Notes on Rendering Focused Directional Virtual Sound Sources in Wave Field Synthesis

Wave field synthesis (WFS) is a technique aiming at the reproduction of a desired sound field. It is based on the Kirchhoff-Helmholtz integral formulated for interior problems [1]. This implies that WFS is per se only capable of recreating the wave field generated by events outside the listening area. In particular, the traditional WFS literature (e.g. [2]) focuses on the reproduction of the sound field of virtual point sources which are positioned outside the listening area (’behind’ the loudspeakers). For both restrictions of the traditional WFS literature virtual point sources outside the listening area extensions have been proposed. In this paper, we briefly review the strategies proposed and comment on the particularities arising in the combination of the extensions, i.e. the reproduction of complex (directional/spatially extended) virtual sources positioned inside the listening area (’in front of’ the loudspeakers). For simplicity, we will restrict the treatment to two-dimensional reproduction.