Active noise control in three dimensions

Available acoustical signal processing algorithms for active noise control (ANC) can only attenuate noise at a finite number of points. Accordingly, they are unable to create continuous quiet zones in 3-D space. This paper proposes a methodology for developing a family of acoustical signal processing algorithms that are able to control sound in three dimensions. The theoretical analysis is carried out for spherical quiet zones; however, the proposed methodology can apply to quiet zones with arbitrary shapes. It is assumed that there is no reflection while sound propagates in media. An arbitrary frequency spectrum for the noise to be canceled is considered. An optimal control system for 3-D ANC is then derived. Also, an efficient method for the implementation of the proposed system is developed. The implementation cost of the proposed system is comparable with that of conventional ANC systems. In addition to the simulation results, different experiments with an experimental ANC system show the validity of the theoretical results.