An automatic model-building algorithm for sparse approximation of room impulse responses with Orthonormal Basis Functions

Abstract

Orthonormal Basis Function (OBF) models are used to define stable fixed-poles infinite impulse response filter structures that allow to incorporate knowledge about the resonant characteristics of a stable, causal and linear system. In the approximation of a room impulse response, OBF models can include knowledge about the room resonances as a set of poles, which appear nonlinearly in the structure. A novel algorithm is pro-posed, that avoids this nonlinear problem by iteratively estimating the poles and building the model. Some of the properties of OBF models, such as orthogonality and linearity-in-the-parameters, are exploited and the final model has the favorable property of being scalable. The OBF model provides a longer response than the all-zero model and is particularly suited in approximating the early response and the predominant resonances for relatively small model orders.