Inter-frequency band correlations in auditory filtered median plane HRTFs

International audienceSpectral 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 (0°) to rear (180°) in 10°-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 120°. Observed negative correlation to Band-1, 3, and 5.Band-5: > 10 kHz, observed level decreases by approximately 20 dB until the median plane angle reaches approximately 120°.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

Sound directivity by PT-symmetric acoustic dipoles

The new physics of open-dissipative, non-Hermitian systems have become a fruitful playground to uncover novel physical phenomena, even in exotic or counterintuitive ways, especially in optics and, more recently, also in acoustics. In this work, we propose a non-Hermitian metasystem in acoustics for the control of the sound field in two dimensions. The building blocks, or meta-atoms composing the arrangements, are pairs of identical Helmholtz resonators with different gain or loss functions. Such Helmholtz resonator dipoles may be designed to hold asymmetric scattering, as was theoretically analyzed and experimentally confirmed. Furthermore, aiming to create a complicated directivity, we explored different ensembles of Helmholtz resonator dipoles and numerically demonstrated a sound concentration with various configurations. The proposed non-Hermitian parity-time- symmetric dipoles made of a pair of Helmholtz resonators may be a potential artificial element for the creation of complex sound fields.Peer ReviewedObjectius de Desenvolupament Sostenible::9 - Indústria, Innovació i Infraestructura::9.5 - Augmentar la investigació científica i millorar la capacitat tecnològica dels sectors industrials de tots els països, en particular els països en desenvolupament, entre d’altres maneres fomentant la innovació i augmentant substancialment, d’aquí al 2030, el nombre de persones que treballen en el camp de la investigació i el desenvolupa­ment per cada milió d’habitants, així com la despesa en investigació i desenvolupament dels sectors públic i privatObjectius de Desenvolupament Sostenible::9 - Indústria, Innovació i InfraestructuraPostprint (author's final draft

PT-symmetric Helmholtz resonator dipoles for sound directivity

Parity-time ( PT )-symmetric or, more generally, non-Hermitian systems have opened a new area for unconventional management of waves, with significant applications, especially in optics. However, fewer proposals are found in acoustics, possibly due to the lack of a simple mechanism for coherent gain. In this paper, we propose a composite non-Hermitian system in acoustics consisting of assemblies of PT -symmetric Helmholtz resonator (HR) dipoles. Like meta-atoms are used as building elements in metamaterials, we propose PT -symmetric dipoles to design non-Hermitian systems intended to engineer complicated directivity fields. We theoretically analyze, numerically confirm, and experimentally show the symmetry breaking in a two-dimensional space of non-Hermitian dipoles consisting of a pair of Helmholtz resonators with different levels of gain and loss. In particular, we explore, as an application, a metastructure to concentrate the sound pressure inside the circular array formed by PT -symmetric dipoles. The proposed HR dipoles may be a convenient composite element for smart control of sound.Peer ReviewedPostprint (published version