Sound Field Reproduction Using Planar and Linear Arrays of Loudspeakers

In this paper, we consider physical reproduction of sound fields via planar and linear distributions of secondary sources (i.e., loudspeakers). The presented approach employs a formulation of the reproduction equation in spatial frequency domain which is explicitly solved for the secondary source driving signals. Wave field synthesis (WFS), the alternative formulation, can be shown to be equivalent under equal assumptions. Unlike the WFS formulation, the presented approach does not employ a far-field approximation when linear secondary source distributions are considered but provides exact results. We focus on the investigation of the spatial truncation and discretization of the secondary source distribution occurring in real-world implementations and present a rigorous analysis of evanescent and propagating components in the reproduced sound field.