Driving function in wave field synthesis with integral approximation considering uneven contribution of loudspeaker units

Wave field synthesis is a spatial audio technique for reproducing the sound field of a target source. This process is implemented by applying driving functions to loudspeakers enclosing a listening space. To reduce computational and hardware costs, several studies assume that the target source is sufficiently far from the loudspeakers, but this assumption depends on source frequency and can lead to errors. A recent method attempted to address this issue using oversampling and averaging; however, this approach increases computational demands, particularly for multiple target sources. Such steps result in high computational costs when there are numerous target sources. In this study, we propose an alternative method using an integral approximation that imitates the linearity of integral operations, taking into account the uneven contributions of loudspeakers. This eliminates the need for oversampling and averaging. Simulation results showed that our method improved sound reproduction compared to the recent method at high frequencies and conventional methods at low frequencies, especially when the target source was close to loudspeakers and not aligned with them. Our approach could potentially be applied to tasks that use the same integrand, widely used to model sources and fields.