Binaural Room Transfer Function Interpolation Via System Inversion

Abstract

This paper is concerned with the spatial interpolation of Binaural Room Transfer Functions (BRTFs). The proposed method is a binaural extension of Room Transfer Function (RTF) interpolation methods framed as inverse problems, and is based on a parametric representation of the sound field using either Plane Waves (PWs) or Equivalent Sources (ESs). Once the parameters are obtained via system inversion, the BRTFs can be synthesised at any other position. Four combinations of acoustic models (PW or ES) and regularisation functions (Tikhonov and l<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>-norm) are tested. The proposed method is shown to have a good performance below 1 kHz, comparable to standard pressure-based RTF interpolation. Using PWs with l<inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</inf>-norm regularisation produces optimal solutions, resulting in a Normalised Mean Squared Error (NMSE) of −15 dB at 700 Hz using 25 BRTF measurements. The important case where the listener’s Head-Related Transfer Function (HRTF) is unknown is also tested, revealing that using a different HRTF for inversion and synthesis did not yield a significant drop in performance. It is hypothesised that this is due to the small variations between individual HRTF magnitudes within the operating frequency range of this class of models.