### ASA 124th Meeting New Orleans 1992 October

## 4pMU3. Maximum-likelihood harmonic matching for fundamental frequency
estimation.

**Xavier Rodet
**

**
**
*IRCAM
*

*
Univ. Paris-6, Paris, France
*

*
*
**Boris Doval
**

**
**
*Univ. Paris-6, Paris, France
*

*
*
This presentation deals with the estimation of fundamental frequency
(f[sub 0]) of pseudoperiodic sound signals with important results for
polyphonic frequency tracking, and voice separation. Given a set of candidate
partials in the signal, the estimation of f[sub 0] is taken in the sense of
finding the optimal period duration(s) according to a criterion of
maximum-likelihood harmonic matching. Excellent results have been obtained on
large databases of speech (40 mn) and music [B. Doval and X. Rodet, Proc.
IEEE-ICASSP, Toronto, May (1991)]. The algorithm has been implemented at IRCAM
to run in real time for live performance frequency tracking. Developments are
in several directions. A combined estimation of f[sub 0] and of a spectral
envelope improves both estimations. Most important is the estimation of the ``a
priori'' distributions of the different random variables on a learning set.
Finally, a hidden Markov model tracks f[sub 0] trajectories between adjacent
frames. The first experiments of polyphonic frequency tracking and voice
separation are very promising. The model can be transposed directly to the
maximum-likelihood estimation of several harmonic sounds since it already
considers more than one f[sub 0] value. [sup a)]Presently on sabbatical at Ctr.
for New Music and Audio Technol. (CNMAT), Univ. of California at Berkeley, 1750
Arch St., Berkeley, CA 94709.