A model of head-related transfer functions based on principal components analysis and minimum-phase reconstruction.

Free-field to eardrum transfer functions (HRTFs) were measured from both ears of 10 subjects with sound sources at 265 different positions. A principal components analysis of the resulting 5300 HRTF magnitude functions revealed that the HRTFs can be modeled as a linear combination of five basic spectral shapes (basis functions), and that this representation accounts for approximately 90% of the variance in the original HRTF magnitude functions. HRTF phase was modeled by assuming that HRTFs are minimum-phase functions and that interaural phase differences can be approximated by a simple time delay. Subjects' judgments of the apparent directions of headphone-presented sounds that had been synthesized from the modeled HRTFs were nearly identical to their judgments of sounds synthesized from measured HRTFs. With fewer than five basis functions used in the model, a less faithful reconstruction of the HRTF was produced, and the frequency of large localization errors increased dramatically.     

Sensitivity of human subjects to head-related transfer-function phase spectra.

Head-related transfer functions (HRTFs) for human subjects in anechoic space were modeled with modified phase spectra, including minimum-phase-plus-delay, linear-phase, and reversed-phase-plus-delay functions. The overall (wide-band) interaural time delay (ITD) for the modeled HRTFs was made consistent with that of the empirical HRTFs by setting the position-dependent, frequency-independent delay in the HRTF for the lagging ear. Signal analysis of the minimum-phase-plus-delay reconstructions indicated that model HRTFs deviate from empirical HRTF measurements maximally for contralateral azimuths and low elevations. Subjects assessed the perceptual validity of the model HRTFs in a four-interval, two-alternative, forced-choice discrimination paradigm. Results indicate that monaural discrimination performance of subjects was at chance for all three types of HRTF models. Binaural discrimination performance was at chance for the linear-phase HRTFs, was above chance for some locations for the minimum-phase-plus-delay HRTFs, and was above chance for all tested locations for the reversed-phase-plus-delay HRTFs. An analysis of low-frequency timing information showed that all of these results are consistent with efficient use of interaural time differences in the low-frequency components of the stimulus waveforms. It is concluded that listeners are insensitive to HRTF phase spectra as long as the overall ITD of the low-frequency components does not provide a reliable cue. In particular, the minimum-phase-plus-delay approximation to the HRTF phase spectrum is an adequate approximation as long as the low-frequency ITD is appropriate. These results and conclusions are all limited to the anechoic case when the HRTFs correspond to brief impulse responses limited to a few milliseconds.     

Spatial symmetry of head-related transfer function

Methods for analyzing the spatial symmetry of head-related transfer function (HRTF) are proposed. The influences of anatomical structures on the symmetry of HRTF are investigated using HRTFs measured on KEMAR mannequin and human subjects. Results show that for KEMAR mannequin, pinnae destroy the front-back symmetry of HRTF above 5 to 6 kHz, while for human subjects the frequency reduces to 2.5 kHz because of the locations of ears. Furthermore, at low and median frequencies, HRTF is approximately left-right symmetrical. While as frequencies increase, the asymmetry caused by the fine anatomical leftright differences appears. The starting frequency and the extent of the left-right asymmetry in HRTF depend on individuals. The analyses demonstrate the spatial symmetrical characteristics of HRTF and the frequency ranges in which the current binaural models are valid.     

Fidelity of three-dimensional-sound reproduction using a virtual auditory display

The fidelity of reproducing free-field sounds using a virtual auditory display was investigated in two experiments. In the first experiment, listeners directly compared stimuli from an actual loudspeaker in the free field with those from small headphones placed in front of the ears. Headphone stimuli were filtered using head-related transfer functions (HRTFs), recorded while listeners were wearing the headphones, in order to reproduce the pressure signatures of the free-field sounds at the eardrum. Discriminability was investigated for six sound-source positions using broadband noise as a stimulus. The results show that the acoustic percepts of real and virtual sounds were identical. In the second experiment, discrimination between virtual sounds generated with measured and interpolated HRTFs was investigated. Interpolation was performed using HRTFs measured for loudspeaker positions with different spatial resolutions. Broadband noise bursts with flat and scrambled spectra were used as stimuli. The results indicate that, for a spatial resolution of about 6 degrees, the interpolation does not introduce audible cues. For resolutions of 20 degrees or more, the interpolation introduces audible cues related to timbre and position. For intermediate resolutions (10 degrees - 15 degrees) the data suggest that only timbre cues were used.     

