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Sound Field Analysis Based on Analytical Beamforming

Abstract

The plane wave decomposition is an efficient analysis tool for multidimensional fields, particularly well fitted to the description of sound fields, whether these ones are continuous or discrete, obtained by a microphone array. In this article, a beamforming algorithm is presented in order to estimate the plane wave decomposition of the initial sound field. Our algorithm aims at deriving a spatial filter which preserves only the sound field component coming from a single direction and rejects the others. The originality of our approach is that the criterion uses a continuous instead of a discrete set of incidence directions to derive the tap vector. Then, a spatial filter bank is used to perform a global analysis of sound fields. The efficiency of our approach and its robustness to sensor noise and position errors are demonstrated through simulations. Finally, the influence of microphone directivity characteristics is also investigated.

References

  1. 1.

    Berkhout AJ, de Vries D, Vogel P: Acoustic control by wave field synthesis. Journal of the Acoustical Society of America 1993,93(5):2764–2778. 10.1121/1.405852

    Article  Google Scholar 

  2. 2.

    de Vries D, Boone MM: Wave field synthesis and analysis using array technology. Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA '99), October 1999, New Paltz, NY, USA 15–18.

    Google Scholar 

  3. 3.

    Poletti MA: Three-dimensional surround sound systems based on spherical harmonics. Journal of the Audio Engineering Society 2005,53(11):1004–1025.

    Google Scholar 

  4. 4.

    Merimaa J, Pulkki V: Spatial impulse response rendering I: analysis and synthesis. Journal of the Audio Engineering Society 2005,53(12):1115–1127.

    Google Scholar 

  5. 5.

    Meyer J, Elko G: A highly scalable spherical microphone array based on an orthonormal decomposition of the soundfield. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '02), May 2002, Orlando, Fla, USA 2: 1781–1784.

    Google Scholar 

  6. 6.

    Abhayapala TD, Ward DB: Theory and design of high order sound field microphones using spherical microphone array. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '02), May 2002 2: 1949–1952.

    Google Scholar 

  7. 7.

    Li Z, Duraiswami R, Grassi E, Davis LS: Flexible layout and optimal cancellation of the orthonormality error for spherical microphone arrays. Proceedings of IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP '04), May 2004, Montreal, Quebec, Canada 4: 41–44.

    Google Scholar 

  8. 8.

    Rafaely B: Analysis and design of spherical microphone arrays. IEEE Transactions on Speech and Audio Processing 2005,13(1):135–143.

    Article  Google Scholar 

  9. 9.

    Van Veen BD, Buckley KM: Beamforming: a versatile approach to spatial filtering. IEEE ASSP Magazine 1988,5(2):4–24.

    Article  Google Scholar 

  10. 10.

    Parra LC: Least-squares frequency-invariant beamforming. Proceedings of IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA '05), October 2005, New Paltz, NY, USA 102–105.

    Google Scholar 

  11. 11.

    Parra LC: Steerable frequency-invariant beamforming for arbitrary arrays. Journal of the Acoustical Society of America 2006,119(6):3839–3847. 10.1121/1.2197606

    Article  Google Scholar 

  12. 12.

    Yan S: Optimal design of FIR beamformer with frequency invariant patterns. Applied Acoustics 2006,67(6):511–528. 10.1016/j.apacoust.2005.09.008

    Article  Google Scholar 

  13. 13.

    Guillaume M, Grenier Y: Sound field analysis with a two-dimensional microphone array. Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP '06), May 2006, Toulouse, France

    Google Scholar 

  14. 14.

    Guillaume M, Grenier Y: Sound field analysis based on generalized prolate spheroidal wave sequences. 120th Convention of the Audio Engineering Society, May 2006, Paris, France

    Google Scholar 

  15. 15.

    Williams EG: Fourier Acoustics. Academic Press, New York, NY, USA; 1999.

    Google Scholar 

  16. 16.

    Morse PM, Feshbach H: Methods of Theoretical Physics. McGraw-Hill, New York, NY, USA; 1953.

    Google Scholar 

  17. 17.

    Ajdler T, Sbaiz L, Vetterli M: The plenacoustic function and its sampling. IEEE Transactions on Signal Processing 2006,54(10):3790–3804.

    Article  Google Scholar 

  18. 18.

    Bronez TP: Spectral estimation of irregularly sampled multidimensional processes by generalized prolate spheroidal sequences. IEEE Transactions on Acoustics, Speech, and Signal Processing 1988,36(12):1862–1873. 10.1109/29.9031

    Article  Google Scholar 

  19. 19.

    Kaiser JF, Schafer RW: On the use of the 10-sinh window for spectrum analysis. IEEE Transactions on Acoustics, Speech, and Signal Processing 1980,28(1):105–107. 10.1109/TASSP.1980.1163349

    Article  Google Scholar 

Download references

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Correspondence to M. Guillaume.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://doi.org/creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Guillaume, M., Grenier, Y. Sound Field Analysis Based on Analytical Beamforming. EURASIP J. Adv. Signal Process. 2007, 094267 (2006). https://doi.org/10.1155/2007/94267

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Keywords

  • Quantum Information
  • Position Error
  • Field Component
  • Filter Bank
  • Field Analysis