Discrete Secondary Source Distributions

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

Abstract

The continuous secondary source distributions treated in the previous chapter can not be implemented with today’s available technology. Continuous distributions have to be approximated by a finite number of discrete loudspeakers. The analogies of this spatial discretization to the discretization continuous time signals are outlined, based on which the consequences of spatial discretization on the properties of the synthesized sound field are analyzed in detail. A discussion of the time-domain structure of the evolving wave fronts is performed and those properties that are most relevant for spatial auditory perception by human listeners are identified and interpreted. Then, the concept of local sound field synthesis is introduced, which allows for a local increase of the accuracy of the synthesized sound field by the cost of stronger artifacts outside the local target region.

Keywords

Wave Front Secondary Source Reconstruction Error Spatial Discretization Sound Field 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. Ahrens, J. (2010). The single-layer potential approach applied to sound field synthesis including cases of non-enclosing distributions of secondary sources. (Doctoral dissertation, Technische Universität Berlin, 2010)Google Scholar
  2. Ahrens, J., & Spors, S. (2008). An analytical approach to sound field reproduction using circular and spherical loudspeaker distributions. Acta Acustica utd. with Acustica, 94(6), 988–999.CrossRefGoogle Scholar
  3. Ahrens, J., & Spors, S. (2009, April). An analytical approach to sound field reproduction with a movable sweet spot using circular distributions of loudspeakers. IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), pp. 273–276.Google Scholar
  4. Ahrens, J., & Spors, S. (2010a, November). On the anti-aliasing loudspeaker for sound field synthesis employing linear and circular distributions of secondary sources. 129th Convention of the AES.Google Scholar
  5. Ahrens, J., & Spors, S. (2010b). Sound field reproduction using planar and linear arrays of loudspeakers. IEEE Transaction on Speech and Audio Processing, 18(8), 2038–2050.CrossRefGoogle Scholar
  6. Ahrens, J., & Spors, S. (2011). Modal analysis of spatial discretization of spherical loudspeaker distributions used for sound field synthesis. IEEE Transaction on Speech and Audio Processing (submitted)Google Scholar
  7. Ajdler, T., Sbaiz, L., & Vetterli, M. (2006). The plenacoustic function and its sampling. IEEE Transaction on Signal Processing, 54(10), 3790–3804.CrossRefGoogle Scholar
  8. Armstrong, M. A. (1988). Groups and symmetry. New York: Springer.MATHGoogle Scholar
  9. Berkhout, A. J., de Vries, D., & Vogel, P. (1993). Acoustic control by wave field synthesis. Journal of the Acoustical Society of America, 93(5), 2764–2778.CrossRefGoogle Scholar
  10. Blauert, J (1997). Spatial hearing. New York: Springer.Google Scholar
  11. Daniel, J. (2001). Représentation de champs acoustiques, applicationà à la transmission età à la reproduction de scènes sonores complexes dans un contexte multimédia [Representations of sound fields, application to the transmission and reproduction of complex sound scenes in a multimedia context]. (PhD thesis, Université Paris 6, Text in French, 2001).Google Scholar
  12. Daniel, J. (2003, May). Spatial sound encoding including near field effect: Introducing distance coding filters and a viable, new ambisonic format. 23rd International Conference of the AES.Google Scholar
  13. de Brujin, W. (2004). Application of wave field synthesis in videoconferencing (PhD thesis, Delft University of Technology, 2004).Google Scholar
  14. de Vries, D. (2009). Wave field synthesis AES monograph. New York: AESGoogle Scholar
  15. Driscoll, J. R., & Healy, D. M. (1994). Computing Fourier transforms and convolutions on the 2-Sphere. Advances in Applied Mathematics, 15(2), 202–250.MathSciNetMATHCrossRefGoogle Scholar
  16. Excell, D. (2003). Reproduction of a 3D sound field using an array of loudspeakers (Bachelor thesis, Australian National University, 2003).Google Scholar
  17. Fazi, F. (2010). Sound field reproduction. (Ph.D. thesis, University of Southampton, 2010).Google Scholar
  18. Fazi, F., Brunel, V., Nelson, P., Hörchens, L., & Seo, J. (2008, May). Measurement and Fourier-Bessel analysis of loudspeaker radiation patterns using a spherical array of microphones. 124th Convention of the AES, p. 7354.Google Scholar
  19. Girod, B., Rabenstein, R., & Stenger, A. (2001). Signals and systems. New York: Wiley.Google Scholar
  20. Gumerov, N. A., & Duraiswami, R. (2004). Fast multipole methods for the Helmholtz equation in three dimensions. Amsterdam: Elsevier.Google Scholar
  21. Hannemann, J., & Donohue, K. D. (2008). Virtual sound source rendering using a multipole-expansion and method-of-moments approach. Journal of the Audio Engineering Society, 56(6), 473–481.Google Scholar
  22. Kennedy, R. A., Sadeghi, P., Abhayapala, T. D., & Jones, H. M. (2007). Intrinsic limits of dimensionality and richness in random multipath fields. IEEE Transaction on Signal Processing, 55(6), 2542–2556.MathSciNetCrossRefGoogle Scholar
  23. Kirkeby, O., & Nelson, P. A. (1993). Reproduction of plane wave sound fields. Journal of the Acoustical Society of America, 94(5), 2992–3000.CrossRefGoogle Scholar