A hybrid algorithm for selecting head-related transfer function based on similarity of anthropometric structures

As the basic data for virtual auditory technology, head-related transfer function (HRTF) has many applications in the areas of room acoustic modeling, spatial hearing and multimedia. How to individualize HRTF fast and effectively has become an opening problem at present. Based on the similarity and relativity of anthropometric structures, a hybrid HRTF customization algorithm, which has combined the method of principal component analysis (PCA), multiple linear regression (MLR) and database matching (DM), has been presented in this paper. The HRTFs selected by both the best match and the worst match have been applied into obtaining binaurally auralized sounds, which are then used for subjective listening experiments and the results are compared. For the area in the horizontal plane, the localization results have shown that the selection of HRTFs can enhance the localization accuracy and can also abate the problem of front-back confusion.     

Fast head-related transfer function measurement via reciprocity

An efficient method for head-related transfer function (HRTF) measurement is presented. By applying the acoustical principle of reciprocity, one can swap the speaker and the microphone positions in the traditional (direct) HRTF measurement setup, that is, insert a microspeaker into the subject's ear and position several microphones around the subject, enabling simultaneous HRTF acquisition at all microphone positions. The setup used for reciprocal HRTF measurement is described, and the obtained HRTFs are compared with the analytical solution for a sound-hard sphere and with KEMAR manikin HRTF obtained by the direct method. The reciprocally measured sphere HRTF agrees well with the analytical solution. The reciprocally measured and the directly measured KEMAR HRTFs are not exactly identical but agree well in spectrum shape and feature positions. To evaluate if the observed differences are significant, an auditory localization model based on work by J. C. Middlebrooks [J. Acoust. Soc. Am. 92, 2607-2624 (1992)] was used to predict where a virtual sound source synthesized with the reciprocally measured HRTF would be localized if the directly measured HRTF were used for the localization. It was found that the predicted localization direction generally lies close to the measurement direction, indicating that the HRTFs obtained via the two methods are in good agreement.     

Influence of measurement methodology of head-related transfer functions on auditory perception

Head-related transfer functions(HRTFs) are the core of virtual auditory display and relevant applications. However,a standard method for HRTF measurements has not been established. This work examines the influence of different HRTF measurement methodologies on auditory perception. First, the diffusion-field equalization was proposed and applied to HRTFs of a single dummy head(KEMAR) from five different datasets. Then,the spectral deviations among the HRTFs were calculated and analyzed. Finally, a series of subjective listening experiments(including localization and discrimination experiments) were conducted. Results indicate the diffusion-field equalization is an effective pre-processing method which reduces the difference in HRTF magnitude spectra caused by different measurement methodologies. Moreover,the HRTFs from different measurement methodologies have similar localization performance below 12 kHz, whereas the inter-dataset differences in timbre are distinct leading to audible discrimination.     

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.     

头相关传输函数的低频特性

提出了一种对测量得到头相关传输函数(HRTF)的低频特性进行修正的方法。通过头部的刚球模型对HRTF的低频特性进行分析,证明了无论对远场或近场HRTF,大约在400 Hz以下,其幅度趋于恒定,而相位接近线性。因而只要通过实验测量得到400 Hz以上的HRTF特性,即可采用理论的结果对其进行修正。理论计算和主观实验证明,所提出的方法是切实可行的。     

On the low frequency characteristics of head-related transfer function

A method to correct the measured head-related transfer functions （HRTFs） at low frequency was proposed. By analyzing the HRTFs from the spherical head model at low frequency, it is proved that below the frequency of 400 Hz, magnitude of HRTF is nearly constant and the phase is a linear function of frequency both for the far and near field. Therefore, if the HRTFs above 400 Hz are accurately measured by experiment, it is able to correct the HRTFs at low frequency by the theoretical model. The results of calculation and subjective experiment show that the feasibility of the proposed method.     

