Directivity control of a finite cylindrical loudspeaker array based on circular harmonics and longitudinal multipole expression

摘要

The directivity control of a finite cylindrical loudspeaker array can be applied to various systems such as personal audio and smart speaker systems. As a conventional directivity control method, the filter coefficients of a cylindrical array may be derived analytically on the basis of cylindrical harmonic expansion when desired directivity patterns are set as the control points in the cylindrical coordinate system. However, it is more convenient to set the control points in the spherical coordinate system when considering practical use. In this paper, we propose a filter design method to control the directivity patterns on a spherical surface for a finite cylindrical array. Although the proposed method is similar to the mode-matching method based on spherical harmonic expansion, it uses a combination of circular harmonics and longitudinal multipoles to express the directivity patterns and filter coefficients. To validate the proposed method, we evaluated the directivity patterns using a prototype 24-element cylindrical loudspeaker array in an anechoic chamber. Consequently, we validated that the three-dimensional directivity pattern formed was the same as that obtained by computer simulations.