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On the use of kernel-based methods in sound synthesis by physical modeling

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Abstract

In this paper we discuss an approach to the modeling of acoustic systems that combines prior information, exploited through physical modeling, and nonlinear dynamics reconstruction, exploited through support vector machine regression. We demonstrate our approach on two case studies, both addressing the broad class of acoustic systems for which the sound generation is obtained through the interaction of a linear system (resonator) and a nonlinear system (excitation). The first case is a physically based impact model, where the resonator is described in terms of its normal modes and the nonlinear contact force is modeled through a simplified collision equation and kernel regression. In the second case study, a model of the voice phonation is illustrated in which the vocal folds are represented by a lumped linear mass-spring system and the nonlinear flow component is modeled through simple Bernoulli-based equations and kernel regression.

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References

  1. Avanzini, F., Rath, M., Rocchesso, D.: Physically-based audio rendering of contact. In: Proc. International Conf. on Multimedia and Expo, vol. 2, pp. 445–448 (2002)

  2. Avanzini, F., Rath, M., Rocchesso, D., Ottaviani, L.: Low-level models: resonators, interactions, surface textures. In: Rocchesso, D., Fontana, F. (eds.) The Sounding Object, pp. 137–171 (2003)

  3. Borin, G., Poli, G.D., Rocchesso, D.: Elimination of delay-free loops in discrete-time models of nonlinear acoustic systems. IEEE Trans. Speech Audio Process. 8(5), 597–605 (2000)

    Article  Google Scholar 

  4. Chen, S., Cowan, C.F.N., Grant, P.M.: Orthogonal least squares learning algorithm for radial basis functions networks. IEEE Trans. Neural Netw. 2(2), 302–309 (1991)

    Article  Google Scholar 

  5. Drioli, C.: A flow waveform-matched low-dimensional glottal model based on physical knowledge. J. Acoust. Soc. Am. 117(5), 3184–3195 (2005)

    Article  Google Scholar 

  6. Elanayar, S., Shin, Y.C.: Radial basis function neural network for approximation and estimation of nonlinear stochastic dynamic systems. IEEE Trans. Neural Netw 5(4), 594–603 (1994)

    Article  Google Scholar 

  7. Espinoza, M., Suykens, J.A.K., De Moor B.: Kernel based partially linear models and nonlinear identification. IEEE Trans. Automat. Contr. 50(10), 1602–1606 (2005)

    Article  Google Scholar 

  8. Ishizaka, K., Flanagan, J.L.: Synthesis of voiced sounds from a two-mass model of the vocal cords. Bell Syst. Tech. J. 51(6), 1233–1268 (1972)

    Google Scholar 

  9. Iske, A.: Radial basis functions: basics, advanced topics, and meshfree methods for transport equations. Rend. Semin. Mat. 61(3), 247–286 (2003)

    MATH  MathSciNet  Google Scholar 

  10. Lindskog, P., Ljung, L.: Tools for semiphysical modelling. Int. J. Adapt. Control Signal Process. 9(6), 509–523 (1995)

    Article  MathSciNet  Google Scholar 

  11. Marhefka, D.W., Orin, D.E.: A compliant contact model with nonlinear damping for simulation of robotic systems. IEEE Trans. Syst. Man Cybern. – Part A, Syst. Humans 29(6), 566–572 (1999)

    Article  Google Scholar 

  12. Morse, B., Yoo, T., Rheingans, P., Chen, D., Subramanian, K.: Interpolating implicit surfaces from scattered surface data using compactly supported radial basis functions. In: Proceedings of IEEE Int. Conf. on Shape Modeling and Applications (SMI ’01), pp. 89–98 (2001)

  13. Rath, M., Fontana, F.: High-level models: bouncing, breaking, rolling, crumpling, pouring. In: Rocchesso, D., Fontana, F. (eds.) The Sounding Object, pp. 173–204 (2003)

  14. Suykens, J., Van Gestel, T., De Brabanter, J., De Moor, B., Vandewalle, J.: Least Squares Support Vector Machines. World Scientific Publishing, Singapore (2002)

    MATH  Google Scholar 

  15. Suykens, J.A.K., Vandewalle, J.: Recurrent least squares support vector machines. IEEE Trans. Circuits Syst. 1 47(7), 1109–1114 (2000)

    Article  Google Scholar 

  16. Välimäki, V., Pakarinen, J., Erkut, C., Karjalainen, M.: Discrete time modeling of musical instruments. Rep. Prog. Phys. 69, 1–78 (2005)

    Article  Google Scholar 

  17. van Lith, P., Betlem, B., Roffel, B.: Combining prior knowledge with data driven modeling of a batch distillation column including start-up. Comput. Chem. Eng. 27(7), 1021–1030 (2003)

    Article  Google Scholar 

  18. Vapnik, V.N.: The Nature of Statistical Learning Theory. Springer-Verlag, Berlin (1995)

    MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Verona, Verona, Italy

    Carlo Drioli & Davide Rocchesso

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  1. Carlo Drioli
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  2. Davide Rocchesso
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Correspondence to Carlo Drioli.

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Drioli, C., Rocchesso, D. On the use of kernel-based methods in sound synthesis by physical modeling. Numer Algor 45, 315–329 (2007). https://doi.org/10.1007/s11075-007-9117-z

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  • DOI: https://doi.org/10.1007/s11075-007-9117-z

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