## 3 SADIE II Binaural Database
### Head Related Transfer Functions
#### 3.2.1 Measurement
\begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Latitude-Longitude** & **0°** & \(\pm\)**15°** & \(\pm\)**17.5°** & \(\pm\)**25°** & \(\pm\)**30°** & \(\pm\)**35.3°** & \(\pm\)**45°** & \(\pm\)**54°** & \(\pm\)**60°** & \(\pm\)**64.8°** & \(\pm\)**75°** & \(\pm\)**90°** \\ \hline  & \(\bullet\) & \(\bullet\) & & \(\bullet\) & & \(\bullet\) & & \(\bullet\) & & \(\bullet\) \\ \hline Tetrahedron & & & & & & & & & & & \\ \hline Octahedron (\(\times\)4 orientations) & \(\bullet\) & & & & & & & & & & \\ \hline Cube & & & & & & & & & & & \\ \hline Bi-Rectangle (\(\times\)3 orientations) & \(\bullet\) & & & & & & \(\bullet\) & & & & \\ \hline
26 pt Lebedev Grid & \(\bullet\) & & & & & \(\bullet\) & & & & & \\ \hline
50 pt Lebedev Grid & \(\bullet\) & & & & \(\bullet\) & & \(\bullet\) & & \(\bullet\) & \(\bullet\) \\ \hline Icoshehedron & \(\approx\) & \(\approx\) & & & & & \(\approx\) & & \(\approx\) & \\ \hline
24 point Tradim and & & & & & & & & & & \(\approx\) & \\ Sloane 7-Design & & \(\approx\) & & \(\bullet\) & & & & & & \\ \hline Pentakis & & & & & & & & & & \\ Icosdedoachendron & \(\bullet\) & & \(\approx\) & & \(\approx\) & & \(\bullet\) & \(\approx\) & \(\bullet\) \\ \hline \hline \end{tabular} \({}^{\dagger}\) \(-90^{\circ}\) modelled by the interpolation of measurements made at \(-81^{\circ}\).  
\end{table} 
Table 3: Distributions considered for HRTF measurement and their corresponding elevations. The black dots indicate the affiliation of a particular elevation angle with a particular configuration. Approximations are indicated by the symbol \(\approx\). Note that elevations correspond to the vertices (not faces) of each distribution. minor displacement in relation to the resolution of the human ear, it is proposed that this error has little perceptual influence. An elevation angle of \(-90^{\circ}\) could not be measured as the area was blocked by the installation of the chair and motor. Instead, a nearest alternative angle of \(-81^{\circ}\) was measured. In post-processing, these measurements were interpolated to approximate a measurement at \(-90^{\circ}\). For each ear, measurements were time aligned by their peak amplitude to the average delay of the subset. A linear interpolation was then performed in the time domain by calculating the average amplitude of each sample. Due to the nature of HRTF measurements made at such low elevations, the majority of high frequency detail is occluded by the legs/torso/chair. It is therefore reasonable to use an interpolated measurement, which will mainly preserve the low frequency cues. As the subject was rotated, the relative azimuthal co-ordinate of each loudspeaker was redefined. A sequence of rotations was programmed such that these coordinates satisfied the intended configurations. At each azimuthal option, the subject was stopped and a 2 s pause allowed any mechanical noise to settle. An overlapped exponential swept sine wave technique [51] was used to quickly and efficiently measure the IRs from all 23 loudspeakers, regardless of their direct affiliation to a configuration. The use of a sinusoidal sweep is an effective technique to measure a source-receiver transfer function over a range of frequencies [52]. The recorded signal is convolved with an inverse (time-reverse and amplitude compensated) copy of the sweep to remove the time-smeared element of the input signal and re-align and normalize the various frequency components in the time domain. This is known as de-convolution and results in the IR of the source being located at the moment the input sweep finishes. To save time, the sweeps' output from the loudspeakers may be overlapped provided that there is no interference between the IRs once the signals are deconvolved [51]. Twenty-four second sweeps separated by 0.15 s were performed with 0.1 s fade in/out half-Hanning windows over the frequency range 200-24 kHz.