The effect of impedance on interaural azimuth cues derived from a spherical head model

Recent implementations of binaural synthesis have combined high-frequency pinna diffraction data with low-frequency acoustic models of the head and torso. This combination ensures that the salient cues required for directional localization in the horizontal plane are consistent with psychophysical expectations, regardless of the accuracy or match of the high-frequency cues, or the fidelity of experimental low-frequency information. This paper investigates the effect of a nonrigid boundary condition on the surface pressure and the resulting interaural cues used for horizontal localization. These are derived from an analytical single sphere diffraction model assuming a locally reacting and uniformly distributed impedance boundary condition. Decreasing the magnitude of a purely resistive surface impedance results in an overall decrease in the sphere surface pressure level, particularly in the posterior region. This produces nontrivial increases in both the interaural level and time difference, especially for sound source directions near the interaural axis. When the surface impedance contains a reactive component the interaural cues exhibit further changes. The basic impedance characteristics of human hair and their incorporation into the sphere diffraction model are also discussed.     

Extracting the frequencies of the pinna spectral notches in measured head related impulse responses

The head related impulse response (HRIR) characterizes the auditory cues created by scattering of sound off a person's anatomy. The experimentally measured HRIR depends on several factors such as reflections from body parts (torso, shoulder, and knees), head diffraction, and reflection/ diffraction effects due to the pinna. Structural models (Algazi et al., 2002; Brown and Duda, 1998) seek to establish direct relationships between the features in the HRIR and the anatomy. While there is evidence that particular features in the HRIR can be explained by anthropometry, the creation of such models from experimental data is hampered by the fact that the extraction of the features in the HRIR is not automatic. One of the prominent features observed in the HRIR, and one that has been shown to be important for elevation perception, are the deep spectral notches attributed to the pinna. In this paper we propose a method to robustly extract the frequencies of the pinna spectral notches from the measured HRIR, distinguishing them from other confounding features. The method also extracts the resonances described by Shaw (1997). The techniques are applied to the publicly available CIPIC HRIR database (Algazi et al., 2001c). The extracted notch frequencies are related to the physical dimensions and shape of the pinna.     

Role of spectral cues in median plane localization

The role of spectral cues in the sound source to ear transfer function in median plane sound localization is investigated in this paper. At first, transfer functions were measured and analyzed. Then, these transfer functions were used in experiments where sounds from a source on the median plane were simulated and presented to subjects through headphones. In these simulation experiments, the transfer functions were smoothed by ARMA models with different degrees of simplification to investigate the role of microscopic and macroscopic patterns in the transfer functions for median plane localization. The results of the study are summarized as follows: (1) For front-rear judgment, information derived from microscopic peaks and dips in the low-frequency region (below 2 kHz) and the macroscopic patterns in the high-frequency region seems to be utilized; (2) for judgment of elevation angle, major cues exist in the high-frequency region above 5 kHz. The information in macroscopic patterns is utilized instead of that in small peaks and dips.     

Head-related transfer function database and its analyses

Based on the measurements from 52 Chinese subjects (26 males and 26 females), a high-spatial-resolution head-related transfer function (HRTF) database with corre- sponding anthropometric parameters is established. By using the database, cues relating to sound source localization, including interaural time difference (ITD), interaural level difference (ILD), and spectral features introduced by pinna, are analyzed. Moreover, the statistical relationship between ITD and anthropometric parameters is estimated. It is proved that the mean values of maximum ITD for male and female are significantly different, so are those for Chinese and western sub- jects. The difference in ITD is due to the difference in individual anthropometric parameters. It is further proved that the spectral features introduced by pinna strongly depend on individual; while at high frequencies (f≥ 5.5 kHz), HRTFs are left-right asymmetric. This work is instructive and helpful for the research on bin- aural hearing and applications on virtual auditory in future.     

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.     

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.     

