A diffuseness of a sound field in the domains of spherical harmonics and plane waves

Sound field diffuseness plays a key role in room acoustics. Although several attempts have been made to characterize diffuseness quantitatively, how to quantify the extent of diffuseness has yet to be understood. This paper considers a directional diffuseness of a sound field from a viewpoint of statistics. Using an existing approach to the evaluation of diffuseness that employs a covariance of electric acoustic signals in the spherical-harmonics domain, a limited-degree directional diffuseness is formulated. In addition, a spherical design is used to model the diffuse sound field composed of finite number of plane waves. The formulation and the model can contribute to a better understanding of the evaluation of the diffuseness. Results also suggest that Gaussianity of a sound field in the spherical-harmonics domain can be interpreted as Gaussianity of plane waves in the diffuse field model.