A sound zone control method is proposed, based on the frequency domain variable span trade-off filter (VAST). Existing VAST methods optimizes the sound field at a set of discrete points, while the proposed method uses kernel interpolation to instead optimize the sound field over a continuous region. When the loudspeaker positions are known, the performance can be improved further by applying a directional weighting to the interpolation procedure. The proposed method is evaluated by simulating broadband sound in a reverberant environment, focusing on the case when microphone placement is restricted. The proposed method with directional weighting outperforms the pointwise VAST over the full bandwidth of the signal, and the proposed method without directional weighting outperforms the pointwise VAST at low frequencies.

Time-domain spatial active noise control (ANC) algorithms based on kernel interpolation of a sound field are proposed. Spatial ANC aims to suppress a primary noise field in a region by synthesizing an anti-noise field using secondary loudspeakers. In contrast to the multipoint pressure control by conventional ANC methods, it is necessary to estimate a sound field from microphone measurements at discrete positions. A promising approach is the kernel-interpolation-based spatial ANC method, which allows for flexible array configurations. However, most of the current methods are formulated only in the frequency domain, which cannot handle broadband noise with straightforward implementation. We formulate two time-domain spatial ANC algorithms based on kernel interpolation using a spatial interpolation filter defined by the kernel function. Numerical simulation results indicate that our filtered-x least-mean-square-based algorithms are effective for reducing nonstationary broadband noise in a region, as compared with multipoint pressure control.

An active noise control (ANC) method to reduce noise over a region in space based on kernel interpolation of sound field is proposed. Current methods of spatial ANC are largely based on spherical or circular harmonic expansion of the sound field, where the geometry of the error microphone array is restricted to a simple one such as a sphere or circle. We instead apply the kernel interpolation method, which allows for the estimation of a sound field in a continuous region with flexible array configurations. The interpolation scheme is used to derive adaptive filtering algorithms for minimizing the acoustic potential energy inside a target region. A practical time-domain algorithm is also developed together with its computationally efficient block-based equivalent. We conduct experiments to investigate the achievable level of noise reduction in a two-dimensional free space, as well as adaptive broadband noise control in a three-dimensional reverberant space. The experimental results indicated that the proposed method outperforms the multipoint-pressure-control-based method in terms of regional noise reduction.