### Bark Relative Bandwidth Mapping Error

The

*slope*of the frequency versus warped-frequency curve can be interpreted as being proportional to critical bandwidth, since a unit interval (one Bark) on the warped-frequency axis is magnified by the slope to restore the band to its original size (one critical bandwidth). It is therefore interesting to look at the

*relative slope error*,

*i.e.*, the error in the slope of the frequency mapping divided by the ideal Bark-map slope. We interpret this error measure as the

*relative bandwidth-mapping error*(RBME). The RBME is plotted in Fig.E.6 for a kHz sampling rate. The worst case is 21% for the Chebyshev case and 20% for both least-squares cases. When the mapping coefficient is explicitly optimized to minimize RBME, the results of Fig.E.7 are obtained: the Chebyshev peak error drops from 21% down to 18%, while the least-squares cases remain unchanged at 20% maximum RBME. A 3% change in RBME is comparable to the 0.03 Bark peak-error reduction seen in Fig.E.5 when using the Chebyshev norm instead of the norm; again, such a small difference is not likely to be significant in most applications.

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Error Significance

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Optimal Frequency Warpings