# Nonlinear Parameter Estimation of Acoustic Models

### Erling Henry Wold

###
EECS Department

University of California, Berkeley

Technical Report No. UCB/CSD-87-354

April 1987

A number of audio signal processing applications analyze a signal in terms of some basic model for its source. The all-pole estimation techniques widely used today exhibit low fidelity and are not well matched to any real physical system. It is our thesis that estimation using more accurate physical models will achieve much higher fidelity. Also, we contend these models will allow the separation of two audio signals from simultaneously sounding sources. To achieve this, we have devised state equation models of several physical systems, including bars, clarinets and voices. Algorithms have been developed which allow estimation of the state and parameters of these systems to be done with reasonable accuracy. These algorithms, which center around a set of extended Kalman filters and optimization techniques such as Newton-Raphson and the Chow-Yorke homotopy method, are far more complex computationally than those used for audio analysis today.

All of the models and estimation algorithms have been included in a software system which has been used to successfully estimate the parameters of signals from the sources mentioned above and to separate signals from pairs of those sources sounding simultaneously. The estimation techniques can be applied to all-pole, pole-zero and sum-of-sines models, allowing comparisons to be made between the performance of these models and ours. The algorithms developed are successful in accomplishing estimations and separations, but are more sensitive to variations in the initial estimates of the parameter positions than those used now. The simpler models are more flexible, but achieve much lower fidelity.

General-purpose processors are much too slow to compute these algorithms in real time. Thus, architectures for these problems have been investigated and some preliminary proposals have been made for a special-purpose machine which could be integrated into the Aquarius supercomputer. The algorithms have been analyzed for their computational complexity, inherent parallelism and memory usage, and the performance of the software system has been profiled to find those areas where significant speedups can be made.

Following this, future research areas are outlined and discussed, including model simplification, symbolic computation, adaptivity, and the use of the Prolog programming language.

**Advisor:** Alvin M. Despain

BibTeX citation:

@phdthesis{Wold:CSD-87-354, Author = {Wold, Erling Henry}, Title = {Nonlinear Parameter Estimation of Acoustic Models}, School = {EECS Department, University of California, Berkeley}, Year = {1987}, Month = {Apr}, URL = {http://www.eecs.berkeley.edu/Pubs/TechRpts/1987/6213.html}, Number = {UCB/CSD-87-354}, Abstract = {A number of audio signal processing applications analyze a signal in terms of some basic model for its source. The all-pole estimation techniques widely used today exhibit low fidelity and are not well matched to any real physical system. It is our thesis that estimation using more accurate physical models will achieve much higher fidelity. Also, we contend these models will allow the separation of two audio signals from simultaneously sounding sources. To achieve this, we have devised state equation models of several physical systems, including bars, clarinets and voices. Algorithms have been developed which allow estimation of the state and parameters of these systems to be done with reasonable accuracy. These algorithms, which center around a set of extended Kalman filters and optimization techniques such as Newton-Raphson and the Chow-Yorke homotopy method, are far more complex computationally than those used for audio analysis today. <p> All of the models and estimation algorithms have been included in a software system which has been used to successfully estimate the parameters of signals from the sources mentioned above and to separate signals from pairs of those sources sounding simultaneously. The estimation techniques can be applied to all-pole, pole-zero and sum-of-sines models, allowing comparisons to be made between the performance of these models and ours. The algorithms developed are successful in accomplishing estimations and separations, but are more sensitive to variations in the initial estimates of the parameter positions than those used now. The simpler models are more flexible, but achieve much lower fidelity. <p> General-purpose processors are much too slow to compute these algorithms in real time. Thus, architectures for these problems have been investigated and some preliminary proposals have been made for a special-purpose machine which could be integrated into the Aquarius supercomputer. The algorithms have been analyzed for their computational complexity, inherent parallelism and memory usage, and the performance of the software system has been profiled to find those areas where significant speedups can be made. <p> Following this, future research areas are outlined and discussed, including model simplification, symbolic computation, adaptivity, and the use of the Prolog programming language.} }

EndNote citation:

%0 Thesis %A Wold, Erling Henry %T Nonlinear Parameter Estimation of Acoustic Models %I EECS Department, University of California, Berkeley %D 1987 %@ UCB/CSD-87-354 %U http://www.eecs.berkeley.edu/Pubs/TechRpts/1987/6213.html %F Wold:CSD-87-354