Cross-spectral analysis of higher-order ambisonic signals for investigating the spatial and statistical properties of captured sound fields

The analysis of spatial and statistical properties of a captured sound field is of significant interest in various fields,including room acoustics, spatial sound capture and reproduction. In this paper, we investigate these properties based on higher-order Ambisonic (HOA) signals. A cross spectral matrix is constructed, where the diagonal and off diagonal entries respectively represent the power spectral densities and the cross-spectral densities of the HOA signals. Through theoretical development, we demonstrate that the numerical properties of the cross-spectral matrix,such as its rank and eigenvalue distribution, are determined by the spatial distribution of incident sound waves and the correlation between source signals. The analysisis performed for simulated and real sound fields, considering various source distributions and Ambisonic order