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The relationship between an objective measure of speech quality (PESQ) and the recognition rate of a given speech recognition system was already investigated by other researchers. In this paper, we present a further investigation on such a relationship. In our research, the speech recognition tests were performed on a wider class of signals and SNR. The experimental setup as well as the speech recognition systems now evaluated were based on the directions given by the Aurora project. Moreover, a new parametric modeling approach for the PESQ-MOS versus speech recognition rate curve, based on the logistic function, is proposed. This new modeling allows some meaningful interpretations of the parameters of the logistic function in terms of system robustness, and permits to make inferences in the regions outside the experimental measures. Furthermore, the PESQ versus SNR characteristic was used to group types of noise, leading to a much better fit of the logistic function over the data points.