Sparse Linear Parametric Modeling of Room Acoustics with Orthonormal Basis Functions

Orthonormal Basis Function (OBF) models provide a stable and well-conditioned representation of a linear system. When used for the modeling of room acoustics, useful information about the true dynamics of the system can be introduced by a proper selection of a set of poles, which however appear non-linearly in the model. A novel method for selecting the poles is proposed, which bypass the non-linear problem by exploiting the concept of sparsity and by using convex optimization. The model obtained has a longer impulse response compared to the all-zero model with the same number of parameters, without introducing substantial error in the early response. The method also allows to increase the resolution in a specified frequency region, while still being able to approximate the spectral envelope in other regions.