This is the master project I conducted under the supervision of Franz Zotter (IEM) and Filippo Fazi (ISVR) in 2012. I spent half of the thesis in Graz, Austria, at the IEM and the second half at the ISVR in Southampton, UK. Half-way through the thesis I was able to present some results at the Ambisonics Symposium 2012 in York. The main question the thesis posed was:
Can we find a set of basis functions for the decomposition of a sound field (similar to spherical harmonics) for arbitrarily shaped rigid objects? Are these frequency independent?
An application would be to build microphone arrays of unconventional shape with different or similar properties like a spherical microphone array.
This thesis deals with compact rigid microphone arrays and their acoustic modal representation for sound field reconstruction and beamforming. A method for obtaining surface modes of arbitrarily shaped rigid microphone arrays based on the boundary element method (BEM) and the singular value decomposition (SVD) is introduced and an analysis of spherical and cylindrical arrays is presented. The modal functions are found to be frequency depen- dent except for frequencies below kr ≈ 1. This indicates that a simplification of the array signal processing can be applied for low frequencies. Further, the spatial resolution properties of different rigid spherical and cylindrical array shapes were analyzed. The different configurations simulated using the BEM were found to have similar vertical and horizontal resolution.
Keywords: acoustic radiation modes, boundary element method, microphone arrays, scattering, singular value decomposition, modal array processing, array modes.