Head-related Transfer Functions Magnitudes Research Articles

Effect of sound-induced vibrations of the pinna on head-related transfer functions: Experimental and numerical investigations.

Numerical simulations of head-related transfer functions (HRTFs) conventionally assume a rigid boundary condition for the pinna. The human pinna, however, is an elastic deformable body that can vibrate due to incident acoustic waves. This work investigates how sound-induced vibrations of the pinna can affect simulated HRTF magnitudes. The work will motivate the research question by measuring the sound-induced vibrational patterns of an artificial pinna with a high-speed holographic interferometric system. Then, finite element simulations are used to determine HRTFs for a tabletop model of the B&K 5128 head and torso simulator for a number of directions. Two scenarios are explored: one where the pinna is modeled as perfectly rigid, and another where the pinna is modeled as linear elastic with material properties close to that of auricular cartilage. The findings suggest that pinna vibrations have negligible effects on HRTF magnitudes up to 5 kHz. The same conclusion, albeit with less certainty, is drawn for higher frequencies. Finally, the importance of the elastic domain's material properties is emphasized and possible implications for validation studies on dummy heads 1as well as the limitations of the present work are discussed in detail.

Head-related transfer functions of rabbits within the front horizontal plane

The head-related transfer function (HRTF) describes the direction-dependent acoustic filtering by the head that occurs between a source signal in free-field space and the signal at the tympanic membrane. HRTFs contain information on sound source location via interaural differences of their magnitude or phase spectra and via the shapes of their magnitude spectra. The present study characterized HRTFs for source locations in the front horizontal plane for nine rabbits, which are a species commonly used in studies of the central auditory system. HRTF magnitude spectra shared several features across individuals, including a broad spectral peak at 2.6kHz that increased gain by 12 to 23dB depending on source azimuth; and a notch at 7.6kHz and peak at 9.8kHz visible for most azimuths. Overall, frequencies above 4kHz were amplified for sources ipsilateral to the ear and progressively attenuated for frontal and contralateral azimuths. The slope of the magnitude spectrum between 3 and 5kHz was found to be an unambiguous monaural cue for source azimuths ipsilateral to the ear. Average interaural level difference (ILD) between 5 and 16kHz varied monotonically with azimuth over ±31dB despite a relatively small head size. Interaural time differences (ITDs) at 0.5kHz and 1.5kHz also varied monotonically with azimuth over ±358 μs and ±260 μs, respectively. Remeasurement of HRTFs after pinna removal revealed that the large pinnae of rabbits were responsible for all spectral peaks and notches in magnitude spectra and were the main contribution to high-frequency ILDs (5–16kHz), whereas the rest of the head was the main contribution to ITDs and low-frequency ILDs (0.2–1.5kHz). Lastly, inter-individual differences in magnitude spectra were found to be small enough that deviations of individual HRTFs from an average HRTF were comparable in size to measurement error. Therefore, the average HRTF may be acceptable for use in neural or behavioral studies of rabbits implementing virtual acoustic space when measurement of individualized HRTFs is not possible.

An individualization approach for head-related transfer function in arbitrary directions based on deep learning.

This paper provides an individualization approach for head-related transfer function (HRTF) in arbitrary directions based on deep learning by utilizing dual-autoencoder architecture to establish the relationship between HRTF magnitude spectrum and arbitrarily given direction and anthropometric parameters. In this architecture, one variational autoencoder (VAE) is utilized to extract interpretable and exploitable features of full-space HRTF spectra, while another autoencoder (AE) is employed for feature embedding of corresponding directions and anthropometric parameters. A deep neural networks model is finally trained to establish the relationship between these representative features. Experimental results show that the proposed method outperforms state-of-the-art methods in terms of spectral distortion.

A mixed-order modeling approach for head-related transfer function in the spherical harmonic domain

Head-related transfer function (HRTF) contains all the relevant cues that humans rely on to perceive the direction of a sound source, and its modeling has been widely studied in the past years. Motivated by the different degree of fluctuations in HRTF magnitude spectrum across frequency, in this paper, a mixed-order modeling approach in the spherical harmonic domain is proposed in which HRTF magnitude spectrum with low fluctuation is modeled by the low-order spherical harmonics and that with high fluctuation is modeled by the high-order spherical harmonics. Furthermore, a data-driven optimization approach is presented to determine the transition frequency that separates HRTF magnitude spectrum into two ranges with different degrees of fluctuations. The effectiveness of the proposed mixed-order modeling approach is examined using FABIAN HRTF database through listening tests. Results show that this mixed-order modeling approach enables to reduce the order of spherical harmonics to 8 in the low frequencies and 18 in the high frequencies without perceptual degradation in sound quality and localization.