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。      

The acoustical cues to sound location in the rat: measurements of directional transfer functions

The acoustical cues for sound location are generated by spatial- and frequency-dependent filtering of propagating sound waves by the head and external ears. Although rats have been a common model system for anatomy, physiology, and psychophysics of localization, there have been few studies of the acoustical cues available to rats. Here, directional transfer functions (DTFs), the directional components of the head-related transfer functions, were measured in six adult rats. The cues to location were computed from the DTFs. In the frontal hemisphere, spectral notches were present for frequencies from approximately 16 to 30 kHz; in general, the frequency corresponding to the notch increased with increases in source elevation and in azimuth toward the ipsilateral ear. The maximum high-frequency envelope-based interaural time differences (ITDs) were 130 mus, whereas low-frequency (<3.5 kHz) fine-structure ITDs were 160 mus; both types of ITDs were larger than predicted from spherical head models. Interaural level differences (ILDs) strongly depended on location and frequency. Maximum ILDs were <10 dB for frequencies <8 kHz and were as large as 20-40 dB for frequencies >20 kHz. Removal of the pinna eliminated the spectral notches, reduced the acoustic gain and ILDs, altered the acoustical axis, and reduced the ITDs.     

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.     

Multiple Scattering Between Adjacent Sound Sources in Head-Related Transfer Function Measurement System

To accelerate head-related transfer functions (HRTFs) measurement, two or more independent sound sources are usually employed in the measurement system. However, the multiple scattering between adjacent sound sources may influence the accuracy of measurement. On the other hand, the directivity of sound source could induce measurement error. Therefore, a model consisting of two spherical sound sources with approximate omni-directivity and a rigid-spherical head is proposed to evaluate the errors in HRTF measurement caused by multiple scattering between sources. An example of analysis using multipole re-expansion indicates that the error of ipsilateral HRTFs are within the bound of ± 1.0 dB below a frequency of 20 kHz, provided that the sound source radius does not exceed 0.025 m, the source distance relative to head center is not less than 0.5 m, and the angular interval between two adjacent sources is not less than 20 degrees. Similar conclusions under different conditions can also be analyzed and discussed by using this calculation method. Furthermore, the results are verified by measurements of HRTFs for a rigid sphere and a KEMAR artificial head.     

An elevation coding method for auditory displays

This paper describes an alternative approach to elevation coding in an auditory display delivered through headphones. Objects in auditory display are presented as sound sources. Direction dependent cues for auditory display construction are most effectively presented by individualised head-related transfer functions (HRTFs), while generalised HRTFs give satisfactory results only in the azimuth. Since measurements of individualised HRTFs are impractical, we propose an alternative method for coding elevation. This method requires some time for the listener to adapt to it. The learning process can be shortened significantly if the coding is similar to natural human perception of sound elevation. To test human capability of distinguishing between different sounds, several sound sets were created and presented to test subjects. Five sound sets with the best resolution were then used to create auditory display of a graphical user interface (GUI). Test subjects were able to learn this display in relatively short time, which justifies the method and gives opportunity for further research.     

Contribution of spectral cues to human sound localization

The contribution of spectral cues to human sound localization was investigated by removing cues in 1/2-, 1- or 2-octave bands in the frequency range above 4 kHz. Localization responses were given by placing an acoustic pointer at the same apparent position as a virtual target. The pointer was generated by filtering a 100-ms harmonic complex with equalized head-related transfer functions (HRTFs). Listeners controlled the pointer via a hand-held stick that rotated about a fixed point. In the baseline condition, the target, a 200-ms noise burst, was filtered with the same HRTFs as the pointer. In other conditions, the spectral information within a certain frequency band was removed by replacing the directional transfer function within this band with the average transfer of this band. Analysis of the data showed that removing cues in 1/2-octave bands did not affect localization, whereas for the 2-octave band correct localization was virtually impossible. The results obtained for the 1-octave bands indicate that up-down cues are located mainly in the 6-12-kHz band, and front-back cues in the 8-16-kHz band. The interindividual spread in response patterns suggests that different listeners use different localization cues. The response patterns in the median plane can be predicted using a model based on spectral comparison of directional transfer functions for target and response directions.     

Estimation of HRTFs on the horizontal plane using physical features

Sound localization can be controlled by using head related transfer functions (HRTFs), which are related to the size of the head, the ears and so on. Since HRTFs are characterized by source directions and subjects, it is necessary to conduct measurements in all directions for all subjects. However, such measurement is expensive and time-consuming. In this paper, we propose a simpler and more useful method that investigates the relationship between HRTFs and physical size by multiple regression analysis. The estimated HRTFs are evaluated by objective and subjective measures. For objective results, the average spectral distortion score is 4.0 dB in a bandwidth ranging from 0 to 8 kHz. Subjective results indicate no significant difference between the measured and the estimated HRTFs in that frequency range. These results support the hypothesis that the proposed method is effective for estimating HRTFs.     

