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Advanced Room-Acoustics Decay Analysis

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Acoustics, Information, and Communication

Part of the book series: Modern Acoustics and Signal Processing ((MASP))

Abstract

Schroeder’s integration method broke the new ground in classical architectural acoustics. Schroeder’s integration method yields sound energy decay functions from room impulse responses. For reverberation time estimation based on a parametric model, a nonlinear regression method has been proposed. The nonlinear regression method yields reverberation time estimates, insensitive to background noise and the upper limit of integration. Recent interest in acoustically coupled-volume systems has prompted new challenges in analyzing sound energy decay characteristics, which are more complicated than just single-rate decays. This chapter will demonstrate a suitable framework for this room-acoustics application using Bayesian inference and the Schroeder’s integration as the foundation of the advanced model-based energy decay analysis. Based on the Schroeder’s integration, two levels of inference, decay order selection and decay parameter estimation, are discussed in details.

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Notes

  1. 1.

    Dr. Wolfgang Ahnert was collaborative in the initial work [17, 18] by drawing this author’s attention to a paper published in the Computation Journal in 1965 dealing with minimizing a sum of squares of nonlinear functions [14].

References

  1. Schroeder, M.R.: New method of measuring reverberation time. J. Acoust. Soc. Am. 37, 409–412 (1965)

    Article  ADS  Google Scholar 

  2. Kuerer, R., Kurze, U.: Integrationsverfahren zur Nachhallauswertung. Acustica 19, 314–322 (1967/1968)

    Google Scholar 

  3. Kuttruff, H., Jusofie, M.: Messungen des Nachhallverlaufs in meheren Räumen ausgefuehrt nach dem Verfahren der integrieten Impulseantworten (Energy decay measurements in rooms using the integrated impusle-response method). Acustica 11, 1–9 (1969)

    Google Scholar 

  4. Bodlund, K.: On the use of the integrated impulse response method for laboratory reverberation measurements. J. Sound Vib. 56, 341–362 (1978)

    Article  ADS  Google Scholar 

  5. Chu, W.T.: Comparison of reverberation measurements using Schroeder’s impulse method and decay-curve averaging method. J. Acoust. Soc. Am. 63, 1444–1450 (1978)

    Article  ADS  Google Scholar 

  6. Luizard, P., Katz, B.F.: Coupled volume multi-slope room impulse responses: a quantitative analysis method. In: Proceedings of IoA, Dublin (2011)

    Google Scholar 

  7. Cremer, L., Müller, H.A., Schultz, T.J.: Principles and Applications of Room Acoustics. Applied Science Publishers, London (1982)

    Google Scholar 

  8. Xiang, N., Jing, Y., Bockman, A.: Investigation of acoustically coupled enclosures using a diffusion equation model. J. Acoust. Soc. Am. 126, 1187–1198 (2009)

    Article  Google Scholar 

  9. Vorländer, M., Bietz, H.: Comparison of methods for measuring reverberation time. Acustica 80, 205–215 (1994)

    Google Scholar 

  10. Hirata, Y.A.: A method of eliminating noise in power responses. J. Sound Vib. 82, 593–595 (1982)

    Article  ADS  Google Scholar 

  11. Xiang, N.: Two approaches to evaluation of reverberation times from Schroeders decay curves. In: Proceedings of 15th ICA, Trondheim, IV 175–178 (1995)

    Google Scholar 

  12. Lundeby, A., Vigran, T.E., Bietz, H., Vorländer, M.: Uncertainties of measurements in room acoustics. Acustica 81, 344–355 (1995)

    Google Scholar 

  13. Schroeder, M.R.: Complementarity of sound buildup and decay. J. Acoust. Soc. Am. 40, 549–551 (1966)

    Article  ADS  Google Scholar 

  14. Xiang, N.: Evaluation of reverberation times using a nonlinear regression approach. J. Acoust. Soc. Am. 98, 2112–2121 (1995)

    Article  ADS  Google Scholar 

  15. Faiget, L., Legros, C., Ruiz, R.: Optimaization of the impulse response length: application to noisy and highly reverberant rooms. J. Audio Eng. Soc. 46, 741–750 (1998)

    Google Scholar 

  16. Xiang, N., Goggans, P., Jasa, T., Robinson, P.: Bayesian characterization of multipleslope sound energy decays in coupled-volume systems. J. Acoust. Soc. Am. 129, 741–752 (2011)

