The optimum receiver for the case where signal is known except for phase has been suggested as a model for auditory detection of sinusoidal signals in noise. We have furthered application of this model in an effort to evaluate some of the parameters of monaural detection that are important for prediction. Of particular interest is bandwidth, or “critical band,” which was found to decrease as signal‐to‐noise ratio increases, the rate of decrease being a function of frequency. Bandwidths were derived from the parametric values of the ROC's that describe the detection performance of our observers. It was found that human ROC's are closely matched by ideal ROC's. The ROC's of our observers were obtained with a six‐category rating scale and our measure of detection wasds. Values ofdswere obtained at 500, 800, 1300, 2500, and 4000 Hz over a range of signal‐to‐noise (S/N) ratios. It was found that the relationship ofdsto S/N ratio at all signal frequencies could be summarized by a single equation, the psychometric function. Other equations are also given so that the psychometric function for any signal frequency may be determined simply from a knowledge of the power per unit bandwidth of the masking noise.