Distribution of Modal Damping in Absorptive Shoebox Rooms

The image-source method is widely applied to compute room impulse responses (RIRs) of shoebox rooms with arbitrary damping. However, with increasing RIR lengths, the number of image sources grows rapidly, leading to slow computation. We propose a method to estimate the damping density of a damped shoebox room, which in turn can provide the energy decay necessary to model the stochastic late reverberation. The damping density is derived from a modal decomposition that is compliant with the ISM solution. We show that the proposed method gives a more accurate estimate of the energy decay than previous methods and can be efficiently computed regardless of the RIR lengths. While we focus on the derivation and evaluation, the main practical applications of the proposed model include, e.g., the faster synthesis of late reverb and the analysis of multi-slope decays.