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Extraction of 3D Information from Circular Array Measurements for Auralization with Wave Field Synthesis


The state of the art of wave field synthesis (WFS) systems is that they can reproduce sound sources and secondary (mirror image) sources with natural spaciousness in a horizontal plane, and thus perform satisfactory 2D auralization of an enclosed space, based on multitrace impulse response data measured or simulated along a 2D microphone array. However, waves propagating with a nonzero elevation angle are also reproduced in the horizontal plane, which is neither physically nor perceptually correct. In most listening environments to be auralized, the floor is highly absorptive since it is covered with upholstered seats, occupied during performances by a well-dressed audience. A first-order ceiling reflection, reaching the floor directly or via a wall, will be severely damped and will not play a significant role in the room response anymore. This means that a spatially correct WFS reproduction of first-order ceiling reflections, by means of a loudspeaker array at the ceiling of the auralization reproduction room, is necessary and probably sufficient to create the desired 3D spatial perception. To determine the driving signals for the loudspeakers in the ceiling array, it is necessary to identify the relevant ceiling reflection(s) in the multichannel impulse response data and separate those events from the data set. Two methods are examined to identify, separate, and reproduce the relevant reflections: application of the Radon transform, and decomposition of the data into cylindrical harmonics. Application to synthesized and measured data shows that both methods in principle are able to identify, separate, and reproduce the relevant events.


  1. Dressler R: Dolby Pro Logic Surround Decoder Principles of Operation. Dolby Laboratories Licensing, San Francisco, Calif, USA; 1993.

    Google Scholar 

  2. Berkhout AJ: A holographic approach to acoustic control. Journal of the Audio Engineering Society 1988,36(12):977-995.

    Google Scholar 

  3. Kleiner M, Dalenback B-I, Svensson P: Auralization—an overview. Journal of the Audio Engineering Society 1993,41(11):861-875.

    Google Scholar 

  4. Hulsebos E, de Vries D, Bourdillat E: Improved microphone array configurations for auralization of sound fields by wave-field synthesis. Journal of the Audio Engineering Society 2002,50(10):779-790.

    Google Scholar 

  5. Berkhout AJ, de Vries D, Baan J, Van den Oetelaar BW: A wave field extrapolation approach to acoustical modeling in enclosed spaces. Journal of the Acoustical Society of America 1999,105(3):1725-1733. 10.1121/1.426710

    Article  Google Scholar 

  6. Blauert J: Sound localization in the median plane. Acustica 1969,22(4):205-213.

    Google Scholar 

  7. Blauert J: Spatial Hearing. MIT Press, Cambridge, Mass, USA; 1983.

    Google Scholar 

  8. Deans SR: The Radon Transform and Some of Its Applications. Jon Wiley & Sons, New York, NY, USA; 1983.

    MATH  Google Scholar 

  9. Toft P: The Radon Transform—Theory and Implementation, Ph.D. thesis. Technical University of Denmark, Lyngby, Denmark; 1996.

    Google Scholar 

  10. Sacchi MD, Ulrych TJ: High-resolution velocity gathers and offset space reconstruction. Geophysics 1995,60(4):1169-1177. 10.1190/1.1443845

    Article  Google Scholar 

  11. Kinsler LE, Frey AR, Coppens AB, Sanders JV: Fundamentals of Acoustics. John Wiley & Sons, New York, NY, USA; 2000. chapter 14

    Google Scholar 

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Correspondence to Diemer de Vries.

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de Vries, D., Hörchens, L. & Grond, P. Extraction of 3D Information from Circular Array Measurements for Auralization with Wave Field Synthesis. EURASIP J. Adv. Signal Process. 2007, 013416 (2007).

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