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

摘要

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 an 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. A set of classification criteria is proposed to distinguish simple types of sound fields on the basis of simple scalar metrics. A companion paper presents the experimental verifications of the theory presented in this paper.