Physical Fundamentals of Sound Fields

  • Jens Ahrens
Part of the T-Labs Series in Telecommunication Services book series (TLABS)


The present chapter outlines the mathematical and physical tools that are employed in the subsequent chapters. It is not written in a tutorial style but serves rather as a reference. The wave equation and its solutions in Cartesian as well as in spherical coordinates are introduced. Then, a number of useful representations of sound fields such as the wavenumber domain, spherical harmonics expansions, the angular spectrum representation, and alike are presented. The basis for the solutions to the problem of sound field synthesis is set by a discussion of useful integral relations such as the Rayleigh Integral and the Kirchhoff Helmholtz Integral.


Plane Wave Spherical Harmonic Sound Pressure Sound Source Helmholtz Equation 
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  1. Abramowitz, M., & Stegun, I.A. (eds) (1999). Handbook of Mathematical Functions. New York: Dover Publications Inc.Google Scholar
  2. Ahrens, J., & Spors, S. (2009, June). Spatial encoding and decoding of focused virtual sound sources. In: Ambisonics Symposium.Google Scholar
  3. Ahrens, J., & Spors, S. (2010, March). An analytical approach to 3D sound field reproduction employing spherical distributions of non- omnidirectional loudspeakers. IEEE International Symposium, on Communications, Control and Signal Processing (ISCCSP) (pp. 1–5).Google Scholar
  4. Arfken, G., & Weber, H. (2005). Mathematical Methods for Physicists. San Diego: Elsevier Academic Press.zbMATHGoogle Scholar
  5. Blackstock, D. T. (2000). Fundamentals of Physical Acoustics. Wiley and Sons, Inc: New York.Google Scholar
  6. Colton, D., & Kress, R. (1998). Inverse Acoustic and Electromagnetic Scattering Theory. Berlin: Springer.zbMATHGoogle Scholar
  7. Condon, E. U., & Shortley, G. H. (1935). The Theory of Atomic Spectra. Cambridge: Cambridge University Press.Google Scholar
  8. Fazi, F., & Nelson, P. (2007). A theoretical study of sound field reconstruction techniques. In: 19th International Congress on Acoustics. (Sept.).Google Scholar
  9. Girod, B, Rabenstein, R, Stenger, A (2001). Signals and Systems. New York: Wiley.Google Scholar
  10. Gumerov, N. A., & Duraiswami, R. (2004). Fast Multipole Methods for the Helmholtz Equation in Three Dimensions. Amsterdam: Elsevier.Google Scholar
  11. Harris, F. J. (1978). On the use of windows for harmonic analysis with the discrete fourier transform. Proceedings of the IEEE, 66, 51–83.CrossRefGoogle Scholar
  12. Jessel, M. (1973). Acoustique Théorique: Propagation et Holophonie [Theoretical acoustics: Propagation and holophony]. New York: Wiley.Google Scholar
  13. Kennedy, R. A., Sadeghi, P., Abhayapala, T. D., & Jones, H. M. (2007). Intrinsic limits of dimensionality and richness in random multipath fields. IEEE Transactions on Signal Processing, 55(6), 2542–2556.MathSciNetCrossRefGoogle Scholar
  14. Marathay, A. S., & Rock, D. F. (1980). Evanescent wave contribution to the diffracted amplitude for spherical geometry. Pramana, 14(4), 315–320.CrossRefGoogle Scholar
  15. Morse, P. M., & Feshbach, H. (1953). Methods of Theoretical Physics. Feshbach Publishing, LLC: Minneapolis.zbMATHGoogle Scholar
  16. Nieto-Vesperinas, M. (2006). Scattering and Diffraction in Physical Optics. Singapore: World Scientific Publishing.zbMATHGoogle Scholar
  17. Rabenstein, R., Steffen, P., & Spors, S. (1980). Representation of twodimensional wave fields by multidimensional signals. EURASIP Signal Processing Magazine, 14(4), 315–320.Google Scholar
  18. Wefers, F. (2008, March). OpenDAFF: Ein freies quell-offenes Software-Paket für richtungsabhängige Audiodaten [OpenDAFF: An open-source software package for direction-dependent audio data]. Proceedings of 34th DAGA (pp. 1059–1060). text in German.Google Scholar
  19. Weisstein, E. W. (2002). CRC Concise Encyclopedia of Mathematics. London: Chapman and Hall/CRC.CrossRefGoogle Scholar
  20. Williams, EG (1999). Fourier Acoustics: Sound Radiation and Nearfield Acoustic Holography. London: Academic.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jens Ahrens
    • 1
  1. 1.Deutsche Telekom LaboratoriesTechnische Universität BerlinBerlinGermany

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