Sound field analysis with a two-dimensional microphone array

Sound field analysis is performed from data recorded by a microphone array in order to extract some spatial information about the sound field. In this article, the assets of the multidimensional Fourier transform are emphasized in order to perform this analysis step. Indeed, the finite number of microphones inevitably introduces spatial aliasing, which is linked to the spectral broadening due to the discrete and finite nature of the analysis window. First, given the geometry of the array, the hypothesis that sound fields satisfie the dispersion relation, obtained from the wave equation, is used to design an optimal analysis window, which minimizes spatial aliasing according to a criterion inspired by prolate spheroidal spectral analysis. Then, several array configurations are compared to analyze sound fields with large frequency bandwidth.