Infinite-impulse-response models of the head-related transfer function

Head-related transfer functions (HRTFs) measured from human subjects were approximated using infinite-impulse-response (IIR) filter models. Models were restricted to rational transfer functions (plus simple delays) so that specific models are characterized by the locations of poles and zeros in the complex plane. The all-pole case (with no nontrivial zeros) is treated first using the theory of linear prediction. Then the general pole-zero model is derived using a weighted-least-squares (WLS) formulation of the modified least-squares problem proposed by Kalman (1958). Both estimation algorithms are based on solutions of sets of linear equations and result in efficient computational schemes to find low-order model HRTFs. The validity of each of these two low-order models was assessed in psychophysical experiments. Specifically, a four-interval, two-alternative, forced-choice paradigm was used to test the discriminability of virtual stimuli constructed from empirical and model HRTFs for corresponding locations. For these experiments, the stimuli were 80 ms, noise tokens generated from a wideband noise generator. Results show that sounds synthesized through model HRTFs were indistinguishable from sounds synthesized from original HRTF measurements for the majority of positions tested. The advantages of the techniques described here are the computational efficiencies achieved for low-order IIR models. Properties of the all-pole and pole-zero estimators are discussed in the context of low-order HRTF representations, and implications for basic and applied contexts are considered.     

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.     

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.     

近场头相关传输函数的测量与分析

设计了测量距离可调整的头相关传输函数的实验测量方法，并采用人工头进行近场头相关传输函数的测量，建立了高空间分辨率的近场头相关传输函数数据库，为进一步开展双耳听觉的研究和虚拟听觉的应用提供了数据基础。根据实验数据，初步分析了远、近场情况下，距离、仰角、方位角等参量对头相关传输函数的影响规律。     

On the detection of dispersion in the head-related transfer function

Because of dispersion in head-related transfer functions (HRTFs), the interaural time difference (ITD) varies with frequency. This physical effect ought to have consequences for the size or shape of the auditory image of broadband noise because different frequency regions of the noise have different ITDs. However, virtual reality experiments suggest that human listeners are insensitive to head-related dispersion. The experiments of this article test that suggestion by experiments that isolate dispersion from amplitude effects in the HRTF and attempt to optimize the opportunity for detecting it. Nevertheless, the experiments find that the only effect of dispersion is to shift the lateralization of the auditory image. This negative result is explained in terms of the cross-correlation function for head-dispersed noise. Although the broad-band cross-correlation function differs considerably from 1.0, the cross-correlation functions within bands characteristic of auditory filters do not. A detailed study of the lateralization shifts show that the experimental shifts can be successfully calculated as an average of stimulus ITDs as weighted by Raatgever's frequency-weighting function (Thesis, Delft, The Netherlands, 1980).     

Finite difference computation of head-related transfer function for human hearing

Modeling the head-related transfer function (HRTF) is a key to many applications in spatial audio. To understand and predict the effects of head geometry and the surrounding environment on the HRTF, a three-dimensional finite-difference time domain model (3D FDTD) has been developed to simulate acoustic wave interaction with a human head. A perfectly matched layer (PML) is used to absorb outgoing waves at the truncated boundary of an unbounded medium. An external source is utilized to reduce the computational domain size through the scattered-field/total-field formulation. This numerical model has been validated by analytical solutions for a spherical head model. The 3D FDTD code is then used as a computational tool to predict the HRTF for various scenarios. In particular, a simplified spherical head model is compared to a realistic head model up to about 7 kHz. The HRTF is also computed for a realistic head model in the presence of a wall. It is demonstrated that this 3D FDTD model can be a useful tool for spatial audio applications.     

Rapid head-related transfer function adaptation using a virtual auditory environment

The paper reports on the ability of people to rapidly adapt in localizing virtual sound sources in both azimuth and elevation when listening to sounds synthesized using non-individualized head-related transfer functions (HRTFs). Participants were placed within an audio-kinesthetic Virtual Auditory Environment (VAE) platform that allows association of the physical position of a virtual sound source with an alternate set of acoustic spectral cues through the use of a tracked physical ball manipulated by the subject. This set-up offers a natural perception-action coupling, which is not limited to the visual field of view. The experiment consisted of three sessions: an initial localization test to evaluate participants' performance, an adaptation session, and a subsequent localization test. A reference control group was included using individual measured HRTFs. Results show significant improvement in localization performance. Relative to the control group, participants using non-individual HRTFs reduced localization errors in elevation by 10° with three sessions of 12 min. No significant improvement was found for azimuthal errors or for single session adaptation.     

Analysis of the spatial discrimination threshold of head-related transfer function magnitude

A binaural-loudness-model-based method for evaluating the spatial discrimination threshold of magnitudes of head-related transfer function(HRTF) is proposed.As the input of the binaural loudness model,the HRTF magnitude variations caused by spatial position variations were firstly calculated from a high-resolution HRTF dataset.Then,three perceptualrelevant parameters,namely interaural loudness level difference,binaural loudness level spectra,and total binaural loudness level,were derived from the binaural loudness model.Finally,the spatial discrimination thresholds of HRTF magnitude were evaluated according to just-noticedifference of the above-mentioned perceptual-relevant parameters.A series of psychoacoustic experiments was also conducted to obtain the spatial discrimination threshold of HRTF magnitudes.Results indicate that the threshold derived from the proposed binaural-loudness-modelbased method is consistent with that obtained from the traditional psychoacoustic experiment,validating the effectiveness of the proposed method.     

