Weighted Pressure Matching Based on Kernel Interpolation For Sound Field Reproduction

A sound field reproduction method called weighted pressure matching is proposed. Sound field reproduction is aimed at synthesizing the desired sound field using multiple loudspeakers inside a target region. Optimization-based methods are derived from the minimization of errors between synthesized and desired sound fields, which enable the use of an arbitrary array geometry in contrast with integral-equation-based methods. Pressure matching is widely used in the optimization-based sound field reproduction methods because of its simplicity of implementation. Its cost function is defined as the synthesis errors at multiple control points inside the target region; then, the driving signals of the loudspeakers are obtained by solving a least-squares problem. However, in pressure matching, the region between the control points is not taken into consideration. We define the cost function as the regional integration of the synthesis error over the target region. On the basis of the kernel interpolation of the sound field, this cost function is represented as the weighted square error of the synthesized pressures at the control points. Experimental results indicate that the proposed weighted pressure matching outperforms conventional pressure matching.