Common mathematical framework for stochastic reverberation models

Roland Badeau (1, 2, 3)

1 Télécom ParisTech
2 S2A - Signal, Statistique et Apprentissage
3 LTCI - Laboratoire Traitement et Communication de l'Information

In the field of room acoustics, it is well known that reverberation can be character-1 ized statistically in a particular region of the time-frequency domain (after the tran-2 sition time and above Schroeder's frequency). Since the 1950s, various formulas have 3 been established, focusing on particular aspects of reverberation: exponential decay 4 over time, correlations between frequencies, correlations between sensors at each fre-5 quency, and time-frequency distribution. In this paper, we introduce a stochastic 6 reverberation model, that permits us to retrieve all these well-known results within 7 a common mathematical framework. To the best of our knowledge, this is the first 8 time that such a unification work is presented. The benefits are multiple: several 9 formulas generalizing the classical results are established, that jointly characterize 10 the spatial, temporal and spectral properties of late reverberation. 11

Mots clés: Reverberation; Diffusion; Room impulse response; Stochastic models

Domaines: Acoustique [physics.class-ph]

Roland Badeau. Common mathematical framework for stochastic reverberation models. Journal of the Acoustical Society of America, 2019, 145 (4), pp.2733-2745. ⟨10.1121/1.5096153⟩. ⟨hal-01958485⟩