title: Inter-frequency band correlations in auditory filtered median plane HRTFs
Creators: name: Iwaya, Yukio
name: Katz, Brian F.G.
name: Magariyachi, Tetsu
name: Suzuki, Yoiti
Publisher: name: EAA Spatial Audio Signal Processing Symposium
Year: 2019
Subjects: HRTF
Median plane
auditory filter

description: Spectral cues in head-related transfer functions (HRTF), such as peaks and notches occurring above 4 kHz, are important for sound localization in the median plane. However, it may be complicated for the auditory system to detect absolute frequency and level peaks and notches, mapping them to three-dimensional positions. In contrast, it may be more reasonable that comparisons are made of the relative level differences between frequency bands due to various peaks and notches. With this approach, it is not necessary to detect peaks and notches directly, only comparisons in levels across frequency bands are needed. In this paper, we analyze level changes of median plane HRTFs in narrow frequency bands using auditory filters and inter-band correlations. These changes are investigated to clarify effects of peaks and notches on comprehensive level changes in the corresponding HRTFs.We investigated 105 HRTF sets from the RIEC (Research Institution of Electrical Communication, Tohoku University) database, available in the SOFA format standard. HRTFs were measured using a spherical loudspeaker array at RIEC for individual listeners. Head-related impulse responses (HRIRs) were acquired in the median plane from front (0o) to rear (180o) in 10o-steps. Each HRIR was then filtered by a band limited auditory filter. A Gammatone filter was employed in this analysis, with 40 equivalent rectangular bandwidth (ERB) over the full audible frequency range (up to 20 kHz). Output power level of the filtered HRIRs for the 19 median plane angles was calculated, resulting in 760 values (19 angles x 40 bands) for each listener. From these values, the level change of individual frequency bands was obtained as a function of angle in median plane. We then calculated the correlation across frequency bands for the level change as a function of angle. This produced 39 cross-correlation values and 1 auto-correlation for each band with a correlation matrix of 40 bands x 40 bands for each listener. Examination of the correlation matrixes showed similarities that could be summarized by clustering the analyzed bands into the following five aggregated approximate frequency bands:Band-1: 0 to 0.7 kHz, almost no level changes observed.Band-2: 0.7 to 1 kHz, observed negative correlation to odd bands (Band-1, Band-3, Band-5, level changes approximately 3 dB.Band-3: 1 kHz to 6 kHz, as the median plane angle increases, observed level decreases by approximately 5 dB.Band-4: 6 kHz to 10 kHz, observed level decreases as the median plane angle exceeds 120o. Observed negative correlation to Band-1, 3, and 5.Band-5: &gt; 10 kHz, observed level decreases by approximately 20 dB until the median plane angle reaches approximately 120o.The general observation shows that while Band-2 has a negative correlation, its actual level change is relatively small, so it may be integrated into Band-1 and Band-3. Furthermore, Band-5 has a positive correlation with Band-1 and Band-3. In contrast, Band-4 has a negative correlation and its level change is significant. In addition, it can be noted that Band-4 includes various spectral cues as notches and peaks in the HRTFs. This means that these negative correlations can be caused by both notches and peaks. It should be noted however, that this correlation was done per HRTF (or per individual) and that the exact frequency delimitations for the five aggregated bands with their respective observed behavior varied across HRTFs. Further discussions concern the effects of peaks and notches in HRTFs based on previous experiments evaluating sound localization in the median plane using binaural representations. For these experiments, HRTFs were simplified; removing peaks and notches, while the levels of each aggregated frequency bands were averaged. Results showed that median plane sound localization remains possible, even without clearly present peaks and notches.