A least-squares digital filter is proposed for impulse-response data acquisition schemes. The filter operates in real time by fitting each signal transient to a filter function. The optimal filter function is found to be the signal waveform for the case of white noise. The signal-to-noise ratio improvement of the filter is proportional to the square root of the number of data points used in the filter-function waveform.
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Nickolaisen et al. (1986) studied this question.