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Auditory localization is a fundamental ability that allows to perceive the spatial location of a sound source in the environment. The present work aims to provide a comprehensive overview of the mechanisms and acoustic cues used by the human perceptual system to achieve such accurate auditory localization. Acoustic cues are derived from the physical properties of sound waves, and many factors allow and influence auditory localization abilities. This review presents the monaural and binaural perceptual mechanisms involved in auditory localization in the three dimensions. Besides the main mechanisms of Interaural Time Difference, Interaural Level Difference and Head Related Transfer Function, secondary important elements such as reverberation and motion, are also analyzed. For each mechanism, the perceptual limits of localization abilities are presented. A section is specifically devoted to reference systems in space, and to the pointing methods used in experimental research. Finally, some cases of misperception and auditory illusion are described. More than a simple description of the perceptual mechanisms underlying localization, this paper is intended to provide also practical information available for experiments and work in the auditory field. [ABSTRACT FROM AUTHOR]

Expressing head-related transfer functions (HRTFs) in the spherical harmonic (SH) domain has been thoroughly studied as a method of obtaining continuity over space. However, HRTFs are functions not only of direction but also of frequency. This paper presents an extension of the SH-based method, utilizing hyperspherical harmonics (HSHs) to obtain an HRTF representation that is continuous over both space and frequency. The application of the HSH approximation results in a relatively small set of coefficients which can be decoded into HRTF values at any direction and frequency. The paper discusses results obtained by applying the method to magnitude spectra extracted from exemplary HRTF measurements. The HRTF representations based on SHs and HSHs exhibit similar reproduction accuracy, with the latter one featuring continuity over both space and frequency and requiring much lower number of coefficients. The developed HSH-based continuous functional model can serve multiple purposes, such as interpolation, compression or parametrization for machine-learning applications. [ABSTRACT FROM AUTHOR]

Head-related transfer function (HRTF) individualization can improve the perception of binaural sound. The interaural time difference (ITD) of the HRTF is a relevant cue for sound localization, especially in azimuth. Therefore, individualization of the ITD is likely to result in better sound spatial localization. A study of ITD has been conducted from a perceptual point of view using data from individual HRTF measurements and subjective perceptual tests. Two anthropometric dimensions have been demonstrated in relation to the ITD, predicting the subjective behavior of various subjects in a perceptual test. With this information, a method is proposed to individualize the ITD of a generic HRTF set by adapting it with a scale factor, which is obtained by a linear regression formula dependent on the two previous anthropometric dimensions. The method has been validated with both objective measures and another perceptual test. In addition, practical regression formula coefficients are provided for fitting the ITD of the generic HRTFs of the widely used Brüel & Kjær 4100 and Neumann KU100 binaural dummy heads. [ABSTRACT FROM AUTHOR]

One of the greatest challenges in the development of binaural machine audition systems is the disambiguation between front and back audio sources, particularly in complex spatial audio scenes. The goal of this work was to develop a method for discriminating between front and back located ensembles in binaural recordings of music. To this end, 22, 496 binaural excerpts, representing either front or back located ensembles, were synthesized by convolving multi-track music recordings with 74 sets of head-related transfer functions (HRTF). The discrimination method was developed based on the traditional approach, involving hand-engineering of features, as well as using a deep learning technique incorporating the convolutional neural network (CNN). According to the results obtained under HRTF-dependent test conditions, CNN showed a very high discrimination accuracy (99.4%), slightly outperforming the traditional method. However, under the HRTF-independent test scenario, CNN performed worse than the traditional algorithm, highlighting the importance of testing the algorithms under HRTF-independent conditions and indicating that the traditional method might be more generalizable than CNN. A minimum of 20 HRTFs are required to achieve a satisfactory generalization performance for the traditional algorithm and 30 HRTFs for CNN. The minimum duration of audio excerpts required by both the traditional and CNN-based methods was assessed as 3 s. Feature importance analysis, based on a gradient attribution mapping technique, revealed that for both the traditional and the deep learning methods, a frequency band between 5 and 6 kHz is particularly important in terms of the discrimination between front and back ensemble locations. Linear-frequency cepstral coefficients, interaural level differences, and audio bandwidth were identified as the key descriptors facilitating the discrimination process using the traditional approach. [ABSTRACT FROM AUTHOR]

