## 3 SADIE II Binaural Database
### Head Related Transfer Functions
#### 3.2.3 Equalisation and Windowing  
Correctly processed HRTFs require either diffuse-field or free-field equalisation. Both measures give a directionally independent common transfer function. Whilst diffuse field equalisation attempts to remove all commonality between a set of measurements, free field equalisation removes only the direct impact of the measurement system. This is demonstrated in Figure 4, where the diffuse field response of each ear of each subject is shown after free field equalisation of both the average loudspeaker and respective binaural microphone responses. For the free-field equalisation, loudspeaker responses were measured using a flat response GRAS 46 AE measurement microphone (www.gras.dk/products/measurement-micophone-sets/product/140-46 ae) placed at the centre of the loudspeaker array. Microphone responses were calculated as follows: a 20-24 KHz sine sweep was output from a Genelec 8040 loudspeaker (www.genelec.com/  
Figure 3: The 275 Hz crossover of a measured HRTF and individually generated low frequency model. support-technology/previous-models/8040a-studio-monitor) in the anechoic chamber. The sweep was simultaneously recorded by a flat-response GRAS 46 AE measurement microphone and each of the individual binaural microphones one at a time. In every case, the binaural microphone was placed as close as possible to the measurement microphone. A Fast Fourier Transform (FFT) was taken of each recording and the spectral response of the measurement microphone was subtracted from that of each binaural microphone. This resulted in the spectral responses of each binaural microphone. Inverse linear-phase FIR filters were computed using Kirkeby and [PERSON] regularization [55], which could be applied by means of convolution. Despite the free-field equalisation, the diffuse field responses of the KEMAR mannequin and human subjects all follow a similar trend, peaking at around 4 kHz. The KEMAR response peaks highest at about 17 dB. It is suspected that this peak is a result of ear canal resonance. This would explain both the similarity and slight variation between subjects as the microphones could not always be placed at exactly the same depth within each participant's ears. It would also explain the amplitude of the KEMAR response whose microphones are housed internally further within the ear canal mould. In contrast, the response of the KU100 is relatively flat. This is to be expected as the dummy head is pre-calibrated with a diffuse field equalisation filter [56]. Consequently, within the SADIE II database, all measurements are diffuse field equalised. This choice was made for a number of reasons:  
* a large enough set of data points was being captured to make diffuse field equalisation viable;
* it would take into account the free field response on the system in situ i.e., influences due to the placement of the microphone capsule within the ear canal;
* it would compensate for any generic response of the post-processing (e.g., windowing);
* it would equate the average frequency response of each dataset to provide a timbral consistency across the database (recall the KU100 is pre-calibrated with a diffuse field equalisation filter [56]);
* it provides a compatible set of measurements for both loudspeaker and headphone reproduction by avoiding the over-reproduction of the transfer function of the external ear [57; 58];
* it helps to ensure the reproduction of accurate tone colour considering the random directions from which many reverberant reflections could emanate from [3]. The equalisation was performed in two stages: before and after a windowing operation imposed to reduce the tap length of the filters. For each stage, the power average response of the dataset was calculated in the frequency domain for each ear of each subject. A weighting was applied to the contribution of each measurement based on a solid angle calculation of neighbouring measurements. This ensured that clustered measurements did not over-represent a particular direction in the average.