Differential microphone arrays (DMAs) can measure and respond to the spatial derivatives of the soundfield, which gives them great potential in high-fidelity acoustic signal acquisition and soundfield measurement. Previous studies on three-dimensional (3D) micro- phone arrays are primarily based on the spherical harmonic decom- position of the soundfield, which inherently limits the array topology to spherical configurations. This paper presents a more flexible 3D DMA and beamformer design method according to the principle of finite difference approximations, offering new insights into the mi- crophone design and soundfield measurement. Using Taylor series expansion, we demonstrate how the spatial derivatives of the sound- field can be approximated by finite differences between microphone signals, laying the foundation of 3D DMAs. Owing to these formula- tions, the differential beamforming method via the spatial difference operator (SDO) can also be extended to the 3D case. Simulation results confirm the effectiveness of the proposed approach.
Zhao et al. (Sat,) studied this question.