## 3 SADIE II Binaural Database
### Head Related Transfer Functions
#### 3.2.3 Equalisation and Windowing
Figure 4: The diffuse field response of each ear of each subject (total 40 responses) after free field equalisation of both the average loudspeaker and respective binaural microphone responses. The responses of the KEMAR and KU100 dummy heads are distinguished from the other human responses. The plot shows a common broad peak at approximately 4 kHz which may be explained by ear canal resonance. Inverse linear-phase FIR filters were calculated from the diffuse field response using Kirkeby and Nelson regularization [55] to perform each equalisation. Stage one was designed to compensate for the response of the measurement system. Input data was left unwindowed to preserve as much of the original signal content as possible. In addition, 1/3 rd octave band smoothing was used to prevent overly-sharp peaks or notches appearing in the frequency response of the inverse filter and exacerbating the time-domain aliasing. IRs were then windowed to 500 samples (approximately their final length) by means of a 20 sample half Hanning window and 130 sample pad before each peak and a 150 sample pad and 200 sample half Hanning window after (see Figure 5). The proportions and relative position of this window affected both the preservation of the filter's frequency response and the final diffuse field response of the dataset. By biasing the length of the fade out over the post-peak pad and shifting the window to preserve more of the pre-peak signal, the diffuse field variance can be reduced. However, accurate preservation of the frequency response generally required as much of the post-peak signal to remain as intact as possible. Systematic frequency domain errors introduced by the windowing operation were compensated for by a second stage of diffuse field equalisation. This equalisation was performed on the windowed IRs with 1/5 th octave band smoothing. As the first stage of equalisation had already considerably smoothed out the diffuse field response, a less smooth filter was required. The IRs were time aligned and trimmed to 512 samples (256 samples at 48/44.1 KHz) inclusive of 10 sample fade in/out half Hanning windows. It was ensured that at least 180 samples remained before each peak and at least 230 samples remained after. This left approximately 100 samples to account for the variances in peak onset time due to ITDs. Figure 6 shows the final normalised diffuse field response of each ear of each subject calculated after all post-processing: deconvolution and separation of original recordings, low frequency compensation, stage 1 diffuse field equalisation, windowing, stage 2 diffuse field equalisation, and trim to 512 samples. Figure 5: Windowing of HRTFs to 500 samples by means of a 20 sample half Hanning window and 130 sample pad before each peak and a 150 sample pad and 200 sample half Hanning window after. Note that the plot has zoomed in on the IR to illustrate the region of windowing. Comparing the magnitudes of the frequency bins of each response, 95% fall within a 0.33 dB range (approximately \(-0.35\) dB and \(-0.65\) dB). The pattern followed by each response below approximately 7 KHz can be attributed to the windowing parameters.