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J. O. Smith, ``Efficient simulation of the reed-bore and bow-string mechanisms,'' in Proceedings of the 1986 International Computer Music Conference, The Hague, pp. 275-280, Computer Music Association, 1986.
Also available in [24].

J. O. Smith, ``Physical modeling using digital waveguides,'' Computer Music Journal, vol. 16, pp. 74-91, Winter 1992.
Special issue: Physical Modeling of Musical Instruments, Part I. Available online at

V. Välimäki and M. Karjalainen, ``Improving the Kelly-Lochbaum vocal tract model using conical tube sections and fractional delay filtering techniques,'' in Proc. 1994 International ConferenceOn Spoken Language Processing (ICSLP-94), vol. 2, (Yokohama, Japan), pp. 615-618, IEEE Press, Sept. 18-22 1994.

V. Välimäki, J. Huopaniemi, M. Karjalainen, and Z. Jánosy, ``Physical modeling of plucked string instruments with application to real-time sound synthesis,'' Journal of the Audio Engineering Society, vol. 44, pp. 331-353, May 1996.

M. Karjalainen, V. Välimäki, and T. Tolonen, ``Plucked string models: From the Karplus-Strong algorithm to digital waveguides and beyond,'' Computer Music Journal, vol. 22, pp. 17-32, Fall 1998.
Available online at

D. P. Berners, Acoustics and Signal Processing Techniques for Physical Modeling of Brass Instruments.
PhD thesis, Elec. Engineering Dept., Stanford University (CCRMA), June 1999.
Available online at

G. De Poli and D. Rocchesso, ``Computational models for musical sound sources,'' in Music and Mathematics (G. Assayag, H. Feichtinger, and J. Rodriguez, eds.), Springer Verlag, 2001.
In press.

J. O. Smith, ``A new approach to digital reverberation using closed waveguide networks,'' in Proceedings of the 1985 International Computer Music Conference, Vancouver, pp. 47-53, Computer Music Association, 1985.
Also available in [24].

D. Rocchesso and J. O. Smith, ``Circulant and elliptic feedback delay networks for artificial reverberation,'' IEEE Transactions on Speech and Audio Processing, vol. 5, no. 1, pp. 51-63, 1997.

D. Rocchesso, ``Maximally-diffusive yet efficient feedback delay networks for artificial reverberation,'' IEEE Signal Processing Letters, vol. 4, pp. 252-255, Sept. 1997.

F. Fontana and D. Rocchesso, ``Physical modeling of membranes for percussion instruments,'' Acustica, vol. 77, no. 3, pp. 529-542, 1998.
S. Hirzel Verlag.

L. Savioja, J. Backman, A. Järvinen, and T. Takala, ``Waveguide mesh method for low-frequency simulation of room acoustics,'' in Proceedings of the 15th International ConferenceOn Acoustics (ICA-95), Trondheim, Norway, pp. 637-640, June 1995.

L. Savioja and V. Välimäki, ``Reducing the dispersion error in th digital waveguide mesh using interpolation and frequency-warping techniques,'' IEEE Transactions on Speech and Audio Processing, vol. 8, pp. 184-194, March 2000.

S. Bilbao, Wave and Scattering Methods for the Numerical Integration of Partial Differential Equations.
PhD thesis, Stanford University, June 2001.
Available online at

F. Fontana and D. Rocchesso, ``Signal-theoretic characterization of waveguide mesh geometries for models of two-dimensional wave propagation in elastic media,'' IEEE Transactions on Speech and Audio Processing, vol. 9, pp. 152-161, Feb. 2001.

D. T. Murphy and D. M. Howard, ``2-D digital waveguide mesh topologies in room acoustics modelling,'' in Proceedings of the ConferenceOn Digital Audio Effects (DAFx-00), Verona, Italy, pp. 211-216, Dec. 2000.
Available online at

P. Huang, S. Serafin, and J. Smith, ``A waveguide mesh model of high-frequency violin body resonances,'' in Proceedings of the 2000 International Computer Music Conference, Berlin, Aug. 2000.

J. O. Smith, ``Principles of digital waveguide models of musical instruments,'' in Applications of Digital Signal Processing to Audio and Acoustics (M. Kahrs and K. Brandenburg, eds.), pp. 417-466, Boston/Dordrecht/London: Kluwer Academic Publishers, 1998.

J. O. Smith and D. Rocchesso, ``Aspects of digital waveguide networks for acoustic modeling applications,'', December 19, 1997.

R. J. Anderson and M. W. Spong, ``Bilateral control of teleoperators with time delay,'' IEEE Transactions on Automatic Control, vol. 34, pp. 494-501, May 1989.

A. Fettweis, ``Pseudopassivity, sensitivity, and stability of wave digital filters,'' IEEE Transactions on Circuit Theory, vol. 19, pp. 668-673, Nov. 1972.

A. Fettweis, ``Wave digital filters: Theory and practice,'' Proceedings of the IEEE, vol. 74, pp. 270-327, Feb. 1986.

J. O. Smith, ``Elimination of limit cycles and overflow oscillations in time-varying lattice and ladder digital filters,'' in Proceedings of the IEEE ConferenceOn Circuits and Systems, San Jose, pp. 197-299, May 1986.
Conference version. Full version available in [24].

J. O. Smith, ``Music applications of digital waveguides,'' Tech. Rep. STAN-M-39, CCRMA, Music Department, Stanford University, 1987.
A compendium containing four related papers and presentation overheads on digital waveguide reverberation, synthesis, and filtering. CCRMA technical reports can be ordered by calling (650)723-4971 or by sending an email request to

D. Rocchesso, Strutture ed Algoritmi per l'Elaborazione del Suono basati su Reti di Linee di Ritardo Interconnesse.
Phd thesis, Università di Padova, Dipartimento di Elettronica e Informatica, Feb. 1996.

