# Bark and ERB bilinear transforms

@article{Smith1999BarkAE, title={Bark and ERB bilinear transforms}, author={Julius Orion Smith and Jonathan S. Abel}, journal={IEEE Trans. Speech Audio Process.}, year={1999}, volume={7}, pages={697-708} }

Use of a bilinear conformal map to achieve a frequency warping nearly identical to that of the Bark frequency scale is described. Because the map takes the unit circle to itself, its form is that of the transfer function of a first-order allpass filter. Since it is a first-order map, it preserves the model order of rational systems, making it a valuable frequency warping technique for use in audio filter design. A closed-form weighted-equation-error method is derived that computes the optimal…

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