# Head-Related Transfer Functions for Dynamic Listeners in Virtual Reality
## 2 HRTF Sets and Analysis  
### HRTF Sets  
Three different HRTF sets were obtained for the experiment: a _measured_, _modeled_, and a _generic_ set. The measured and modeled HRTFs were produced for the same group of people (\(N=12\)), who also participated in the subjective experiments. A fourth HRTF set was derived from the generic HRTF set by keeping only the measurement points located in the horizontal plane and utilized in the second subjective listening experiment.  
Individual HRTFs were measured in a semi-anechoic chamber at 1.2 m distance with a procedure described in [28]. The measurement setup comprised an array of 64 loudspeakers mounted on a semi-circle in elevation direction. A multiple exponential sweep was used to allow overlapping signal playback from multiple loudspeakers in parallel. The spatial resolution was \(5^{\circ}\) in azimuth and \(2.5^{\circ}\) in elevation covering the full azimuth circle and elevations from +90\({}^{\circ}\) to -70\({}^{\circ}\) resulting in \(Q=4608\) measurement positions with a filter length of 386 samples. The measurements were made at the entrance to the blocked ear canal. The floor reflection was cut out from the measurements in post-processing, and a low-frequency boost was applied to compensate for the non-flat magnitude response of the small drivers in the measurement setup.  
The modeled HRTFs were based on high-precision 3D scans of the participants' pinnae and a set of anthropometric measurements of the head size and ear position. The measurements were used to scale the shape and dimensions of a scanned generic head-and-torso model, onto which the individual pinna models were stitched. A boundary element method numerical simulation then produced the modeled HRTFs [29]. Each modeled HRTF set had the same distribution and distance of measurement points and the same filter length as the measured HRTF set.  
The generic binaural head (Neumann KU100) HRTFs were obtained from the spatial audio for domestic interactive entertainment (SADIE) database ([[https://www.york.ac.uk/sadie-project/index.html](https://www.york.ac.uk/sadie-project/index.html)]([https://www.york.ac.uk/sadie-project/index.html](https://www.york.ac.uk/sadie-project/index.html)) (accessed on 29 May 2019)). These measurements comprise \(Q=1550\) measurement positions at 1.5 m distance with azimuthal increments of \(5^{\circ}\) and elevation increments of \(10^{\circ}\) with added measurement points to satisfy specific Ambisonics reproduction setups. The head-related impulse response length is 256 samples. Notably, the KU100 binaural head does not include a torso, removing the shoulder reflection effect from the generic HRTFs. The measured, modeled, and generic HRTF set signal processing chains were level aligned to 68 dB\({}_{A}\) sound pressure level at 1 m distance using pink noise and a binaural head with a virtual sound source rendered directly in front.  
Following [4, 30], we employed a decoupled equalization technique using a reference sound field, in our case the diffuse field, to equalize the measured HRTFs and the head-phones. This technique is opposed to a non-decoupled equalization, where a headphone transfer function (HPTF) is measured with the same measurement setup (including the head and microphones) as for the recording of the HRTFs. The decoupled equalization technique is found to offer the same degree of fidelity as using the HPTF approach, but with the added flexibility of equalizing the recording system and reproduction system in independent sessions using different equipment. The HRTFs were diffuse-field equalized for this experiment by calculating the average magnitude over all directions, inverting it, and creating a minimum-phase filter, which was then convolved with the HRTFs. The KU100 binaural head readily produces diffuse-field equalized measurements.