Newsgroups: comp.speech
Path: pavo.csi.cam.ac.uk!pipex!uunet!munnari.oz.au!uniwa!swanee.ee.uwa.oz.au!rama!robert
From: robert@swanee.ee.uwa.edu.au (Roberto Togneri)
Subject: Re: Wanted: LPC to Melcepstral Conversion Routine
Message-ID: <robert.718595609@swanee>
Sender: news@swanee.ee.uwa.oz.au
Organization: Elec Eng, Univ of Western Australia
References: <1992Oct7.141959.1268@walter.bellcore.com>
Date:  9 Oct 92 01:53:29 GMT
Lines: 46

In <1992Oct7.141959.1268@walter.bellcore.com> dpepper@thumper.bellcore.com (David J. Pepper) writes:

>Does anyone have a reference to the bilinear transform algorithm that
>goes directly from LPC parameters to Mel scale cepstral parameters?
>I have seen many people who say that they are using this algorithm,
>but I have never been able to track down the actual conversion routine.

>BTW, for those that are interested in LPC analysis and conversions,
>the book J.D. Markel and A.H. Gray, Jr., "Linear Prediction of Speech,"
>Springer--Verlag, 1976 is very good.  It contains a variety of transformation
>routines and FORTRAN code for those transformations.  Also, a good paper
>on Mel-cepstral parameters (from an FFT type spectrum) is S.B. Davis and
>P. Mermelstein, "Comparison of Parametric Representations for Monosyllabic
>Word Recognition in Continuously Spoken Sentences," IEEE Trans. ASSP,
>vol. 28, pp. 357--366, August 1980.

>			Thanks in advance,
>			David Pepper


I'd like to extend the request to the algorithm which goes directly from
LPC parameters to mel-spaced cepstral co-effcients (as distinct from
linearly spaced cepstral co-efficients). As far as LPC to linear-scale
cepstral co-efficients go here is the recursive relation:
(ref: "Digital Speech, Processing, Synthesis, and Recognition" by
Sadaoki Furui, Marcel Dekker, Inc, 1989, ISBN 0-8247-7965-7)

c(1) = a(1)

c(n) = -a(n) - sum from m=1 to m=n-1 of {(1 - m/n)a(m)c(n-m)}  for 1 < n <= p

c(n) = - sum from m=1 to m=p of {(1-m/n)a(m)c(n-m)} for p < n

where a(i) for i=1,2 ... p are the p-order LPC co-efficients 
and c(n) are the cepstral co-efficients.

So how does one do the same trick for LPC to mel-spaced (or bark-scale spaced)
cepstral co-efficients?


--
Dr. Roberto Togneri                        Phone: +61-9-380-2535     _--_|\
Centre for Intelligent Information Processing Systems               /      \ 
Dept. of Electrical & Electronic Engineering                        *_.--._/
The University of Western Australia        Fax:   +61-9-380-1101          v 
NEDLANDS WA 6009 Australia                 Email: robert@swanee.ee.uwa.edu.au