A virtual‐sound catch ball game system was developed to improve the quality of life of the visually impaired. Computer‐generated virtual sound balls were represented by stereo sounds, comprising localization parameters such as the interaural time and level differences, echo, and head‐related transfer function. Ball‐catching success was determined by images of the hand captured by a USB camera. Two sessions of experiments with blind subjects demonstrated the importance of distance recognition for human localization capability. Moreover, the addition of an echo parameter enhanced the sound‐source image position and sense of enjoyment. The results showed that a virtual sound game is a good active‐entertainment option for the visually impaired. [ABSTRACT FROM AUTHOR]

Utilizing spherical harmonic (SH) domain has been established as the default method of obtaining continuity over space in head-related transfer functions (HRTFs). This paper concerns different variants of extending this solution by replacing SHs with four-dimensional (4D) continuous functional models in which frequency is imagined as another physical dimension. Recently developed hyperspherical harmonic (HSH) representation is compared with models defined in spherindrical coordinate system by merging SHs with one-dimensional basis functions. The efficiency of both approaches is evaluated based on the reproduction errors for individual HRTFs from HUTUBS database, including detailed analysis of its dependency on chosen orders of approximation in frequency and space. Employing continuous functional models defined in 4D coordinate systems allows HRTF magnitude spectra to be expressed as a small set of coefficients which can be decoded back into values at any direction and frequency. The best performance was noted for HSHs and SHs merged with reverse Fourier–Bessel series, with the former featuring better compression abilities, achieving slightly higher accuracy for low number of coefficients. The presented models can serve multiple purposes, such as interpolation, compression or parametrization for machine learning applications, and can be applied not only to HRTFs but also to other types of directivity functions, e.g. sound source directivity. • Hyperspherical harmonics are the most efficient 4D basis for storing HRTFs. • Frequency approximation order should be higher than maximum spherical harmonic order. • Utilizing 4D HRTF representations allows for a massive reduction of data size. • HRTF model evaluations are stable for different subjects from the same databases. [ABSTRACT FROM AUTHOR]

As binaural audio continues to permeate immersive technologies, it is vital to develop a detailed understanding of the perceptual relevance of HRTFs. Previous research has explored the benefit of individual HRTFs with respect to localisation. However, localisation is only one metric with which it is possible to rate spatial audio. This paper evaluates the perceived timbral and spatial characteristics of both individual and non-individual HRTFs and compares the results to overall preference. To that end, the measurement and evaluation of a high-resolution multi-environment binaural Impulse Response database is presented for 20 subjects, including the KU100 and KEMAR binaural mannequins. Post-processing techniques, including low frequency compensation and diffuse field equalisation are discussed in relation to the 8802 unique HRTFs measured for each mannequin and 2818/2114 HRTFs measured for each human. Listening test results indicate that particular HRTF sets are preferred more generally by subjects over their own individual measurements. [ABSTRACT FROM AUTHOR]

• Near-field head-related transfer functions were measured at distances of 0.2, 0.3, 0.4 and 0.5 m on a head mannequin. • A laser-induced 'spark' was used as a sound source to overcome problems with mounting a loudspeaker too close to the head. • Low-frequency extension was applied using a rigid-sphere model. • The collected database is shared to facilitate further research. This paper presents a database of near-field head-related transfer functions (HRTFs) of an artificial head, measured at four distances (0.2, 0.3, 0.4 and 0.5 m), with 49 positions recorded at each distance, for a total of 196 measurement points. The HRTFs were recorded using an acoustic pulse created by a laser-induced breakdown of air (LIB), which realizes a close to ideal, massless, monopole sound source. While the LIB produces a high amplitude pressure pulse, the amplitude decays toward low frequencies, which introduced a low frequency limit of about 200 Hz for this particular setup. Thus, a spherical head model based on the analytical expression for scattering by a rigid sphere was fitted to the measured data, and used to extend the low frequency range of the measurements. A brief evaluation of the processed dataset was undertaken, considering interaural time and level differences. The measured and processed database, as well as the low frequency extension procedure are made publicly available to support future research into nearby sound localization, and virtual/augmented reality applications. [ABSTRACT FROM AUTHOR]

We present a novel spatial audio rendering technique to handle sound sources that can be represented by either an area or a volume in VR environments. As opposed to point-sampled sound sources, our approach projects the area-volumetric source to the spherical domain centered at the listener and represents this projection area compactly using the spherical harmonic (SH) basis functions. By representing the head-related transfer function (HRTF) in the same basis, we demonstrate that spatial audio which corresponds to an area-volumetric source can be efficiently computed as a dot product of the SH coefficients of the projection area and the HRTF. This results in an efficient technique whose computational complexity and memory requirements are independent of the complexity of the sound source. Our approach can support dynamic area-volumetric sound sources at interactive rates. We evaluate the performance of our technique in large complex VR environments and demonstrate significant improvement over the naive point-sampling technique. We also present results of a user evaluation, conducted to quantify the subjective preference of the user for our approach over the point-sampling approach in VR environments. [ABSTRACT FROM AUTHOR]