Typical data and cluster analysis on head-related transfer functions from Chinese subjects

Head-related transfer functions (HRTFs) vary with individuals. To obtain consistent results in binaural analysis, typical or representative HRTFs are needed. Moreover, matched or customized HRTFs are also needed to improve the localization performance in virtual auditory display (VAD). Based on a HRTF baseline database with 52 subjects, the present work derives the typical HRTFs of Chinese subjects and sets of matched HRTFs data for scientific researches and VAD applications. Similarities among the HRTF magnitudes of different subjects are first analyzed. Then the typical HRTFs are obtained by searching for the HRTFs of an individual that, in the sense of average, are most similar with the HRTFs of other individuals in the baseline database. Moreover, individualized cluster analysis is applied to the baseline database and the matched HRTFs are selected from the nearest cluster center. The results indicate that the magnitudes of typical HRTFs highly correlate with most of other 51 subjects in the database, exhibiting an average normalized cross-correlation coefficient of 0.888. In addition, cluster analysis indicates that HRTF magnitudes for most subjects can be classified into seven clusters and represented by the corresponding nearest cluster centers, with average normalized cross-correlation coefficient between the nearest cluster center and other subjects within the cluster exceeding 0.882. By comparing the similarity between the Chinese HRTFs and those of Western subjects, it is also proved that Chinese and Western HRTFs differ significantly on statistics, and therefore separately analyzing the similarity and cluster of Chinese HRTFs is necessary and reasonable. Psychoacoustic experiments validate that, the typical HRTFs yield reasonable virtual source localization performance and for four out of seven subjects, matched HRTFs selected from the nearest cluster center reduce the reversal and in-head-localization errors.

Auditory discrimination on the distance dependence of near-field head-related transfer function magnitudes

Distance dependence of head-related transfer functions (HRTFs) for nearby sound sources within 1 m is regarded as one of auditory distance perception cues. Accordingly, the near-field HRTFs have been used to synthesize sound sources at different distances in virtual auditory display. The present work analyzes the audibility of variation in near-field HRTF magnitudes with source distance. The calculated near-field HRTFs from KEMAR artificial head with a distance resolution of 0.01 m and a binaural model are used in analysis. The changes in loudness level spectra and interaural level difference are used as audible criteria. The result indicates that, as source distance decreases, the variation in HRTF magnitude with source distance become prominent and thereby audible. A psychoacoustic experiment is also carried out to validate the analysis. This work provides insight into the distance resolution of near-field HRTFs required in binaural virtual source synthesis.

Consistency among the head-related transfer functions from different measurements

Empirical measurement is a common approach to obtaining head-related transfer functions (HRTFs). Due to differences in experimental conditions and possible errors, some deviations exist among the data from different measurements even for the same subject. This work aims to evaluate deviations of HRTFs from different measurements. Five sets of KEMAR HRTFs from three groups including MIT-media Lab, CIPIC Interface Lab, and our lab are used. A free-field equalization is applied to the original data so as to eliminate the influence caused by the difference in the response of electro-acoustic measuring chain. The deviations among HRTF magnitudes for different measurements are specified by spectral distortion. Results indicate that the magnitude deviation increases with increasing frequency and reaches more than 10 dB above the frequency of 6 kHz. Salient deviations often occur in contralateral source directions or in ipsilateral source directions near the frequency of pinna-related notch. Nevertheless, most deviations can be effectively reduced after an auditory filter smoothing. This work suggests that the inconsistency in measured HRTF data and its impact on auditory perception should be taken into account when comparing and standardizing HRTFs from different measurements. [Work supported by National Nature Science Fund of China Grant No. 11004064]

Conventional and spatial principal component analysis on near-field head-related transfer functions

Head-related transfer functions (HRTFs) vary with both frequency and source position. The near-field HRTFs with source distance less than 1.0 m are particularly complicated due to their distance dependence. Principal component analysis (PCA), which is conventionally carried out in the frequency or time domain, has been widely applied to reduce the dimensionality of far-field HRTF data with source distance greater than 1.0 m. The present work first extends the conventional PCA, and then proposes a spatial PCA method in the spatial domain rather than in the frequency or time domain to reduce the dimensionality of near-field HRTF data. An illustrative case indicates that near-field HRTF magnitudes at 9 distances with 493 directions for each distance can be approximately represented by the weighted sum of 15 spectral shape basis functions using the conventional PCA or the weighted sum of 15 spatial basis functions using the spatial PCA. Both representations account for more than 98% energy variation of the original data, and reduce the dimensionality of the original data to about a quarter. The proposed method is also applicable to the head-related impulse responses in the time domain. Furthermore, the spatial PCA scheme is potentially applicable to simplify near-field HRTF measurement.

