Audio Engineering Society Convention Paper Presented at the 124th Convention 2008 May 17–20 Amsterdam, The Netherlands The papers at this Convention have been selected on the basis of a submitted abstract and extended precis that have been peer reviewed by at least two qualified anonymous reviewers. This convention paper has been reproduced from the author’s advance manuscript, without editing, corrections, or consideration by the Review Board. The AES takes no responsibility for the contents. Additional papers may be obtained by sending request and remittance to Audio Engineering Society, 60 East 42 nd Street, New York, New York 10165-2520, USA; also see www.aes.org. All rights reserved. Reproduction of this paper, or any portion thereof, is not permitted without direct permission from the Journal of the Audio Engineering Society. The Theory of Wave Field Synthesis Revisited Sascha Spors 1 , Rudolf Rabenstein 2 , and Jens Ahrens 1 1 Deutsche Telekom Laboratories, Berlin University of Technology, Ernst-Reuter-Platz 7, 10587 Berlin, Germany 2 Multimedia and Signal Processing, University of Erlangen-Nuremberg, Cauerstrasse 7, 91058 Erlangen, Germany Correspondence should be addressed to Sascha Spors (Sascha.Spors@telekom.de) ABSTRACT 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 repro- duction. The paper additionally gives an overview on the artifacts resulting in practical setups and briefly discusses some extensions to the traditional concepts of WFS. 1. INTRODUCTION Wave field synthesis (WFS) is a spatial sound field reproduction technique that utilizes a high number of loudspeakers to create a virtual auditory scene over a large listening area. It overcomes some of the limitations of stereophonic reproduction techniques, like e. g. the sweet-spot. A first concept, of what is nowadays known as WFS, was presented by Snow et al. [1] more than 50 years ago. However, technical constraints prohibited the employment of a high number of loudspeakers for sound reproduction. The authors therefore em- ployed only some few loudspeakers and essentially laid the theoretical fundament for stereophonic tech- niques. It took quite some time until the initial ideas of Snow have been taken up again. The theoretical framework of WFS was initially for- mulated by Berkhout et al. at the Delft University of Technology almost 20 years ago [2]. However, it seems that the term ’wave field synthesis’ has been mentioned the first time some years later [3]. Also around that time first laboratory setups of WFS sys-