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Sound Field Analysis Based on Generalized Prolate Spheroidal Wave Sequences

In this article, an array processing is described to improve the quality of sound field analysis, which aims to extract spatial properties of a sound field. In this domain, the notion of spatial aliasing inevitably occurs due to the finite number of microphones used in the array. It is linked to the Fourier transform of the discrete analysis window, which is constituted of a mainlobe, fixing the resolution achievable by the spatial analysis, and also from sidelobes which degrade the quality of spatial analysis by introducing artifacts not present in the original sound field. A method to design an optimal analysis window with respect to a particular wave vector is presented, aiming to realize the best localization possible in the wave vector domain. Then the efficiency of the approach is demonstrated for several geometrical configurations of the microphone array, on the whole bandwidth of sound fields.

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