Use of an adaptive filter to characterize signal-noise relationships

A recently-described adaptive filtering process for recovering either fixed or variable latency responses offers a number of statistical byproducts which may be analyzed to explore signal-noise relationships. The process cross-correlates each of a series of digitized response records against an initial template (usually, the time-locked average of all records). At some lag of k i ∗ points, the ith record attains maximum correlation r i ∗ with the template. Translation of the origin by |k i ∗| , for all i, tends to synchronize responses. A time-locked average of the shifted records provides a new template for the next cycle of correlations, shifting and averaging. Continued iteration converges to an unchanging representation of the response in the final template, together with two key outputs, (1) the mean r of the final set of r i ∗ , and (2) a stable distribution of shifts, f(k i ∗) . Background (noise) activity is represented in the final output in proportion to the consistency of noise patterns throughout the set of records. Thus, output “signal” incorporates total activity of highest mutual correlation among the records and in this sense reflects “organization” of the evoked response patterns. The statistic r is a quantitative measure of this activity. It does not distinguish between noise patterns located in or near the area-rich portion of the response and positively correlated with it (“signal-associated” noise) and other, unrelated noise patterns. This distinction can be made by analysis of f(k i ∗) which, after suitable reduction, generally appears well fitted by an exponential distribution whose parameter λ reflects signal-associated noise. Computations with various time-locked waveforms, including multi-peaked signals, in band-limited white noise, show r and λ to be fairly stable, largely independent functions of signal-noise ratio and noise bandwidth. Two estimates of prefiltered signal-noise levels are proposed, one based on r and an à priori estimate (from noise-only data) of equivalent white-noise bandwidth, the other using r and λ. Comparison of these estimates may aid in assessing the effects of stimulus on pre-existing background activity. Possible applications of these statistical methods to experiments in neurophysiology are mentioned, as well as the need to extend present studies to variable latency signals.