This paper describes the development of an optimal sigmoidal rate-level function that is a component of many models of the peripheral auditory system. The optimization makes use of a set of criteria defined exclusively on the basis of physical attributes of the input sound that are inspired by physiological evidence. The criteria developed attempt to discriminate between a degraded speech signal and noise to preserve the maximum amount of information in the linear region of the sigmoidal curve, and to minimize the effects of distortion in the saturating regions. The performance of the proposed optimal sigmoidal function is validated by text-independent speaker-verification experiments with signals corrupted by additive noise at different SNRs. The experimental results suggest that the approach presented in combination with cepstral variance normalization can lead to relative reductions in equal error rate as great as 40% when compared with the use of baseline MFCC coefficients for some SNRs. (C) 2013 Elsevier By. All rights reserved.