Synthesis of Directional Sources Using Wave Field Synthesis, Possibilities, and Limitations
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Research Article Synthesis of Directional Sources Using Wave Field Synthesis, Possibilities, and Limitations E. Corteel1, 2 1 IRCAM, 2 Sonic
1 Place Igor Stravinsky, 75004 Paris, France Emotion, Eichweg 6, 8154 Oberglatt, Switzerland
Received 28 April 2006; Revised 4 December 2006; Accepted 4 December 2006 Recommended by Ville Pulkki The synthesis of directional sources using wave field synthesis is described. The proposed formulation relies on an ensemble of elementary directivity functions based on a subset of spherical harmonics. These can be combined to create and manipulate directivity characteristics of the synthesized virtual sources. The WFS formulation introduces artifacts in the synthesized sound field for both ideal and real loudspeakers. These artifacts can be partly compensated for using dedicated equalization techniques. A multichannel equalization technique is shown to provide accurate results thus enabling for the manipulation of directional sources with limited reconstruction artifacts. Applications of directional sources to the control of the direct sound field and the interaction with the listening room are discussed. Copyright © 2007 E. Corteel. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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INTRODUCTION
Wave field synthesis (WFS) is a physics-based sound reproduction technique [1–3]. It allows for the synthesis of wave fronts that appear to emanate from a virtual source at a defined position. WFS thus provides the listener with consistent spatial localization cues over an extended listening area. WFS mostly considers the synthesis of virtual sources exhibiting omnidirectional directivity characteristics. However, the directive properties of sound sources contribute to immersion and presence [4], both notions being related to spatial attributes of sound scenes used in virtual or augmented environments. Directivity creates natural disparities in the direct sound field at various listening positions and governs the interaction with the listening environment. This article focuses on the synthesis of the direct sound associated to directional sources for WFS. In a first part, an extended WFS formulation is proposed for the synthesis of elementary directional sources based on a subset of spherical harmonics. The latter are a versatile representation of a source field enabling a flexible manipulation of directivity characteristics [4]. We restrict on the derivation of WFS for a linear loudspeaker array situated in the horizontal plane. Alternative loudspeaker geometries could be considered following a similar framework but are out of the scope of this article. This array can be regarded as an acoustical aperture
through which an incoming sound field propagates into the listening area. Therefore, directivity characteristics of virtual sources may be synthesized and controlled only in a single plane through the array only, genera
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