Analytical Method of 2.5D Exterior Sound Field Synthesis by Using Multipole Loudspeaker Array

We propose an analytical method of 2.5-dimensional exterior sound field reproduction by using a multipole loudspeaker array. The method reproduces the sound field modeled by expansion coefficients of spherical harmonics based on multipole superposition. We also present an analytical method for converting the expansion coefficients of spherical harmonics to weighting coefficients for multipole superposition. In contrast to pressure-matching methods, which tend to be ill-conditioned problems, the proposed method gives stable solutions based on an analytical conversion from the expansion coefficients of spherical harmonics. We derive the analytical method by converting the sound field modeled by expansion coefficients of spherical harmonics to a linear combination of ’basic multipoles’ for obtaining the weighting coefficients of each multipole. Computer simulation results indicate that the proposed method reproduces the sound field more accurately than existing pressure-matching based method.