Analysis and Improvement of Pre-equalization in 2.5-Dimensional Wave Field Synthesis

Wave field synthesis (WFS) is a well established high-resolution spatial sound reproduction technique. Typical 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 reproduced 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 investigates 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.