Time-domain representation of wave field synthesis based on the spatial-shifting filter for a linear loudspeaker array

Synthesizing virtual sound sources that traverse a linear loudspeaker array poses a challenge for wave field synthesis (WFS) due to singularities. To address this issue, we propose a time-domain representation of WFS based on the spatial-shifting filter, derived via analytical inverse temporal and spatial Fourier transforms. By applying the stationary phase approximation, the proposed method derives the driving function suitable for sample-by-sample processing, thereby eliminating frame-length latency. The validity of the proposed method is demonstrated through numerical simulations.