Time-Domain Local Wave Field Synthesis of Virtual Point Sources

Wave field synthesis is a sound field synthesis technique that is based on a high-frequency/far-field approximation of the Kirchhoff-Helmholtz integral equation. The sound field synthesized by a loudspeaker array with a finite spacing exhibits spatial aliasing artifacts above a certain frequency. Recent studies have shown that the synthesis accuracy can be improved within a local area, which commonly comes at the expense of increased errors in other regions. In this paper, we consider a local wave field synthesis approach that is based on spatial band-limitation of the target sound field up to a finite order. The time-domain driving function for virtual point sources is derived by representing the spatially band-limited sound field in terms of continuously distributed point sources on a sphere. Examining the time-of-arrival of the individual components enables us to express the driving function as a surface integral on the sphere, which can be derived analytically. The modal impulse responses of the driving function are described by the associated Legendre polynomials, which are implemented as FIR filters. Numerical experiments for a 2.5-dimensional configuration demonstrate the improved accuracy of the synthesized wavefront within pre-defined target regions.