Distance-varying filters to synthesize head-related transfer functions in the horizontal plane from circular boundary values

Abstract

This paper derives a continuous-space model to describe variations in magnitude of complex head-related transfer functions (HRTFs) along angles and radial distances throughout the horizontal plane. The radial part of this model defines a set of horizontal-plane distance-varying filters (HP-DVFs) that are used to synthesize the HRTFs for arbitrary sound source positions on the horizontal plane from initial HRTFs obtained for positions on a circular boundary at a single distance from the head of a listener. The HP-DVFs are formulated in terms of horizontal-plane solutions to the three-dimensional acoustic wave equation, which are derived by assuming invariance along elevation angles in spherical coordinates. This prevents the free-field inaccurate distance decay observed when assuming invariance along height in cylindrical coordinates. Furthermore, discontinuities along the axis connecting the ears are also overcome, which appear when assuming invariance along the polar angle in interaural coordinates. This paper also presents a magnitude-dependent band-limiting threshold (MBT) for restricting the action of filters to a limited angular bandwidth, which is necessary in practice to enable discrete-space models that consider a finite number of sources distributed on the initial circle. Numerical experiments using a model of a human head show that the overall synthesis accuracy achieved with the proposed MBT outperforms the one achieved with the existing frequencydependent threshold, especially at low frequencies and close distances to the head.

Design theory for binaural synthesis: Combining microphone array recordings and head-related transfer function datasets

“…The initial HRTF dataset is typically obtained for an array of positions at a single distance from the head center [27][28][29]. From this initial dataset, the HRTFs for arbitrary target positions that are not contained in the initial dataset are synthesized by interpolation along angle [59][60][61][62][63] or extrapolation along radial distance [64][65][66][67].…”

“…The HRTF datasets allow the inclusion of the auditory localization cues that correspond to the individual traits of the listeners, provided that individual HRTF datasets can be obtained directly for each listener or by means of anthropometric personalization [68,69] or individualization methods [70,71]. Moreover, HRTFs for dense sets of positions can be calculated based on interpolation methods [59][60][61][62][63][64][65][66][67]. In general, this class of binaural synthesis methods aim at rendering a sound pressure field sampled at the positions where a set of HRTFs is given.…”