Department of Electrical Engineering and Computer Science, INTELSIG, University of Liège, Sart-Tilman B28, B-4000 Liège, Belgium.
J Acoust Soc Am. 2011 Sep;130(3):1381-9. doi: 10.1121/1.3623747.
The ergodic propriety of a room has strong effects on its reverberation. If the room is ergodic, the reverberation can be broken up in two steps: a deterministic process followed by a stochastic one. The late reverberation can be then modeled by a reverberation algorithm instead of more computationally consuming methods. In this study, the free path temporal distribution obtained by ray-tracing is used as an indicator of the room's mixing: the energetic average of the path lengths is computed at each time step. Ergodic rooms are thus characterized by rapidly convergent distributions. The free path value becomes independent of time. On the other hand, path selection mechanism and orbits are observed in non-ergodic rooms. The transition time from the deterministic process to the stochastic one is also studied through the evaluation of the room's time constant. It is shown that its value depends only on the mean free path and the boundaries scattering value. An empirical expression is obtained which agrees well with simulations carried out in a concert hall. This transition time from a deterministic model to a stochastic one can be used to speed up the acoustical predictions and auralizations in ergodic rooms.
房间的遍历性对混响有很大的影响。如果房间是遍历的，混响可以分为两步来分解：一个是确定性过程，另一个是随机过程。然后，可以使用混响算法而不是更耗时的方法来对后期混响进行建模。在这项研究中，射线追踪得到的自由路径时间分布被用作房间混合的指标：在每个时间步长计算路径长度的能量平均值。遍历性房间的分布收敛迅速。自由路径值与时间无关。另一方面，在非遍历性房间中观察到路径选择机制和轨道。通过评估房间的时间常数来研究从确定性过程到随机过程的过渡时间。结果表明，它的值仅取决于平均自由路径和边界散射值。得到了一个经验表达式，与音乐厅中的模拟结果吻合较好。从确定性模型到随机模型的这种过渡时间可用于加速遍历性房间中的声学预测和听觉化。
