A spatio-temporal generalized fourier domain framework to acoustic modeling in enclosed spaces

In this paper, we present a spatio-temporal framework for multichannel acoustic modeling in enclosed spaces. Reverberation occurs when the sound field is enclosed between reflective boundaries (e.g. walls). We model the reverberated sound field by proper sampling of the (generalized) Fourier representation of the free-field sound field. We show that the spatial aliasing introduced by spectral sampling represents all the (damped) reflections. From the samples of the generalized spectrum, we compute the spatio-temporal sound field in the enclosed space with very low-complexity, of O(N log N) per measuring position, with N proportional to the reverberation time.