Prediction of energy decay in room impulse responses simulated with an image-source model

TLDR

The authors propose a method to approximate the acoustic energy decay curve of image‑source simulated room impulse responses and to predict enclosure reflection coefficients for a target reverberation level. By geometrically analyzing the image‑source principle, they derive a closed‑form expression for the energy decay curve that applies to both uniform and nonuniform wall absorption. Simulations across various room sizes and reverberation levels confirm the approximation’s accuracy, allowing designers to conduct preliminary reverberant‑environment analyses without costly image‑method simulations.

Abstract

A method is proposed that provides an approximation of the acoustic energy decay (energy–time curve) in room impulse responses generated using the image-source technique. A geometrical analysis of the image-source principle leads to a closed-form expression describing the energy decay curve, with the resulting formula being valid for a uniform as well as nonuniform definition of the enclosure’s six absorption coefficients. The accuracy of the proposed approximation is demonstrated on the basis of impulse-response simulations involving various room sizes and reverberation levels, with uniform and nonuniform sound absorption coefficients. An application example for the proposed method is illustrated by considering the task of predicting an enclosure’s reflection coefficients in order to achieve a specific reverberation level. The technique presented in this work enables designers to undertake a preliminary analysis of a simulated reverberant environment without the need for time-consuming image-method simulations.