A Scalable Algorithm for Physically Motivated and Sparse Approximation of Room Impulse Responses With Orthonormal Basis Functions

Abstract

Abstract-Parametric modeling of room acoustics aims at representing room transfer functions (RTFs) by means of digital filters and finds application in many acoustic signal enhancement algorithms. In previous work by other authors, the use of orthonormal basis functions (OBFs) for modeling room acoustics has been proposed. Some advantages of OBF models over all-zero and pole-zero models have been illustrated, mainly focusing on the fact that OBF models typically require less model parameters to provide the same model accuracy. In this paper, it is shown that the orthogonality of the OBF model brings several additional advantages, which can be exploited if a suitable algorithm for identifying the OBF model parameters is applied. Specifically, the orthogonality of OBF models does not only lead to improved model efficiency (as pointed out in previous work), but also leads to improved model scalability and model stability. Its appealing scalability property derives from a previously unexplored interpretation of the OBF model as an approximation to a solution of the inhomogeneous acoustic wave equation. Following this interpretation, a novel identification algorithm is proposed that takes advantage of the OBF model orthogonality to deliver efficient, scalable and stable OBF model estimates, which is not necessarily the case for nonlinear estimation techniques that are normally applied.

Low-Rank Tensor Modeling of Room Impulse Responses

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“…There are several different ways of modeling the RIR, including as an infinite impulse response (IIR) filter (see e.g. [6]), and as a finite impulse response (FIR) filter (see e.g. [7]).…”

An Automatic Design Procedure for Low-order IIR Parametric Equalizers

“…The initialization of the parameters of each new parametric filter in the cascade, as well as the selection of either a peaking or a shelving filter, is performed in an automatic way by means of a grid search using a discrete set of possible frequency and bandwidth values. A pole grid is defined, similarly to [31], where the radius and angle of complex poles determine respectively the bandwidth f b and central frequency f0 of the peaking filters. The radius of the real poles defines the transition frequencies fc of LF (positive real poles) and HF (negative real poles) shelving filters.…”

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Joint Estimation of the Room Geometry and Modes with Compressed Sensing

“…In literature, sparse plane wave representation has been used not only for the representation of the wavefield in a room in low frequency domain, but also for efficient storage of highly correlated recordings of dense microphone arrays [8]. Besides sparse plane wave representation an interesting sparse approach to the estimation of RTF is a recent approach with orthonormal basis functions based on infinite impulse response filters (IIR) [9]. Though not exploring plane wave sparsity, the solution relying on the weighted spatio-temporal representation [10] also gives promising room impulse response interpolations.…”