In this paper, we propose a method for sound ?eld reproduction using an elliptical loudspeaker array and a circular microphone array. This study aims to reproduce the interior sound ?eld of the elliptical loudspeaker array in a 2-dimensional sound ?eld. The solutions of the Helmholtz equation in an elliptical coordinate system, which are known as Mathieu functions, are used to expand the sound ?eld in an elliptical-coordinate-system-based wave domain. We provide a method to transform the signals recorded by a circular microphone array that are generally expanded with circular harmonics to the Mathieu expansion coef?cients. These coef?cients can be applied to derive the driving functions of loudspeakers. Computer simulations show that the method is valid for sound ?eld reproduction.
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