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

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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).

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