinusoids, white noise, evoked potentials contaminated by a background EEG, and the EEG recorded with the subject's eyes closed.