A physically motivated parametric model for compact representation of room impulse responses based on orthonormal basis functions

A Room Impulse Response (RIR) shows a complex time-frequency structure, due to the presence of sound re ections and room resonances at low frequencies. Many acoustic signal enhancement applications, such as acoustic feedback cancellation, dereverberation and room equalization, require simple yet accurate models to represent a RIR. Parametric modeling of room acoustics attempts at approximating the Room Transfer Function (RTF), for given positions of source and receiver inside a room, by means of rational functions in the z-domain that can be implemented through digital lters. However, conventional parametric models, such as all-zero and pole-zero models, have some limitations. In this paper, a particular xed-pole In nite Impulse Response (IIR) lter based on Orthonormal Basis Functions (OBFs) is used as an alternative, motivated by its analogy to the physical de nition of the RIR as a Green's function of the acoustic wave equation. An accurate estimation of the model parameters allows arbitrary allocation of the spectral resolution, so that the room resonances can be described well and a compact representation of a target RIR can be achieved. The model parameters can be estimated by a scalable matching pursuit algorithm called OBF-MP, which selects the most prominent resonance at each iteration. A modi ed version of the algorithm, called OBF-GMP (Group Matching Pursuit), is introduced for the estimation of a common set of poles from multiple RIRs measured at di erent positions inside a room. A new database of RIRs measured in a rectangular room using a subwoofer is also presented. Simulation results using this database show that, in comparison to OBF-MP, the OBF-GMP signi cantly reduces the number of parameters necessary to represent the RIRs.