Design of a Planar First-Order Loudspeaker Array for Global Active Noise Control

Abstract

This paper proposes a method to design a planar first-order loudspeaker array structure for global active noise control. Compared with the traditional spherical loudspeaker array, the planar array provides a practical design with flexible source locations. The planar array is capable of achieving global noise control, provided that the loudspeakers have general variable first-order responses in elevation. On $\boldsymbol {x{-}y}$ plane, we use spherical harmonics to analyze the required first-order loudspeakers consisting of monopole and tangential dipole components. By exploiting the properties of the associated Legendre functions and its derivative, we can divide the primary soundfield into even harmonics controlled by the monopole component, and odd harmonics controlled by the dipole component. Through the appropriate choice of radii of circles, we avoid the ill-conditioning problem of matrix inversion and derive a robust solution for loudspeaker weights to suppress the primary noise field. Besides, we use the closely-located monopole pairs, instead of the ideal general first-order loudspeakers, to design an alternative planar array for practical implementation. As an illustration, we use several simulation examples to validate the performance of the two proposed planar loudspeaker arrays.