Understanding the physiological mechanisms that underlie the exquisite frequency discrimination abilities of listeners remains a central problem in auditory science. We describe a computational model of the cochlea and auditory nerve that was developed to evaluate the frequency analysis capabilities of a system in which the output of a basilar membrane filter, transduced into a probability-of-firing function by an inner hair cell, is encoded on the auditory nerve as the instantaneous sum of firings on a critical band of fibers surrounding that filter channel and transmitted to the central nervous system for narrow-band frequency analysis. Performance of the model on vowels over a wide range of input levels was found to be robust and accurate, comparable to the Average Localized Synchronized Rate results of Young and Sachs [J. Acoust. Soc. Am. 1979, 66, 1381-1403]. Model performance in perceptual threshold simulations was also evaluated. The model succeeded in replicating psychophysical results reported in classic studies of critical band masking.