The Bark bilinear transform

Use of a bilinear conformal map to achieve a frequency warping nearly identical to the Bark scale is described. Because the map takes the unit circle to itself, its form is that of an allpass transfer function. Since it is a first-order map, it preserves the model order of rational systems. A direct-form expression for computing the optimal allpass coefficient as a function of sampling rate is developed, and a filter design example is presented.