Parameter Analysis for Range Extrapolation of Head-Related Transfer Functions using Virtual Local Wave Field Synthesis

Binaural synthesis utilizing head-related transfer functions (HRTFs) is a common approach to auralize virtual acoustic sources. HRTFs represent the acoustic free field transmission path from the source to the outer ears. They capture the acoustic characteristics of the outer ears which are exploited by the human auditory system in order to deduce spatial information. HRTFs differ amongst individuals due to varying anatomy. They are additionally depending on the head/body-orientation and position with respect to the source. HRTFs are typically measured in anechoic environments. For a virtual acoustic scene, left and right ear drum signals are rendered by filtering an anechoic signal of a virtual sound source with the left and right ear HRTFs. In order to enable arbitrary positioning of the virtual sound source, a (densely) sampled grid of HRTFs is necessary. It is obvious that the measurement effort for the required HRTF dataset would be considerable. Hence, typical datasets are available for various source directions (on a circle or on a sphere) but only for a few distances up to 3 meters [1]. The characteristics of the HRTFs are generally assumed to be invariant with regard to source distances exceeding this threshold [2]. However, HRTFs of nearby sound sources significantly depend on the distance [2]. In the past several approaches have been proposed to extrapolate an HRTF for a desired distance from an available HRTF dataset. Two of them expand the HRTFs into surface spherical harmonics in order to perform extrapolation in the spherical harmonics domain [3, 4]. Other methods interpret the available HRTF measurements as a virtual loudspeaker array, which has be to driven according to the desired source position. While some of these techniques [5, 6] are based on Higher Order Ambisonics (HOA), a numerically stable and computationally efficient method uses Wave Field Synthesis (WFS) [7]. The latter method was further refined in [8] using Local Wave Field Synthesis (LWFS) [9], which utilizes a distribution of focused sources as so-called virtual secondary sources. These are placed more densely and nearer to the listener than the original HRTF dataset. This paper analyses, in how far the number of the virtual secondary sources and their distance to the listener influences the accuracy of this extrapolation method. This is done by comparing the extrapolated HRTFs with measured ones with regard to important characteristics, i.e. the magnitude spectrum and the average Interaural Level Difference (ILD). n0 x0