Generation of Far-Field Head-Related Transfer Functions using Virtual Sound Field Synthesis

Head-related transfer functions (HRTFs) or impulse responses (HRIRs) capture the acoustic transmission path from an acoustic source to the ears. For ease of illustration we restrict our considerations to HRTFs H{L,R}(α0, R, ω) captured from sources in a plane, were (α0,R) denotes the position of the sound source. Note, the generalization of the proposed technique is straightforward. HRTFs are typically measured for a fixed source distance in the range of R = 1.5 − 3 m. For virtual auditory environments extrapolation to other distances than the measured ones is desirable in order to be able to place virtual sources at arbitrary positions within the virtual space. For some applications far-field HRTFs are of interest. These are defined as the transfer function H̄{L,R}(αpw, ω) of a plane wave with incidence angle αpw to the ears. Far-field HRTFs can be beneficial for dynamic data-based binaural synthesis were plane wave representations of sound fields are combined with HRTFs [1]. A least two different strategies have been presented in the past to perform range extrapolation of measured HRTFs: (1) extrapolation using a representation of HRTFs in terms of spherical harmonics/Bessel functions [2] and (2) virtual higher-order Ambisonics [3]. In this paper, we present an approach which is closely related to the latter category.