Sparse parametric modeling of the early part of acoustic impulse responses

Acoustic channels are typically described by their Acoustic Impulse Response (AIR) as a Moving Average (MA) process. Such AIRs are often considered in terms of their early and late parts, describing discrete reflections and the diffuse reverberation tail respectively. We propose an approach for constructing a sparse parametric model for the early part. The model aims at reducing the number of parameters needed to represent it and subsequently reconstruct from the representation the MA coefficients that describe it. It consists of a representation of the reflections arriving at the receiver as delayed copies of an excitation signal. The Time-Of-Arrivals of reflections are not restricted to integer sample instances and a dynamically estimated model for the excitation sound is used. We also present a corresponding parameter estimation method, which is based on regularized-regression and nonlinear optimization. The proposed method also serves as an analysis tool, since estimated parameters can be used for the estimation of room geometry, the mixing time and other channel properties. Experiments involving simulated and measured AIRs are presented, in which the AIR coefficient reconstruction-error energy does not exceed 11.4% of the energy of the original AIR coefficients. The results also indicate dimensionality reduction figures exceeding 90% when compared to a MA process representation.