On the design of differential beamformers with arbitrary planar microphone array geometry

This letter deals with the problem of differential beamforming with microphone arrays of arbitrary planar geometry. By approximating the beampattern with the Jacobi-Anger expansion, it develops an algorithm that can form any specified frequency-invariant beampattern with a microphone array of any planar geometry as long as the sensors' coordinates are given and the spacing between neighboring sensors is smaller than the smallest wavelength. This method is rather general and it can be used to design differential beamformers with linear, circular, and concentric circular differential microphone arrays as well as differential arrays of arbitrary planar geometry where sensors are placed in any specified positions.