Elevation localization and head-related transfer function analysis at low frequencies

Monaural spectral features due to pinna diffraction are the primary cues for elevation. Because these features appear above 3 kHz where the wavelength becomes comparable to pinna size, it is generally believed that accurate elevation estimation requires wideband sources. However, psychoacoustic tests show that subjects can estimate elevation for low-frequency sources. In the experiments reported, random noise bursts low-pass filtered to 3 kHz were processed with individualized head-related transfer functions (HRTFs), and six subjects were asked to report the elevation angle around four cones of confusion. The accuracy in estimating elevation was degraded when compared to a baseline test with wideband stimuli. The reduction in performance was a function of azimuth and was highest in the median plane. However, when the source was located away from the median plane, subjects were able to estimate elevation, often with surprisingly good accuracy. Analysis of the HRTFs reveals the existence of elevation-dependent features at low frequencies. The physical origin of the low-frequency features is attributed primarily to head diffraction and torso reflections. It is shown that simple geometrical approximations and models of the head and torso explain these low-frequency features and the corresponding elevations cues.     

头相关传输函数幅度谱的听觉空间分辨阈值的分析

提出一种分析头相关传输函数(head-related transfer function,HRTF)幅度谱的听觉空间分辨阈值模型。采用数值计算得到的高空间分辨率HRTF数据,计算了声源空间位置变化引起的HRTF幅度谱的变化,进一步利用Moore响度模型分析双耳响度级差、双耳响度级谱和总响度级等三个听觉感知量的变化。根据现有的3个听觉感知量最小可察觉差异,模型利用双耳响度级差和双耳响度级谱的变化得到的估计结果与心理声学实验一致,因此是一种有效预测听觉空间分辨阈值的方法,可用于为简化虚拟听觉信号处理和数据储存。     

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.     

A localization algorithm based on head-related transfer functions

Two sound localization algorithms based on the head-related transfer function were developed. Each of them uses the interaural time delay, interaural level difference, and monaural spectral cues to estimate the location of a sound source. Given that most localization algorithms will be required to function in background noise, the localization performance of one of the algorithms was tested at signal-to-noise ratios (SNRs) from 40 to -40 dB. Stimuli included ten real-world, broadband sounds located at 5 degrees intervals in azimuth and at 0 degrees elevation. Both two- and four-microphone versions of the algorithm were implemented to localize sounds to 5 degrees precision. The two-microphone version of the algorithm exhibited less than 2 degrees mean localization error at SNRs of 20 dB and greater, and the four-microphone version committed approximately 1 degrees mean error at SNRs of 10 dB or greater. Potential enhancements and applications of the algorithm are discussed.     

The bat head-related transfer function reveals binaural cues for sound localization in azimuth and elevation

Directional properties of the sound transformation at the ear of four intact echolocating bats, Eptesicus fuscus, were investigated via measurements of the head-related transfer function (HRTF). Contributions of external ear structures to directional features of the transfer functions were examined by remeasuring the HRTF in the absence of the pinna and tragus. The investigation mainly focused on the interactions between the spatial and the spectral features in the bat HRTF. The pinna provides gain and shapes these features over a large frequency band (20-90 kHz), and the tragus contributes gain and directionality at the high frequencies (60 to 90 kHz). Analysis of the spatial and spectral characteristics of the bat HRTF reveals that both interaural level differences (ILD) and monaural spectral features are subject to changes in sound source azimuth and elevation. Consequently, localization cues for horizontal and vertical components of the sound source location interact. Availability of multiple cues about sound source azimuth and elevation should enhance information to support reliable sound localization. These findings stress the importance of the acoustic information received at the two ears for sound localization of sonar target position in both azimuth and elevation.     

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.     

A hybrid compression method for head-related transfer functions

The paper proposes a hybrid compression method to resolve the storage problem of a large number of head-related transfer functions (HRTFs). First, each HRTF is approximated by a minimum-phase HRTF and an all pass filter whose group delay equals the interaural time delay (ITD). Second, principal component analysis is applied to the entire HRTF set to derive several basis functions, with a weight vector set defining the contribution of the basis functions to each HRTF. Third, the weight set is vector quantized with the designed codebook. At last, the ITD is curved surface fitted with a cosine series bivariate polynomial. As a result, the HRTF can be reconstructed from the basis functions, codebook indexes, and ITD polynomial coefficients. Simulation results reveal that the proposed method may reduce the data size greatly with similar reconstruction precision comparing with the principal component analysis method.     

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.     

近场头相关传递函数的数值计算与特性分析

建立了近场头相关传递函数(HRTF)的边界元算法,针对刚性圆球人头简化模型,利用解析计算结果对其进行了验证,然后依据GB/T2428-1998建立了一个椭球人头模型,利用边界元算法计算了中低频多个空间方位的近场HRTF,并对其随方位和距离的变化特性进行了分析。     

Observations on a principal components analysis of head-related transfer functions.

A recent principal components analysis (Kistler and Wightman, 1992) has shown that the transfer functions of the human external ear, for a wide range of source locations, can be expressed as weighted sums of a small number of basis vectors. Directional transfer functions obtained in this laboratory, using substantially different measurement techniques, yielded principal component basis vectors that are remarkably similar to those reported by Kistler and Wightman. When this subject population was divided in half according to the overall physical sizes of subjects, basis vectors computed for the subpopulation of smaller subjects were shifted systematically to higher frequencies relative to those computed for the subpopulation of larger subjects.     

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.