W. C. Elmore and M. A. Heald, Physics of Waves.
New York: McGraw Hill, 1969.
Dover Publ., New York, 1985.

P. M. Morse, Vibration and Sound.
(516)349-7800 x 481: American Institute of Physics, for the Acoustical Society of America, 1981.
1st ed. 1936, 4th ed. 1981.

P. M. Morse and K. U. Ingard, Theoretical Acoustics.
New York: McGraw-Hill, 1968.

A. Askenfelt, ed., Five lectures on the acoustics of the piano.
Stockholm: Royal Swedish Academy of Music, 1990.

G. Weinreich, ``Coupled piano strings,'' Journal of the Acoustical Society of America, vol. 62, pp. 1474-1484, Dec 1977.
Also contained in [29]. See also Scientific American, vol. 240, p. 94, 1979.

R. W. Newcomb, Linear Multiport Synthesis.
New York: McGraw-Hill, 1966.

D. Rocchesso, ``The ball within the box: a sound-processing metaphor,'' Computer Music Journal, vol. 19, pp. 47-57, Winter 1995.

L. P. Franzoni and E. H. Dowell, ``On the accuracy of modal analysis in reverberant acoustical systems with damping,'' Journal of the Acoustical Society of America, vol. 97, pp. 687-690, Jan 1995.

S. A. Van Duyne and J. O. Smith, ``Physical modeling with the 2-d digital waveguide mesh,'' in Proc. International Computer Music Conference, (Tokyo, Japan), pp. 40-47, ICMA, 1993.

S. A. Van Duyne and J. O. Smith, ``The tetrahedral waveguide mesh: Multiply-free computation of wave propagation in free space,'' in Proceedings of the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics, (Mohonk, NY), Oct. 1995.

G. Putland, ``Every one-parameter acoustic field obeys webster's horn equation,'' Journal of the Audio Engineering Society, vol. 41, pp. 435-451, June 1993.

J. O. Smith, ``Waveguide simulation of non-cylindrical acoustic tubes,'' in Proceedings of the 1991 International Computer Music Conference, Montreal, pp. 304-307, Computer Music Association, 1991.

R. D. Ayers, L. J. Eliason, and D. Mahgerefteh, ``The conical bore in musical acoustics,'' American Journal of Physics, vol. 53, pp. 528-537, June 1985.

P. P. Vaidyanathan, Multirate Systems and Filter Banks.
Englewood Cliffs, NY: Prentice Hall, 1993.

V. Belevitch, Classical Network Theory.
San Francisco: Holden-Day, 1968.

M. R. Wohlers, Lumped and Distributed Passive Networks.
New York: Academic Press, Inc., 1969.

M. E. Van Valkenburg, Introduction to Modern Network Synthesis.
New York: John Wiley and Sons, Inc., 1960.

T. W. Parks and C. S. Burrus, Digital Filter Design.
New York: John Wiley and Sons, Inc., June 1987.

N. Amir, G. Rosenhouse, and U. Shimony, ``Discrete model for tubular acoustic systems with varying cross section - the direct and inverse problems. Part 1: Theory,'' Acta Acustica, vol. 81, pp. 450-462, 1995.

N. H. Fletcher and T. D. Rossing, The Physics of Musical Instruments.
New York: Springer-Verlag, 1991.

A. Benade, ``Equivalent circuits for conical waveguides,'' Journal of the Acoustical Society of America, vol. 83, pp. 1764-1769, May 1988.


0\framebox(25,32)0=37mm10=010 by29mm-10 0to 28.5mm 00=0mm0=0mm0Rocchessois a PhD candidate at the Dipartimento di Elettronica e Informatica, Università di Padova - Italy. He received his Electrical Engineering degree from the Università di Padova in 1992, with a dissertation on real-time physical modeling of music instruments. In 1994 and 1995, he was visiting scholar at the Center for Computer Research in Music and Acoustics (CCRMA), Stanford University. He has been collaborating with the Centro di Sonologia Computazionale (CSC) dell'Università di Padova since 1991, as a researcher and a live-electronic designer/performer. His main interests are in audio signal processing, physical modeling, sound reverberation and spatialization, parallel algorithms. Since 1995 he has been a member of the Board of Directors of the Associazione di Informatica Musicale Italiana (AIMI).


0\framebox(25,32)0=37mm10=010 by29mm-10 0to 28.5mm 00=0mm0=0mm0O. Smithreceived the B.S.E.E. degree from Rice University, Houston, TX, in 1975. He received the M.S. and Ph.D. degrees in E.E. from Stanford University, Stanford, CA, in 1978 and 1983, respectively. His Ph.D. research involved the application of digital signal processing and system identification techniques to the modeling and synthesis of the violin, clarinet, reverberant spaces, and other musical systems. From 1975 to 1977 he worked in the Signal Processing Department at ESL, Sunnyvale, CA, on systems for digital communications. From 1982 to 1986 he was with the Adaptive Systems Department at Systems Control Technology, Palo Alto, CA, where he worked in the areas of adaptive filtering and spectral estimation. From 1986 to 1991 he was employed at NeXT Computer, Inc., responsible for sound, music, and Signal processing software for the NeXT computer workstation. Since then he has been an Associate Professor at the Center for Computer Research in Music and Acoustics (CCRMA) at Stanford teaching courses in Signal processing and music technology, and pursuing research in Signal processing techniques applied to music and audio. For more information, see

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``Generalized Digital Waveguide Networks'', by Julius O. Smith III and Davide Rocchesso, preprint submitted for publication, Summer 2001.
Copyright © 2008-03-12 by Julius O. Smith III and Davide Rocchesso
Center for Computer Research in Music and Acoustics (CCRMA),   Stanford University
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