    Article  ADS  Google Scholar 

  17. Xiang, N., Ahnert, W., Feistel, R.: A nonlinear regression approach to the evaluation of reverberation times using Schroeder’s integrated impulse response method (A). J. Acoust. Soc. Am. 94, 1846 (1993)

    Article  ADS  Google Scholar 

  18. Xiang, N., Ahnert, W., Feistel, R.: Nachhallauswertung mittels nicht-linearer Regression (Reverberation time evaluation using nonlinear regression). In: Proceedings of Fortschritte der Akustik, DAGA93, pp. 255–258 (1993)

    Google Scholar 

  19. Xiang, N., Vorländer, M.: Using iterative regression for estimating reverberation times in two coupled spaces (A). J. Acoust. Soc. Am. 104, 1763 (1998)

    Article  ADS  Google Scholar 

  20. Xiang, N., Goggans, P.M.: Evaluation of decay times in coupled spaces: Bayesian parameter estimation. J. Acoust. Soc. Am. 110, 1415–1424 (2001)

    Article  ADS  Google Scholar 

  21. Xiang, N., Goggans, P.M.: Evaluation of decay times in coupled spaces: Bayesian decay model selection. J. Acoust. Soc. Am. 113, 2685–2697 (2003)

    Article  ADS  Google Scholar 

  22. Schroeder, M.R.: Digital simulation of sound transmission in reverberant spaces. J. Acoust. Soc. Am. 47, 424–431 (1970)

    Article  ADS  Google Scholar 

  23. Jaffe, J.C.: Innovative approaches to the design of symphony halls. Acoust. Sci. Tech. 26, 240–243 (2005)

    Article  Google Scholar 

  24. MacKay, D.: Information Theory, Inference and Learning Algorithms, Chapters 28, 29. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  25. Jasa, T., Xiang, N.: Efficient estimation of decay parameters in acoustically coupled spaces using slice sampling. J. Acoust. Soc. Am. 126, 1269–1279 (2009)

    Article  Google Scholar 

  26. Skilling, J.: Nested sampling. In: Fisher, R. et al. (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, American Institute of Physics, vol. 735, pp. 395–405 (2004)

    Google Scholar 

  27. Jasa, T., Xiang, N.: Using nested sampling in the analysis of multi-rate sound energy decay in acoustically coupled rooms. In: Knutz, K. et al. (eds.) Bayesian Inference and Maximum Entropy Methods in Science and Engineering, American Institute of Physics, vol. 803, pp. 189–196 (2005)

    Google Scholar 

  28. Sivia, D., Skilling, J.: Bayesian Data Analysis—A Bayesian Tutorial, 2nd edn. Oxford University Press, New York (2006)

    MATH  Google Scholar 

  29. Jasa, T., Xiang, N.: Nested sampling applied in the Bayesian room-acoustics decay analysis. J. Acoust. Soc. Am. 132, 3251–3262 (2012)

    Article  ADS  Google Scholar 

  30. Xiang, N., Goggans, P.M., Jasa, T., Kleiner, M.: Evaluation of decay times in coupled spaces: reliability analysis of Bayeisan decay time estimation. J. Acoust. Soc. Am. 117, 3707–3715 (2005)

    Article  ADS  Google Scholar 

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Acknowledgments

The author would like to dedicate this work to the memory of Manfred Robert Schroeder whose great interest in the author’s work on room-acoustic energy decay analysis has inspired him to continue this endeavor. The author is thankful to Tomislav Jasa and Jonathan Botts for their insightful discussions and for implementing the nested sampling for this work, to Jean-Dominique Polack, Dejan Ciric, and Brian Katz for their critical comments on an early version of this chapter, and to Cameron Fackler and Paul Luizard for proofreading the final version of the chapter.

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Authors and Affiliations

  1. Graduate Program in Architectural Acoustics School of Architecture, Rensselaer Polytechnic Institute, Troy, NY, 12180, USA

    Ning Xiang

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  1. Ning Xiang
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Correspondence to Ning Xiang .

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Editors and Affiliations

  1. The School of Architecture, Rensselaer Polytechnic Institute, Troy, New York, USA

    Ning Xiang

  2. Darmstadt University of Technology, Darmstadt, Germany

    Gerhard M. Sessler

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Xiang, N. (2015). Advanced Room-Acoustics Decay Analysis. In: Xiang, N., Sessler, G. (eds) Acoustics, Information, and Communication. Modern Acoustics and Signal Processing. Springer, Cham. https://doi.org/10.1007/978-3-319-05660-9_3

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