Re: frequency to mel formula

[Dan Ellis <dpwe@xxxxxxxxxxxxxxx>]

We discussed this last year.  See
http://www.auditory.org/mhonarc/2008/msg00191.html
http://www.auditory.org/mhonarc/2008/msg00189.html
and the surrounding thread.

I think the actual origin is Fant in a paper in Swedish from 1949,
summarized in his 1973 book:

Fant, C G M "Analys av de svenska konsonantljuden" LM Ericsson
protokoll H/P 1064, 1949: 139pp.

referenced on p. 48 of
Fant, G "Speech Sounds and Features", MIT Press, 1973.

but Fant uses log(1+f/1000).  The log(1+f/700) was attributed to

O'Shaughnessy, D. (1978) Speech communication: Human and machine.
Addison-Wesley, New York, page 150.

  DAn.


On Wed, Jul 15, 2009 at 2:11 PM, James W.
Beauchamp<jwbeauch@xxxxxxxxxxxxxxxxxxxxxx> wrote:
> Dear List,
>
> On the Wikipedia page
>  http://en.wikipedia.org/wiki/Mel_frequency_scale
>
> a formula for computing frequency in terms of mels is given as:
>
> mel = log(1 + fr/700)*1127 .
>
> It is easily inverted to fr = 700*exp(mel/1127 - 1) .
>
> My question is: Where do these formulas come from? I.e., I need
> a journal reference for these formulas.
>
> Thanks much,
>
> Jim Beauchamp
> Univ. of Illinois at Urbana-Champaign
>