Common-acoustical-pole and residue model and its application to spatial interpolation and extrapolation of a room transfer function

A method is proposed for modeling a room transfer function (RTF) by using common acoustical poles and their residues. The common acoustical poles correspond to the resonance frequencies (eigenfrequencies) of the room, so they are independent of the source and receiver positions. The residues correspond to the eigenfunctions of the room. Therefore, the residue, which is a function of the source and receiver positions, can be expressed using simple analytical functions for rooms with a simple geometry such as rectangular. That is, the proposed model can describe RTF variations using simple residue functions. Based on the proposed common-acoustical-pole and residue model, methods are also proposed for spatially interpolating and extrapolating RTFs. Because the common acoustical poles are invariant in a given room, the interpolation or extrapolation of RTFs is reformulated as a problem of interpolating or extrapolating residue values. The experimental results for a rectangular room, in which the residue values are interpolated or extrapolated by using a cosine function or a linear prediction method, demonstrate that unknown RTFs can be well estimated at low frequencies from known (measured) RTFs by using the proposed methods.