A priori mesh grading for the numerical calculation of the head-related transfer functions

Head-related transfer functions (HRTFs) describe the directional filtering of the incoming sound caused by the morphology of a listener’s head and pinnae. When an accurate model of a listener’s morphology exists, HRTFs can be calculated numerically with the boundary element method (BEM). However, the general recommendation to model the head and pinnae with at least six elements per wavelength renders the BEM as a time-consuming procedure when calculating HRTFs for the full audible frequency range. In this study, a mesh preprocessing algorithm is proposed, viz., a priori mesh grading, which reduces the computational costs in the HRTF calculation process significantly. The mesh grading algorithm deliberately violates the recommendation of at least six elements per wavelength in certain regions of the head and pinnae and varies the size of elements gradually according to an a priori defined grading function. The evaluation of the algorithm involved HRTFs calculated for various geometric objects including meshes of three human listeners and various grading functions. The numerical accuracy and the predicted sound-localization performance of calculated HRTFs were analyzed. A-priori mesh grading appeared to be suitable for the numerical calculation of HRTFs in the full audible frequency range and outperformed uniform meshes in terms of numerical errors, perception based predictions of sound-localization performance, and computational costs.     

头相关传输函数空间对称性的分析

提出了分析头相关传输函数空间对称性的方法。利用对KEMAR人工头/躯干系统和真人受试者进行测量得到的头相关传输函数,分析了生理结构对头相关传输函数空间对称性的影响。结果表明,在5 kHz至6 kHz以上的频率,耳廓破坏了头相关传输函数的前后对称性;而受耳道入口位置的影响,真人受试者的头相关传输函数在2.5 kHz以上的频率就开始出现前后不对称。另一方面,在中、低频的情况下,头相关传输函数近似左右对称,然而随着频率的升高,生理外形在细微结构上的左右差异将导致头相关传输函数的左右不对称。这种左右不对称的起始频率和程度存在个体差异。上述分析可以反映出头相关传输函数空间对称性的规律和现有双耳听觉模型的适用范围。     

HRTF personalization based on artificial neural network in individual virtual auditory space

The synthesis of individual virtual auditory space (VAS) is an important and challenging task in virtual reality. One of the key factors for individual VAS is to obtain a set of individual head related transfer functions (HRTFs). A customization method based on back-propagation (BP) artificial neural network (ANN) is proposed to obtain an individual HRTF without complex measurement. The inputs of the neural network are the anthropometric parameters chosen by correlation analysis and the outputs are the characteristic parameters of HRTFs together with the interaural time difference (ITD). Objective simulation experiments and subjective sound localization experiments are implemented to evaluate the performance of the proposed method. Experiments show that the estimated non-individual HRTF has small mean square error, and has similar perception effect to the corresponding one obtained from the database. Furthermore, the localization accuracy of personalized HRTF is increased compared to the non-individual HRTF.     

不同测量对头相关传输函数的听觉影响

头相关传输函数(HRTF)是虚拟听觉重放的核心·目前,HRTF的实验室测量缺乏统一的规范。本文研究了不同测量对HRTF的听觉影响。首先提出了扩散场均衡的预处理方法,并对来自5个不同数据库的KEMAR假人的HRTF数据进行了扩散场均衡;然后,采用谱差异评估了不同数据库HRTF测量的频谱差异;最后,采用HRTF合成的虚拟声信号开展了一系列的主观听音实验,包括定位实验和区分实验·结果表明,扩散场均衡是一种有效的HRTF预处理方法,可以减小不同测量对HRTF频谱的影响;不同测量基本上不影响HRTF在12 kHz以下的定位效果,但对音色的影响较大,从而导致听觉上的可区分.     

基于个体张量分解与模态的头相关传输函数重构

远场头相关传输函数(HRTF)随声源方向、频率以及个体变化。完整HRTF的数据量很大,且测量或计算每个人的高方向分辨率HRTF是很困难的。本文提出一种从少量方向的测量或计算重构高方向分辨率HRTF的方法。基于HRTF张量分解,远场HRTF可分解为方向模态、频率模态和少量个体模态的张量组合。通过对已有的基线HRTF数据库进行统计分析,可得到与个体无关的方向模态矩阵和频率模态矩阵。而对于任何新的个体,只要少量方向的测量或计算HRTF即可估计出个体模态的变化,并重构出高方向分辨率的HRTF数据。对两个HRTF数据库的计算表明,采用11个个体模态即可表示超过98%的个体相关的HRTF能量变化,并从大约30个方向的测量或计算HRTF重构出高方向分辨率的HRTF幅度。心理声学实验验证了提出的方法。该方法可用于简化个性化HRTF的测量或计算。     