Recovery of individual head-related transfer functions from a small set of measurements

Head-related transfer functions (HRTFs) vary with individuals, and in practice, measuring HRTFs with high directional resolution for each individual is tiresome. Based on a basis functions representation of HRTFs, the present work proposes a method for recovering individual HRTFs from a small set of measurements. The HRTFs are represented by a combination of a small set of spatial basis functions (SBFs) with frequency- and individual-dependent weights. The SBFs are derived by applying spatial principal component analysis to a baseline HRTF dataset with high directional resolution. The individual weights for any subject outside the dataset are estimated from measurements at a few source directions, and then the HRTFs with high directional resolution are recovered by combining the SBFs and the individual weights. In an illustrative case, the SBFs derived from a baseline dataset that includes 20 subjects are used to recover the HRTF magnitudes for six subjects outside the baseline dataset. Results show that individual HRTF magnitudes can be recovered from measurements at 73 directions with a mean signal-to-distortion ratio of 19 dB. The proposed method is also applicable to recovering head-related impulse responses. The results of psychoacoustic experiments indicate that in most cases the recovered and measured HRTFs are indistinguishable.

Analysis on the audibility in directional differences of head-related transfer function magnitudes

A head-related transfer function (HRTF) varies as a function of sound source directions. In a dynamic virtual auditory display (VAD) based on HRTF filtering, dynamic binaural synthesis requires HRTFs to be updated constantly to accommodate the transient virtual source direction relative to listener. A HRTFs set with appropriate directional resolution can generate smooth transition when switching between HRTFs, and at the same time, simplifies dynamic binaural synthesis. Based on the measured HRTFs from KEMAR mannequin and human subjects with supper high directional resolution, the directional difference in HRTF magnitude spctra, binaural loudness level spectra and interaural localization cues are analyzed in present work. Combined with the statistical results of psychoacoustic experiments, psychometric functions for directional discrimination of HRTF magnitudes are derived. Finally, in terms of resultant audibility in directional differences of HRTF magnitudes, the directional resolutions of HRTFs for dynamically synthesizing virtual source at various directions are suggested.

Similarity and cluster analysis on magnitudes of individual head-related transfer functions

Although head-related transfer functions (HRTFs) vary with individuals, non-individualized HRTFs are typically employed in virtual auditory display (VAD) due to the difficulty in measuring individual HRTFs. Similarity among the HRTFs of different individuals allows for customizing a matched set of HRTFs for a user from an existing database and thereby improving performance of VADs. The first step of HRTF customization is evaluation of the similarities among individual HRTFs. In the present work, based on a HRTF database of 52 Chinese subjects, the similarities are evaluated by calculating the directional-mean of normalized cross-correlation coefficient (MCC) of HRTF magnitudes between each pair of subjects and then applying cluster analysis to the resultant MCC. The results indicate that MCC depends on subject pair with values ranging from 0.934 to 0.562 (mean 0.842) and from 0.948 to 0.635 (mean 0.863) for the left and right ear, respectively. HRTF magnitudes for most subjects can be classified into six to eight clusters and represented by the corresponding cluster centers. Some singleton clusters are also observed on a few subjects, which reflect the diversity in HRTFs and should be careful in practice. Psychoacoustic experiment also validates above analyses.

Calculation and Analysis of Near-Field Head-Related Transfer Functions from a Simplified Head-Neck-Torso Model

To evaluate the overall effect of the neck and torso on the head-related transfer function (HRTF), a simplified head-neck-torso (HNT) model, which consists of a spherical head, spherical torso and cylindrical neck, is proposed and the corresponding HRTFs are calculated using the boundary element method (BEM). The results indicate that the HRTF magnitudes for the HNT model are different from those of the existing spherical head-and-torso model (HAT) above 0.5 kHz, especially in the near-field and contralateral region. The discrepancy in the HRTF magnitudes leads to a discrepancy in the interaural level differences (ILDs) for the HNT and HAT models, which reaches a level of ±10 dB at source distance of 0.2 m. As the source distance increases, the discrepancy in the results of the HNT and HAT models reduces. Measurement on practical HNT and HAT models validates the analysis. Therefore, the neck influences near-field HRTFs and should be included in the near-field HRTF calculation.

Spatial principal components analysis on head-related transfer functions and individualized customization from fewer measurements.

Head-related transfer function (HRTF) is an individual-dependent and continuous function of sound source position and frequency. Measurement is a common way to obtain individual HRTFs. It is difficult or even impractical to measure HRTFs with high directional resolution for individual, however. To solve the problem, spatial principal components analysis (SPCA) of HRTFs and resulting customization of individual HRTF from fewer measurements were proposed in present paper. In SPCA, HRTF is decomposed as a weighted combination of common spatial basis functions (CSBFs) which are only direction-dependent, while the weights are frequency- and individual-independent. The CSBFs were derived from the measured HRTFs of 20 subjects with high directional resolution. Based on the calculated CSBFs, for any new subject, the weight coefficients can be estimated from fewer measured HRTFs data, and subsequently the individual HRTFs with high directional resolution can be customized. SPCA were applied to HRTF magnitudes and head-related impulse responses, respectively, and the individual data were customized for six subjects. Psychoacoustic experiments were also conducted to evaluate the customization performance. Theoretical and experimental results validate the performance of proposed method. [Work supported by of National Nature Science Fund of China Grant No. 10774049.]