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There are many ways to reproduce a sound field over a wide spatial area using an array of loudspeakers, as for example, wavefield synthesis (WFS), ambisonics, and spectral division methods. A new approach, called sound field reconstruction (SFR), optimally reproduces a desired sound field in a given listening area while keeping loudspeaker driver signals within physical constraints. The reproduction of a continuous sound field is represented as an inversion of the discrete acoustic channel from a loudspeaker array to a grid of control points. Extensive simulations comparing WFS, which is the state of the art, with SFR show that on average SFR provides better reproduction accuracy.

Authors: Kolundzija, Mihailo; Faller, Christof; Vetterli, Martin
Affiliation: School of Computer and Communications Sciences, Ecole Polytechnique Fédérale Lausanne (EPFL), Lausanne, Switzerland
JAES Volume 59 Issue 10 pp. 721-734; October 2011
Publication Date: November 22, 2011

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Gary Eickmeier	Comment posted November 27, 2011 @ 20:40:50 UTC (Comment permalink) My objection, or question, about this article has to do with the definition of "sound field." If they are going to claim Sound Field Reconstruction, then they need to be referring to the commonly understood definition, which I understand as all fields within an enclosed space. These are the direct, early reflected, and reverberant fields. If we can reconstruct all sound fields we will have reached the goal of maximum accuracy and realism of reproduction. Ambisonics is an attempt at sound field reconstruction. Dolby Digital 5.1 and 7.1 are attempts. These systems employ full surround speakers in order to reproduce the reflected fields found in the original. As far as I can see, both WFS and SFR feature no such attempt, and have only a line of speakers at the front of the room. This approach can only reproduce the direct field, which stereophonic two and three channel can already do just fine. I would appreciate a more practical explanation of what the authors think they have achieved with this system, and what they mean by a "sound field." Gary Eickmeier (Respond to this comment)
Author Response Mihailo Kolundzija	Comment posted December 13, 2011 @ 18:08:17 UTC (Comment permalink) By the term sound field we mean any physical sound field that is described by the wave equation. The direct sound field that you mention is a sound field that gets formed in free space (no boundary conditions), whereas the reflected/reverberant sound fields are "residuals" that come as a consequence of having boundary conditions (reflection/diffraction on walls/objects etc.). Our approach is not limited to a line of speakers, and can use any speaker arrangement. If one wants to reproduce a sound field that emanates from sources distributed towards arbitrary directions (including virtual sources that model reflections from walls, for instance), an enclosing loudspeaker configuration needs to be used. This, however, changes nothing in the procedure described in the paper. A line of loudspeakers was used for a fair comparison with WFS. (Respond to this comment)

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