Audio Engineering Society Convention Paper Presented at the 128th Convention 2010 May 22–25 London, UK 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. Analysis and Improvement of Pre-equalization in 2.5-Dimensional Wave Field Synthesis Sascha Spors and Jens Ahrens Deutsche Telekom Laboratories, Technische Universit¨at Berlin, Ernst-Reuter-Platz 7, 10587 Berlin, Germany Correspondence should be addressed to Sascha Spors (Sascha.Spors@telekom.de) ABSTRACT Wave field synthesis (WFS) is a well established high-resolution spatial sound reproduction technique. Typi- cal WFS systems aim at the reproduction in a plane using loudspeakers enclosing the plane. This constitutes a so-called 2.5-dimensional reproduction scenario. It has been shown that a spectral correction of the re- produced wave field is required in this context. For WFS this correction is known as pre-equalization filter. The derivation of WFS is based on a series of approximations of the physical foundations. This paper in- vestigates on the consequences of these approximations on the reproduced sound field and in particular on the pre-equalization filter. An exact solution is provided by the recently presented spectral division method and is employed in order to derive an improved WFS driving function. Furthermore, the effects of spatial sampling and truncation on the pre-equalization are discussed. 1. INTRODUCTION Wave Field Synthesis (WFS) is a well established high-resolution spatial sound reproduction tech- nique [1]. It aims at synthesizing the sound field of a desired acoustic scene within a given listening area. The original theory of WFS considers the reproduc- tion in a planar listening area using a linear dis- tribution of loudspeakers (loudspeaker array). It is assumed that the reproduction in a plane only is suitable for most applications. Typical implementa- tions of WFS systems surround the listening area by piecewise linear or curved loudspeaker arrays. The original theory has been extended in various aspects for this purpose. In this paper we will focus on the traditional concept covering a linear distribution of loudspeakers. The foundations of WFS are given by the first Rayleigh integral. This integral states that a con- tinuous planar distribution of appropriately driven point sources (secondary sources) is suitable to syn-