Acoustical source mapping based on deconvolution approaches for circular microphone arrays

Recently, the aeroacoustic community has examined various methods based on deconvolution to improve the visualization of acoustic fields scanned with planar arrays of microphones. These methods are based on the assumption that the beamforming map in an observation plane parallel to the array can be approximated by a convolution of the actual sources and the beamformer’s point spread-function, i.e., the beamformer’s response to a point source. By deconvolving the resulting map, the resolution is improved and the side-lobes effect is reduced or even eliminated compared to conventional beamforming. Even though these methods are originally designed for planar sparse arrays, they can be adapted to uniform circular arrays for mapping the sound over 360º. Such geometry has the advantage that the beamforming response has always the same shape around the focusing direction, or in other words, that the beamformer’s point-spread function is shift-invariant, which makes it possible to apply spectral procedures on the entire region of interest so that the deconvolution algorithm becomes computationally more efficient. This investigation examines the matter by means of computer simulations and experimental measurements.