Modelling room transfer functions using the decimated Padé approximant

Abstract

The numerical issues involved in modelling measured room transfer functions (RTFs) are examined. This is explored using a nonlinear parametric estimation technique known as the decimated Padé approximant (DPA). The DPA combines the well-known methodology of Padé rational polynomial approximation with beamspace windowing. This combination helps to overcome the severe numerical instabilities encountered in calculations with large data records. The aim is to accurately extract the parameters that reliably quantify the analytic structure of signals composed of decaying sinusoidal oscillations. DPA parameter estimation provides the ability to construct a high-resolution spectral estimate of such signals for either specific spectral regions or the entire Nyquist interval. As demonstrated in the authors' previous work (O'Sullivan and Cowan, 2006), this technique, developed in quantum chemistry, readily cross-fertilises to the field of acoustics, where it can fully reconstruct the complicated spectra of experimental RTFs. A noise-filtering technique using the removal of Froissart doublets to obtain an irreducible rational model is investigated. This noise filtering can be used to find an order of the parametric model that is inherent in the data. Additionally, an example is shown suggesting that such a process may be useful in room spatialisation problems.