The effect of hair on auditory localization cues

Previous empirical and analytical investigations into human sound localization have illustrated that the head-related transfer function (HRTF) and interaural cues are affected by the acoustic material properties of the head. This study utilizes a recent analytical treatment of the sphere scattering problem (which accounts for a hemispherically divided surface boundary) to investigate the contribution of hair to the auditory cues below 5 kHz. The hair is modeled using a locally reactive equivalent impedance parameter, and cue changes are discussed for several cases of measured hair impedance. The hair is shown to produce asymmetric perturbations to the HRTF and the interaural time and level differences. The changes in the azimuth plane are explicated via analytical examination of the surface pressure variations with source angle. Experimental HRTFs obtained using a sphere with and without a hemispherical covering of synthetic hair show a good agreement with analytical results. Additional experimental and analytical investigations illustrate that the relative contribution of the hair remains robust, regardless of the placement of the pinnas, or inclusion of a cylindrical neck.     

Influence of fundamental frequency and source elevation on the vertical localization of complex tones and complex tone pairs

This study investigates the vertical localization of single complex tones (monads) and simultaneous complex tone pairs (dyads), especially as it is affected by their fundamental frequency and source elevation. Two complex tone timbres are considered: one consisting of five low-order harmonics, and the other of all odd harmonics (a square wave). Sound sources were at -15, 0, 15, and 30 deg from the horizontal plane at ear height. For eight subjects, this source array was in the median plane, and for a further nine subjects, it was directly to the subject's left (lateral plane). The subjects localized the angle of the auditory image(s) of one or two complex tones around the vertical plane containing the sound sources. Mean responses for the five-harmonic complex tones show a systematic effect (referred to as Pratt's effect) of fundamental frequency on vertical localization--whereby high-frequency complex tones are localized to positions higher than low-frequency complex tones for equivalent source positions. For the square wave, the sound-source position dominates localization, although some effect of fundamental frequency is evident for median plane sources.     

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.     

Auditory localization of nearby sources. III. Stimulus effects

A series of experiments has examined the auditory localization of a nearby (< 1 m) sound source under four conditions: (1) a fixed-amplitude condition where loudness-based distance cues were available; (2) a monaural condition where the contralateral ear was occluded by an ear-plug and muff; (3) a high-pass condition where the stimulus bandwidth was 3 Hz to 15 kHz; and (4) a low-pass condition where the stimulus bandwidth was 200 Hz to 3 kHz. The results of these experiments were compared to those of a previous experiment that measured localization performance for a nearby broadband, random-amplitude source [Brungart et al., J. Acoust. Soc. Am. 106, 1956-1968 (1999)]. Directional localization performance in each condition was consistent with the results of previous far-field localization experiments. Distance localization accuracy improved slightly in the fixed-amplitude condition relative to the earlier broadband random-amplitude experiment, especially near the median plane, but was severely degraded in the monaural condition. Distance accuracy was also found to be highly dependent on the low-frequency energy of the stimulus: in the low-pass condition, distance accuracy was similar to that in the broadband condition, while in the high-pass condition, distance accuracy was significantly reduced. The results suggest that low-frequency interaural level differences are the dominant auditory distance cue in the proximal region.     

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.     

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.     

Reducing individual differences in the external-ear transfer functions of the Mongolian gerbil

This study examines individual differences in the directional transfer functions (DTFs), the directional components of head-related transfer functions of gerbils, and seeks a method for reducing these differences. The difference between the DTFs of a given animal pair was quantified by the intersubject spectral difference (ISSD), which is the variance in the difference spectra of DTFs for frequencies between 5 and 45 kHz and for 361 source directions. An attempt was made to reduce the ISSD by scaling the DTFs of one animal in frequency and/or rotating the DTFs along the source coordinate sphere. The ISSD was reduced by a median of 12% after optimal frequency scaling alone, by a median of 19% after optimal spatial rotation alone, and by a median of 36% after simultaneous frequency scaling and spatial rotation. The optimal scaling factor (OSF) and the optimal coordinate rotation (OCR) correlated strongly with differences in head width and pinna angles (i.e., pinna inclination around the vertical and front-back axes), respectively. Thus, linear equations were derived to estimate the OSF and OCR from these anatomical measurements. The ISSD could be reduced by a median of 22% based on the estimated OSF and OCR.