For an approximation to the optimal Chebyshev ERB frequency mapping, the arctangent formula becomes
where is in kHz. This formula is plotted along with the various optimal curves in Fig.E.12a, and the approximation error is shown in Fig.E.12b. The performance of the arctangent approximation can be seen in Fig.E.13.
The performance of this formula is shown in Fig.E.16. It follows the optimal Chebyshev map parameter very well.
Blackman Window Example
ERB Relative Bandwidth Mapping Error