The number of components in profile analysis tasks.

Abstract

The central issue of this paper is how detection of a change in spectral shape depends on the number of components m that define the spectrum. First, a channel theory is reviewed and the predictions relating the detectability of such a change as a function of the number of components are derived. Second, the existing literature is reviewed. Most of it concerns the detection of an increment in a single tone of an m-component, equal-amplitude complex. The data are close (+/- 2 dB) to the predictions of the theory, which suggests that there is a relatively small change in threshold as the number of components increases. The consistency of the data is also discussed and hypotheses for discrepancies are presented. Finally, the results of an experiment measuring the detectability of a special spectral shape change is explored. In this case, all the changes are equal in size but some are opposite in sign, so that the summed change is zero. The results using this "balanced" spectral change are also consistent with the predictions of the theory and show that for this special kind of spectral change thresholds improve by nearly 7 dB as m increases from 4 to 24 components.