Reproduction of a plane-wave sound field using planar and linear arrays of loudspeakers

In this paper, we consider the physical reproduction of plane-wave sound fields via continuous planar respectively linear distributions of secondary point sources. Our approach employs a formulation of the reproduction equation in the spatial frequency domain to explicitly solve it for the appropriate secondary source driving signals. This constitutes a generalization of the Ambisonics approach which is typically formulated for spherical and circular secondary source arrangements. For planar arrays, the alternative formulation provided by the Kirchhoff-Helmholtz integral equation is equivalent. For linear arrays, the Kirchhoff-Helmholtz formulation appears as a far-field/high-frequency approximation of the presented approach.