Beamforming Regularization, Scaling Matrices, and Inverse Problems for Sound Field Extrapolation and Characterization: Part I — Theory
The underlying hypothesis in spatial sound reproduction technologies is that a listener immersed in a physical reconstruction of a target sound field will experience the appropriate perception over a large listening area. The aim of this paper is twofold: to develop and describe a method of spatial sound field extrapolation (SFE) based on microphone array measurements of arbitrary geometry, and to develop and define a sound field characterization method and a sound field classification based on known objective and subjective metrics. To achieve SFE, a recently developed method was proposed and further analyzed. Once SFE was achieved, the inverse problem solution was investigated to evaluate different sound field metrics: energy density, sound intensity, direction of arrival, diffuseness, velocity vector, energy vector, directional energy, interaural time difference, incident directivity factor, incident directivity index, and directional diffusion.
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