Damping Density of an Absorptive Shoebox Room Derived from the Image-Source Method

TL;DR

This paper introduces a closed-form damping density model for shoebox rooms that accurately predicts energy decay and enables fast reverberation synthesis, improving computational efficiency over traditional image-source methods.

Contribution

It derives a novel closed-form damping density expression for multi-slope energy decay, enhancing accuracy and speed in room impulse response modeling.

Findings

Model accurately matches late reverberation simulations.

Outperforms existing approximation methods in decay prediction.

Enables fast stochastic synthesis of reverberation.

Abstract

The image-source method is widely applied to compute room impulse responses (RIRs) of shoebox rooms with arbitrary absorption. However, with increasing RIR lengths, the number of image sources grows rapidly, leading to slow computation. In this paper, we derive a closed-form expression for the damping density, which characterizes the overall multi-slope energy decay. The omnidirectional energy decay over time is directly derived from the damping density. The resulting energy decay model accurately matches the late reverberation simulated via the image-source method. The proposed model allows the fast stochastic synthesis of late reverberation by shaping noise with the energy envelope. Simulations of various wall damping coefficients demonstrate the model's accuracy. The proposed model consistently outperforms the energy decay prediction accuracy compared to a state-of-the-art approximation method. The paper elaborates on the proposed damping density's applicability to modeling multi-sloped sound energy decay, predicting reverberation time in non-diffuse sound fields, and fast frequency-dependent RIR synthesis.