Common mathematical framework for stochastic reverberation models.

Abstract

In the field of room acoustics, it is well known that reverberation can be characterized statistically in a particular region of the time-frequency domain (after the transition time and above Schroeder's frequency). Since the 1950s, various formulas have been established, focusing on particular aspects of reverberation: exponential decay over time, correlations between frequencies, correlations between sensors at each frequency, and time-frequency distribution. In this paper, the author introduces a stochastic reverberation model, which permits us to retrieve all these well-known results within a common mathematical framework. To the best of the author's knowledge, this is the first time that such a unification work is presented. The benefits are multiple: several formulas generalizing the classical results are established that jointly characterize the spatial, temporal, and spectral properties of late reverberation.