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The synthesis of sound figures

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Abstract

In this paper we discuss a novel technique to control the spatial distribution of sound level within a synthesized sound field. The problem is formulated by separating the sound field into regions with high acoustic level, so-called bright regions, and zones with low acoustic level (zones of quiet) by time independent virtual boundaries. This way, the propagating sound field obtains a static spatial shape, which we call sound figure. This problem is treated with a generic approach for creating sound figures. We give an analytic solution to the problem and highlight, how our findings can be applied using established sound field synthesis techniques. We furthermore show the limitations of our approach, provide simulation results to prove the concept and discuss some application areas.

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Notes

  1. A manifold of dimension \(n\) is a topological space that resembles an \(n-\)dimensional Euclidean space in a neighborhood of each point (Boothby 1975).

  2. A non-overlapping manifold \(\Omega \) does not exhibit any nodes. This property is necessary for defining differential operators on \(\Omega \).

  3. In differential geometry, the Laplace operator can be generalized to operate on functions defined on surfaces in Euclidean space and, more generally, on Riemannian and pseudo-Riemannian manifolds. This more general operator goes by the name Laplace–Beltrami operator. The Laplace–Beltrami operator, like the Laplacian, is the divergence of the gradient.

  4. Note that the triangle does not represent the dependency between \(k_x\) and \(k_y\) but should exemplary reference to the general complex amplitude of the spectrum.

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Acknowledgments

We thank the reviewers for their thorough reading of the manuscript and highly appreciate the comments and suggestions.

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Authors and Affiliations

  1. Quality and Usability Lab, Telekom Innovation Laboratories, Technische Universität Berlin, Ernst-Reuter-Platz 7, 10587 , Berlin, Germany

    Karim Helwani

  2. Institut für Nachrichtentechnik, Universität Rostock, Richard-Wagner-Str. 31, 18119 , Rostock, Warnemünde, Germany

    Sascha Spors

  3. Machine Learning Group, Technische Universität Berlin, Franklinstr. 28/29, 10587 , Berlin, Germany

    Herbert Buchner

Authors
  1. Karim Helwani
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  2. Sascha Spors
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  3. Herbert Buchner
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Correspondence to Karim Helwani.

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Helwani, K., Spors, S. & Buchner, H. The synthesis of sound figures. Multidim Syst Sign Process 25, 379–403 (2014). https://doi.org/10.1007/s11045-013-0261-4

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