Directionally characterized pseudo-perfect diffuseness: A detailed comparison of its theoretical formulations

Abstract

Perfectly diffuse sound fields can be modeled by using an infinite number of random coefficients of spherical wave functions or random plane waves. The statistical properties of the spherical harmonic coefficients and the plane-wave amplitudes in these models directionally define the perfect diffuseness, yielding the established theoretical formulations of directionally characterized perfect diffuseness. However, sound fields in real rooms are not perfectly diffuse. These models and formulations of perfect diffuseness thus provide limited insight into understanding pseudo-perfect diffuseness, the diffuseness of real sound fields. This requires a theory that efficaciously describes pseudo-perfectly diffuse sound fields. Here, we rigorously compare existing formulations of directionally characterized pseudo-perfect diffuseness, aiming to determine its better formulation for the diffuseness evaluations of real sound fields. Our theoretical and numerical results indicate the advantages of the formulation using random coefficients of truncated- or finite-degree spherical wave functions over the formulation using a finite number of random plane waves.