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.     

Interpretations on principal components analysis of head-related impulse responses in the median plane

A principal components analysis of the median-plane head-related impulse responses (HRIRs) in the CIPIC HRTF database reveals that the individual HRIRs can be reconstructed by a linear combination of 12 principal components (PCs) within 5% of error in the least-squares sense. The PCs include the intersubject and interelevation variations in the median-plane HRIRs. Each PC provides sound cues for the front-back discrimination and/or the vertical perception. There exist common systematic elevation dependencies in the weights of lower-numbered PCs which contribute to the pinna/head diffractions, whereas the elevation dependencies in the weights of higher-numbered PCs are different from subject to subject.     

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。     

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.     

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.     

人工头近场头相关传输函数及其特性

采用球形正十二面体声源及其空间定位系统,测量并建立了KEMAR人工头的近场头相关传输函数(HRTF)数据库。基于数据库分析了近场HRTF在频域和时域随声源距离变化的规律;讨论了用近场HRTF算得的双耳声级差(TLD)和双耳时间差(ITD)所包含的声源距离定位信息。结果表明,测量系统和所得数据具有较好的重复性和准确性,保留了1 kHz以下的低频定位信息。并且,近场HRTF幅度谱和ILD随声源距离的变化明显;用相关法算得2 kHz以下频段的ITD随声源距离略有变化。本文数据库及其分析结果将为声源距离定位的应用提供基础。     

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.     

Design and validation on a multiple sound source fast-measurement system of near-field head-related transfer functions

Near-field head-related transfer functions(HRTFs) are essential to scientific researches of binaural hearing and practical applications of virtual auditory display. High efficiency, accuracy and repeatability are required in a near-field HRTF measurement. Hence,there is no reference which intents on solving the measuring difficulties of near-field HRTF for human subjects. In present work, an efficient near-field HRTF measurement system based on computer control is designed and implemented, and a fast calibration method for the system is proposed to first solve the measurement of near-field HRTF for human subjects. The efficiency of measurement is enhanced by a comprehensive design on the acoustic, electronic and mechanical parts of the system. And the accuracy and repeatability of the measurement are greatly improved by carefully calibrating the positions of sound source, subject and binaural microphones.This system is suitable for near-field HRTF measurement at various source distances within 1.0 m, for both human subject and artificial head. The time costs of HRTF measurement at a single sound source distance and full directions has been reduced to less than 20 minutes. The measurement results indicate that the accuracy of the system satisfies the actual requirements.The system is applicable to scientific research and can be used to establish an individualized near-field HRTF database for human subjects.     

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.     

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.     

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。     

近场头相关传输函数的多声源快速测量系统设计与验证

近场头相关传输函数(HRTF)是双耳听觉科学研究和虚拟听觉重放应用的重要基础数据。近场HRTF测量系统要求具有高的测量效率、精度和重复性,以至于目前未见文献解决真人受试者的近场HRTF测量困难。本文研究并实现了一种计算机控制的近场HRTF的高效测量系统,并提出系统的快速校准方法,首先实现了真人受试者的近场HRTF测量。通过声学、机械与电子硬件和软件的综合设计,提高了测量效率。通过准确校准声源、受试者和双耳传声器的位置,提高了测量精确度和重复性。系统可用于1.0 m范围内不同声源距离的真人受试者以及人工头的近场HRTF测量,单个声源距离的全空间近场HRTF测量时间减少至20 min以内。测量结果表明,系统测量精度满足实际需求,可用于科学研究和个性化近场HRTF测量及数据库建立。     

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.     

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.     

The role of spectral components of the head-related transfer functions in evaluation of the virtual sound source motion in the vertical plane

Perception of virtual sound sources moving in the range of elevation from −45° to 45° (at zero azimuth) was studied with participation of listeners aged 57–73. The virtual sound source trajectory was created using nonindividualized head-related transfer functions and artificially synthesized spectral components specific to these functions. The percentage of correct responses in determining the direction of virtual motion depended on the way of imitation by increasing from low to high for the following succession of imitation methods: (i) displacement of the spectral minimum of broadband noise pulses within a frequency band of 5–12 kHz (the minimum retained a constant width of 1 kHz), (ii) variation of the spectral minimum width of noise pulses within 6–12 kHz, (iii) variation of the spectral maximum width within 4–8 kHz, (iv) simultaneous variation of the spectral minimum and maximum widths, (v) displacement of the spectral minimum and simultaneous variation of the spectral maximum width, and (vi) displacement of the spectral minimum and simultaneous variation of the spectral maximum width and power. For the latter stimulus, the mean percentage of correct responses (90 ± 5)% did not differ from the corresponding percentage (94 ± 3)% observed for the stimulus that was synthesized on the basis of nonindividualized head-related transfer functions and used as reference in synthesizing the spectral components.     

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.     

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.     

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。     

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.