Common-slope modeling of late reverberation

The decaying sound field in rooms is typically described in terms of energy decay functions (EDFs). Late reverberation can deviate considerably from the ideal diffuse field, for example, in scenes with multiple connected rooms or non-uniform absorption material distributions. This paper proposes the common-slope model of late reverberation. The model can be used to describe spatial and directional late reverberation variations as linear combinations of exponential decays with fixed decay times. Its fundamental idea is to determine a set of common decay times that is representative of multiple EDFs. Consequently, all spatial and directional EDF variations are described solely with amplitude changes of the respective decaying exponentials. After deriving the common-slope model, we explore different approaches for determining the common decay times for large EDF sets, whose EDFs describe different source-receiver configurations of the same environment. Among the presented approaches, the k-means clustering of decay times is the most general. Our evaluation shows that the common-slope model introduces only a small error between the modeled and the true EDF, although the common-slope model is considerably more compact than the traditional multi-exponential model. Due to its compactness, the common-slope model yields interpretable room acoustic analysis results. The common-slope model has potential applications in all fields relying on late reverberation models, such as source separation, dereverberation, echo cancellation, and parametric spatial audio rendering.