Median plane localization using a parametric model of the head-related transfer function based on spectral cues

To examine a simulation method for vertical sound localization, and to clarify which peaks and notches in head-related transfer functions (HRTFs) play a role as spectral cues, localization tests in the median plane were carried out using a parametric HRTF model, which is recomposed only of extracted spectral peaks and notches. The results show that the parametric HRTF recomposed using the first and second notches (N1 and N2) and the first peak (P1) provides almost the same localization accuracy as the measured HRTFs. Observations of the spectral peaks and notches indicate that N1 and N2 change remarkably as the source elevation changes, whereas P1 does not depend on the source elevation. In conclusion, N1 and N2 can be regarded as spectral cues, and the hearing system could utilize P1 as the reference information to analyze N1 and N2.     

Effect of Sound Source Scattering on Measurement of Near-Field Head-Related Transfer Functions

A simple spherical head and pulsating spherical sound source model are proposed to investigate the effect of multiple scattering between the head and the sound source on near-field head-related transfer function (HRTF) measurement. Multipole expansion method is used to calculate HRTFs of the model, then the relationships among the magnitude error of HRTF with frequency, source direction, source size, and the distance between the head centre and the sound source are analysed. The results show that to ensure the magnitude error of HRTF within 1.0dB up to 20kHz, for source distance not less than 0.15m or 0.20m, the radius of the sound source should not exceed 0.03m or 0.05m, respectively. The conclusion suggests an appropriate size of sound source in near-field HRTF measurement.     

Perceptually based head-related transfer function database optimization

In the context of binaural audio rendering, choosing the best head-related transfer function (HRTF) for an individual from large databases poses several problems. This study proposes a method to reduce the size of a given HRTF database. Participants, 45 in total, were asked to rate the quality of binaural synthesis for 46 HRTFs. The lack of reciprocity in the ratings was noted. Results were used to create a perceptually optimized HRTF subset which satisfied all participants' judgments. The subset was validated using localization tests on a separate group of subjects with results showing reduced errors when subjects were given their best choice, rather than their worst choice HRTF.     

The role of spectral modulation cues in virtual sound localization

Sound localization cues generally include interaural time difference, interaural intensity difference, and spectral cues. The purpose of this study is to investigate the important spectral cues involved in so-called head related transfer functions (HRTFs) using a combination of HRTF analyses and a virtual sound localization (VSL) experiment. Previous psychoacoustical and physiological studies have both suggested the existence of spectral modulation frequency (SMF) channels for analyzing spectral information (e.g., the spectral cues coded in HRTFs). SMFs are in a domain related to the Fourier transform of HRTFs. The relationship between various SMF regions and sound localization was tested here by filtering or enhancing HRTFs in the SMF domain under a series of conditions using a VSL experiment. Present results revealed that azimuth localization was not significantly affected by HRTF manipulation. Applying notch filters between 0.1 and 0.4 cyclesoctave or between 0.35 and 0.65 cyclesoctave resulted in significantly less accurate elevation responses at low elevations, while spectral enhancement in these two SMF regions did not produce a significant change in sound localization. Likewise, low-pass filtering at 2 cyclesoctave did not significantly influence localization accuracy, suggesting that the major cues for sound localization are in the SMF region below 2 cyclesoctave.     

Estimating head-related transfer functions of human subjects from pressure-velocity measurements

Direct measurements of individual head-related transfer functions (HRTFs) with a probe microphone at the eardrum are unpleasant, risky, and unreliable and therefore have not been widely used. Instead, the HRTFs are commonly measured from the blocked ear canal entrance, which excludes the effects of the individual ear canals and eardrums. This paper presents a method that allows obtaining individually correct magnitude frequency responses of HRTFs at the eardrum from pressure-velocity (PU) measurements at the ear canal entrance with a miniature PU sensor. The HRTFs of 25 test subjects with nine directions of sound incidence were estimated using real anechoic measurements and an energy-based estimation method. To validate the approach, measurements were also conducted with probe microphones near the eardrums as well as at blocked ear canal entrances. Comparisons between the different methods show that the method presented is a valid and reliable technique for obtaining magnitude frequency responses of HRTFs. The HRTF filters designed using the PU measurements are also shown to yield more correct frequency responses at the eardrum than the filters designed using measurements from the blocked ear canal entrance.