Comparison and Fitting of Analytical Expressions to Existing Data for the Critical-Band Concept

The existing analytical expressions describing the frequency dependencies of critical bandwidth and equivalentrectangular bandwidth were derived from the results of diff erent sets of listening experiments. As the corresponding band-rate scales are constructed by integrating the reciprocal bandwidth function over frequency, also the band-rate functions are based on the respectively selected experiments. The critical-bandwidth formula converges to 100 Hz at frequencies below about 500 Hz and the critical-band-rate function is not invertible in closed form, which complicates the application of the critical-band concept in modeling. In order to overcome these restrictions, the data used earlier to construct and validate the bandwidth functions were re-evaluated separately for the critical-band and the equivalent-rectangular-band concepts, and also combined. It is shown that the shape of a critical-bandwidth-frequency formula derived from a cochlear frequency-position function that results in an invertible critical-band-rate formula can be fitted to both data sets. Depending on frequency, the formulae predict about 1.53 to 1.55 times larger critical than equivalent-rectangular bandwidths. Low-frequency critical bandwidths, which are overestimated compared to the data by the earlier formula, are represented more accurately and at the same time suited better to avoid modeling artifacts. The determined functions are compared against each other and against the previously proposed bandwidth and band-rate formulae. The results indicate that a common function shape with a simple parameter variation is suited to account for the data used earlier to validate two different sets of formulae.