Characterization of Acoustical Environments by Numerical Simulation

The state of the art to solve problems of active noise control and acoustic echo cancellation is to use adaptive control systems [1]. For acoustic echo cancellation, adaptive algorithms have to provide a correct estimate of the room impulse response of loudspeaker-enclosuremicrophone systems during operation. Test and evaluation of such algorithms requires either a real-time implementation or measured appropriate impulse responses. However, these impulse responses are only valid for one special room setup and cannot be applied to other situations. Simulations of acoustical environments can help to overcome this problem. Impulse responses computed from realistic room models can replace measured ones for test purposes. The different methods used for computational modeling of room acoustics can be divided into three groups [2]: Statistical models, Ray-based models and Wavebased models. The propagation of sound waves in the air is governed by the wave equation. Unfortunately the wave equation can only be solved analytically for special cases like free field conditions or three-dimensional enclosures with very simple geometries. Therefore the solution must be approximated using more simple models for the sound propagation. Statistical models try to model the statistical properties of the sound intensity and are therefore not useful in our context. Ray-based models suppose that the sound behaves like optical rays. As a result the effects caused by the wave nature of sound, like diffraction, cannot be handled by these methods. Wave-based methods try to find numerical simulations for the wave equation. Because they use distributed parameter models, they are able to handle all relevant physical effects, namely wave propagation, reflection, transmission and diffraction. To meet the high simulation quality requirements of the proposed application, wave-based methods are the only ones suitable here. Among various other methods developed in the last two decades, we present here a direct method to computational acoustics, which leads from the partial differential equations to a state space description of the simulation algorithm.