Sound field synthesis based on plane wave decomposition reconfiguring Lamé function loudspeaker array

Sound field synthesis aims to physically generate acoustic fields. When considering sound field synthesis in real environments, most indoor shapes are rectangular. Despite this, conventional sound field control methods often employ circular loudspeaker array configurations, which may not efficiently utilize space and may impact usable areas. Therefore, a method based on non-circular loudspeaker array configurations is needed. Lamé function is an algebraic curve whose shape can transition circular to rectangular by increasing its order. By using Lamé function to formulate the distance from the center, plane wave generation based on non-circular layout has been verified. In this paper, we propose a method for sound fields synthesis by combining multiple plane waves, applying the principle of plane wave decomposition based on a loudspeaker array geometry using the Lamé function. We start by reformulating the existing approach for loudspeaker array configurations using the Lamé function to establish our theoretical framework. Then, we validate the feasibility of our method through MATLAB simulations of two-dimensional point source field synthesis and evaluate the synthesis performance under various parameters, offering a comparison with ideal sound field situation and conventional methods.