[vorbis-dev] References for the BARK/MEL stuff

[Timothy J. Wood]

  Could someone point me to the BARK/MEL tables that these macros (from vorbis/scales.h) are trying to approximate?

#define toBARK(f)   (13.1*atan(.00074*(f))+2.24*atan((f)*(f)*1.85e-8)+1e-4*(f))
#define fromBARK(z) (102.*(z)-2.*pow(z,2.)+.4*pow(z,3)+pow(1.46,z)-1.)
#define toMEL(f)    (log(1.+(f)*.001)*1442.695)
#define fromMEL(m)  (1000.*exp((m)/1442.695)-1000.)

  I was wondering if I could come up with different functions that were easier to compute that would still be good approximations (also, can anyone comment on what a good metric is for judging the 'goodness' of an approximation function).

  Looking at a graph of toBark() in Mathematica over 0-30,000 makes it look like something way simpler than atan could be used (of course, maybe I've implemented toBark incorrectly in Mathematica, which is why I want to look at the original tables :)

-tim

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