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Beamforming Regularization, Scaling Matrices and Inverse Problems for Sound Field Extrapolation and Characterization: Part I - Theory

Sound field extrapolation (SFE) is aimed at the prediction of a sound field in an extrapolation region using a microphone array in a measurement region. For sound environment reproduction purposes, sound field characterization (SFC) aims at a more generic or parametric description of a measured or extrapolated sound field using different physical or subjective metrics. In this paper, a SFE method recently introduced is presented and further developed. The method is based on an inverse problem formulation combined with a beamforming matrix in the discrete smoothing norm of the cost function. The results obtained from the SFE method are applied to SFC for subsequent sound environment reproduction. A set of classification criteria is proposed to distinguish simple types of sound fields on the basis of two simple scalar metrics. A companion paper presents the experimental verifications of the theory presented in this paper.

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