Wave field synthesis for a moving point source under the near-field assumption.

In wave field synthesis, the target source is typically assumed to be static. Some previous studies have extended this framework by introducing time-varying driving functions to reproduce moving sources. More recently, a study applied the stationary phase approximation under the assumption that the source frequency or velocity is sufficiently high. However, in real scenarios, object speeds are often slower than those considered in that study and natural sounds tend to have greater spectral energy in the low-frequency range. In such cases, the stationary phase approximation may result in substantial errors. To address this, we propose a driving function that incorporates a near-field assumption appropriate for low-frequency or slow-moving sources. We further generalize the method by combining it with a previously established approach. MATLAB (The MathWorks, Inc., Natick, MA) simulations reveal that the proposed method reduces reproduction error when the source is either slow-moving or exhibits low frequency. By comparing the proposed method with existing techniques, we show that it serves as a generalization of previous approaches. As such, this study helps bridge the gap between studies on static and moving sources.