Modelling Room Reverberation Directivity using von Mises-Fisher Mixture Distribution

In this paper, we propose a novel approach to room reverberation analysis based on the angular power distribution model of the reverberant field developed using a von Mises-Fisher (vMF) mixture function. The statistical features of the complex reverberant power distribution convey the directional strength of inhomogeneous room reflections. The model is primarily designed for directivity study and also helps in encapsulating the extensive raw data into a convenient set of parameters of the density function. Initially, we conducted impulse response measurements of the test room and determined the reverberant field power values using the spatial correlation model in the spherical harmonics domain. The proposed technique transforms this data into directional power vectors to estimate the parameters of a convex vMF mixture function. A power distribution model is generated from these parameters to represent the directional characteristics of room reverberation. The paper evaluates the performance of the model for a test room, and the results conform to the real room environment. The directivity model identifies directions of distinct reflections and exhibits the potential for further functional enhancements to evolve as a reliable statistical room acoustic model.