Wave field synthesis is a spatial sound field reproduction technique aiming at authentic reproduction of auditory scenes. Its theoretical foundation has been developed almost 20 years ago and has been improved considerably since then. Most of the original work on wave field synthesis is restricted to the reproduction in a planar listening area using linear loudspeaker arrays. Extensions like arbitrarily shaped distributions of secondary sources and three-dimensional reproduction in a listening volume have not been discussed in a unified framework so far. This paper revisits the theory of wave field synthesis and presents a unified theoretical framework covering arbitrarily shaped loudspeaker arrays for two- and three-dimensional reproduction. The paper additionally gives an overview on the artifacts resulting in practical setups and briefly discusses some extensions to the traditional concepts of WFS.
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