in the weighted equation error solution Eq.(21) can be
multiplied by any desired application-dependent weighting.
Audio conformal maps can be adjusted by using a more general error
weighting versus frequency. For example, the weighting can be set to
zero above some frequency limit along the unit circle. A more general
weighting can also be used to obtain improved accuracy in specific
desired frequency ranges. Again, these refinements would seem to be
of interest primarily for the ERB-scale and other mappings, since the
Bark-scale warping is excellent already. The diagonal weighting matrix
in the weighted equation error solution Eq.(21) can be
multiplied by any desired application-dependent weighting.
As another variation, an auditory frequency scale could be defined based on the cochlear frequency-to-place function [6]. In this case, a close relationship still exists between equal-place increments along the basilar membrane and equal bandwidth increments in the defined audio filterbank. Preliminary comparisons [6, Fig. 9] indicate that the first-order conformal map errors for this case are qualitatively between the ERB and Bark-scale cases. The first-order conformal map works best when the auditory filter bandwidths level off to a minimum width at low frequencies, as they do in the Bark-scale case below 500 Hz. Thus, the question of the ``audio fidelity'' of the first-order conformal map is directly tied to the question of what is really the best frequency resolution to provide at low frequencies in the auditory filterbank.