  24. Kolundžija, M., Faller, C., & Vetterli, M. (2009, May). Sound field reconstruction: An improved approach for wave field synthesis. 126th Convention of the AES, p. 7754.Google Scholar
  25. Litovsky, R. Y., Colburn, H. S., Yost, W. A., & Guzman, S. J. (1999). The precedence effect. Journal of the Acoustical Society of America, 106(4), 1633–1654.CrossRefGoogle Scholar
  26. Mitchell, D. P., & Netravali, A. N. (1988). Reconstruction filters in computer graphics. Computer Graphics, 22(4), 221–228.CrossRefGoogle Scholar
  27. Mohlenkamp, M. J. (1999). Fast transform for spherical harmonics. Journal of Fourier Analysis and Applications, 5(2/3), 159–184.MathSciNetMATHCrossRefGoogle Scholar
  28. Poletti, M. A. (2005). Three-dimensional surround sound systems based on spherical harmonics. Journal of the Audio Engineering Society, 53(11), 1004–1025.Google Scholar
  29. Pueo, B., Lopez, J. J., Escolano, J., & Bleda, S. (2007). Analysis of multiactuator panels in space-time wavenumber domain. Journal of the Audio Engineering Society, 55(12), 1092–1106.Google Scholar
  30. Rafaely, B., Weiss, B., & Bachmat, E. (2007). Spatial aliasing in spherical microphone arrays. IEEE Transactions on Signal Processing, 55(3), 1003–1010.MathSciNetCrossRefGoogle Scholar
  31. Saff, E. B., & Kuijlaars, A. B. J. (1997). Distributing many points on the sphere. Mathematical Intelligencer, 19(1), 5–11.MathSciNetMATHCrossRefGoogle Scholar
  32. Sanson, J., Corteel, E., & Warusfel, O. (2008, May). Objective and subjective analysis of localization accuracy in wave field synthesis. 124th Convention of the AES, p. 7361.Google Scholar
  33. Spors, S. (2006, March). Spatial aliasing artifacts produced by linear loudspeaker arrays used for wave field synthesis. IEEE International Symposium on Communication, Control and Signal Processing, pp. 1–4.Google Scholar
  34. Spors, S. (2008, March). Investigation of spatial aliasing artifacts of wave field synthesis in the temporal domain. 34rd German Annual Conference on Acoustics (DAGA), pp. 223-224.Google Scholar
  35. Spors, S., Rabenstein, R. (2006, May). Spatial aliasing artifacts produced by linear and circular loudspeaker arrays used for wave field synthesis. 120th Convention of the AES, p. 6711.Google Scholar
  36. Spors, S., & Ahrens, J. (2007, March). Analysis of near-field effects of wave field synthesis using linear loudspeaker arrays. 30th Intern. Conference of the AES, p. 29.Google Scholar
  37. Spors, S., & Ahrens, J. (2008, Oct). A Comparison of wave field synthesis and higher-order ambisonics with respect to physical properties and spatial sampling. 125th Convention of the AES, p. 7556.Google Scholar
  38. Spors, S., & Ahrens, J. (2010a, May). Analysis and improvement of preequalization in 2.5-dimensional wave field synthesis. 128th Convention of the AES.Google Scholar
  39. Spors, S., & Ahrens, J. (2010b, March). Reproduction of focused sources by the spectral division method. IEEE International Symposium on Communication, Control and Signal Processing (ISCCSP).Google Scholar
  40. Spors, S., Rabenstein, R., & Ahrens, J. (2008, May). The theory of wave field synthesis revisited. 124th Convention of the AES.Google Scholar
  41. Spors, S., Wierstorf, H., Geier, M., & Ahrens, J. (2009, Oct). Physical and perceptual properties of focused sources in wave field synthesis. 127th Convention of the AES, p. 7914.Google Scholar
  42. Start, E. W. (1997). Direct sound enhancement by wave field synthesis. (PhD thesis, Delft University of Technology, 1997).Google Scholar
  43. The Chebfun Team. (2009). The Chebfun Project. http://www2.maths.ox.ac.uk/chebfun. Online: Accessed 09- Dec-2009.Google Scholar
  44. Theile, G. (2004, March). Spatial perception in WFS rendered sound fields. Proceedings of the Joint Congress CFA/DAGA, pp. 27–30.Google Scholar
  45. Verheijen, E. N. G. (1997). Sound reproduction by wave field synthesis. (PhD thesis, Delft University of Technology, 1997).Google Scholar
  46. Vogel, P. (1993). Application of wave field synthesis in room acoustics. (PhD thesis, Delft University of Technology, 1993).Google Scholar
  47. Ward, D. B., & Abhayapala, T. D. (2001). Reproduction of a plane-wave sound field using an array of loudspeakers. IEEE Transaction on Speech and Audio Processing, 9(6), 697–707.CrossRefGoogle Scholar
  48. Weisstein, E. W. (2002). CRC concise encyclopedia of mathematics. London: Chapman and Hall/CRCGoogle Scholar
  49. Williams, E. G. (1999). Fourier acoustics: Sound radiation and nearfield acoustic holography. London: Academic Press.Google Scholar
  50. Wittek, H. (2007). Perceptual differences between wavefield synthesis and stereophony. (PhD thesis, University of Surrey, 2007).Google Scholar
  51. Wu, Y. J., & Abhayapala, T. D. (2009). Theory and design of soundfield reproduction using continuous loudspeaker concept. IEEE Transaction on Audio, Speech and Language Processings, 17(1), 107–116.CrossRefGoogle Scholar
  52. Zayed, A. I. (1993). Advances in Shannon’s sampling theory. New York: CRC Press.MATHGoogle Scholar
  53. Zotter, F. (2009). Analysis and synthesis of sound-radiation with spherical arrays. (Doctoral Thesis, Institute of Electronic Music and Acoustics, University of Music and Performing Arts Graz, 2009).Google Scholar
  54. Zotter, F., Pomberger, H., & Frank, M. (2009, May). An alternative ambisonics formulation: Modal source strength matching and the effect of spatial aliasing. 126th Convention of the AES.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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