Subject:Re: Origin of the Mel frequency scale equation?From:"James D. Miller" <jamdmill@xxxxxxxx>Date:Mon, 10 Mar 2008 10:25:08 -0400List-Archive:<http://lists.mcgill.ca/scripts/wa.exe?LIST=AUDITORY>Gunnar Fant long ago suggested the Technical Mel(TM) scale and it is in his 1974 Book "Speech Sounds and Features (MIT Press 1974). He gave us TM = [1000/log(2)]*log[1+f/1000], Where the log is to the base 10 and f is in Hz. This fits the Mel Scale of Stevens and Volkman (1940) except at the very high frequencies. See the figure in Fant's book. I have developed a quadratic that fits the 1940 scale very accurately and modification of the Fant equation that also fits the 1940 scale over its entire range. I have no idea of where the Mel = C*log (1 + f/700) came from in the the speech-engineering literature. With the appropriate choice of C, I expect it doesn't differ too much from Fant's TM over the ranges of interest to speech engineers. Jim Miller jamdmill@xxxxxxxx Quoting Christine Rankovic <rankovic@xxxxxxxx>: > It might be: > > Stevens, S., and J. Volkmann (1940). The relation of pitch to > frequency: A revised scale. Am. J. Psychol. 53:329-353. > > Sincerely, > > Christine Rankovic, PhD > rankovic@xxxxxxxx > > > ----- Original Message ----- From: "Arturo Camacho" <acamacho@xxxxxxxx> > To: <AUDITORY@xxxxxxxx> > Sent: Monday, March 10, 2008 1:09 AM > Subject: Origin of the Mel frequency scale equation? > > >> Dear members of the list, >> >> I am looking for the reference of first use of the equation >> >> m = C log(1+f/700) >> >> known as mel frequency scale transformation. In Wikipedia says that the >> scale was originated by Stevens, Volkman and Newman in 1937 (J. Acoust. >> Soc. Am 8(3) 185--190), but the paper only has tabulated data and no >> equation. The paper by S.B. Davis & P. Mermelstein (1980), "Comparison of >> parametric representations for monosyllabic word recognition in >> continuously spoken sentences", IEEE Trans. on ASSP 28, 357-366 is usually >> cited in the speech recognition community as origin of MFCCs, but the >> equation is absent there as well. >> >> Thanks, >> >> Arturo >> >> -- >> __________________________________________________ >> >> Arturo Camacho, PhD >> Alumni >> Computer and Information Science and Engineering >> University of Florida >> >> E-mail: acamacho@xxxxxxxx >> Web page: www.cise.ufl.edu/~acamacho >> __________________________________________________ >> > --

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