author =      {Eric A. Lehmann and Anders M. Johansson},
  title =       {Prediction of Energy Decay in Room Impulse Responses Simulated with the Image-Source Model},
  type =        {{NICTA/WATRI} Technical Report},
  number =      {PRJ-NICTA-PM-025},
  institution = {Western Australian Telecommunications Research Institute},
  address =     {Perth, Australia},
  month =       {June},
  year =        {2008},
  abstract =    {Image source methods have become a widely-used analysis tool in many fields of acoustics and engineering. In this paper, a technique is proposed for approximating the energy decay (energy--time curve) in the room impulse responses simulated using the image source model. To this purpose, a modified version of the image method is considered: the computations are carried out in the frequency domain and negative reflection coefficients are used, which leads to more natural-looking impulse responses. A geometrical analysis of the image source principle leads to an analytical formula describing the energy decay curve, which is valid for either a uniform or non-uniform definition of the enclosure's six absorption coefficients. The proposed approximation is investigated and compared to image source results on the basis of simulations involving various room sizes and reverberation levels, and with uniform as well as non-uniform sound absorption coefficients. It is shown that the proposed formula provides a good approximation of the energy--time curve computed from a simulated room impulse response: the predicted curve accurately ``mimics'' the overall slope as well as the specific curvature of the energy decay. The result presented in this work thus enables designers to undertake a preliminary analysis of a simulated reverberant environment without the need for time-consuming image method simulations.
A potential implementation example for the proposed method is also considered in this work. Currently available formulae for the prediction of an enclosure's reverberation time, such as the well-known formulae by Sabine and Eyring, do not provide accurate results when used in conjunction with the image method. In this paper, it is shown how the proposed energy decay approximation can be used to effectively determine the enclosure's absorption coefficients in order to achieve a desired reverberation time. This approach hence ensures that the image source model effectively generates impulse responses with a correct level of reverberation, which is of particular importance, for instance, for the purpose of assessing the performance of acoustic signal processing algorithms operating in reverberant conditions.}