Principal components analysis (PCA) is frequently used for modelling the magnitude of the head-related transfer functions (HRTFs). Assuming that the HRTFs are minimum phase systems, the phase is obtained from the Hilbert transform of the log-magnitude. In recent years, the PCA applied to HRTFs is also used to model individual HRTFs relating the PCA weights with anthropometric measurements of the head, torso and pinnae. The HRTF log-magnitude is the most used format of input data to the PCA, but it has been shown that if the input data is HRTF linear magnitude, the cumulative variance converges faster, and the mean square error (MSE) is smaller. This study demonstrates that PCA applied directly on HRTF complex values is even better than the two formats mentioned above, that is, the MSE is the smallest and the cumulative variance converges faster after the 8th principal component. Different objective experiments around all the median plane put in evidence the differences which, although small, seem to be perceptually detectable. To elucidate this point, psychoacoustic discrimination tests are done between measured and reconstructed HRTFs from the three types of input data mentioned, in the median plane between -45°. and +9°. [ABSTRACT FROM AUTHOR]

Abstract: Multichannel acoustic signal processing has undergone major development in recent years. The incorporation of spatial information into an immersive audiovisual virtual environment or into video games provides better sense of “presence” to applications. Spatial sound consists in reproducing audio signals with spatial cues (spatial information embedded in the sound) through headphones. This spatial information allows the listener to identify the virtual positions of the sources corresponding to different sounds. Headphone-based spatial sound is obtained by filtering different sound sources through special filters called Head Related Transfer Functions (HRTFs) prior to render them through headphones. Efficient computation plays an important role when the number of sources to be managed is high. This situation increases the number of filtering operations, requiring high computing capacity specially when the virtual sources are moving. Graphics Processing Units (GPUs) are high parallel programmable co-processors that provide massive computation when the needed operations are properly parallelized. This paper discusses the design, the implementation and the performance of a headphone-based spatial audio application whose processing is totally carried out on a GPU. This application is able to interact with the listener who can select and change the location of the sound sources in real-time. This work analyzes also specific computational aspects inside the CUDA environment in order to successfully exploit GPU resources. Results show that the proposed application is able to move up to 2500 sources simultaneously, while leaving free CPU resources for other tasks. This work emphasizes the importance of analyzing all CUDA aspects, since they can influence drastically the performance. [Copyright &y& Elsevier]

Abstract: The most important acoustic cues available to the brain for sound localization are produced by the interaction of sound with the animal’s head and external ears. As a first step in understanding the relation between these cues and their neural representation in a vocal new-world primate, we measured head-related transfer functions (HRTFs) across frequency for a wide range of sound locations in three anesthetized marmoset monkeys. The HRTF magnitude spectrum has a broad resonance peak at 6–12kHz that coincides with the frequency range of the major call types of this species. A prominent first spectral notch (FN) in the HRTF magnitude above this resonance was observed at most source locations. The center frequency of the FN increased monotonically from ∼12 to 26kHz with increases in elevation in the lateral field. In the frontal field FN frequency changed in a less orderly fashion with source position. From the HRTFs we derived interaural time (ITDs) and level differences (ILDs). ITDs and ILDs (below 12kHz) varied as a function of azimuth between ±250μs and ±20dB, respectively. A reflexive orienting behavioral paradigm was used to confirm that marmosets can orient to sound sources. [Copyright &y& Elsevier]

Although sound image control and sound field reproduction based on head-related transfer functions (HRTFs) have been studied for years, they have not been put to practical use. The main reason is that individual differences in HRTFs have not been overcome. In the present paper, we propose the parametric notch-peak HRTF model (PNP model), which can continuously change the parameters corresponding to individual differences in HRTFs by using knowledge of spectral notches and peaks and an HRTF database. We then develop a toolkit that can generate individual HRTFs by having the listener adjust the parameters. Finally, localization tests are carried out in order to examine the performance of the individualized HRTFs using the PNP model. [ABSTRACT FROM AUTHOR]

Personalized Head-Related Transfer Functions (HRTFs) are needed as part of the binaural sound individualization process in order to provide a high-quality immersive experience for a specific user. Signal processing methods for performing HRTF measurements in non-anechoic conditions are of high interest to avoid the complex and inconvenient access to anechoic facilities. Non-anechoic HRTF measurements capture the effect of room reflections, which should be correctly identified and eliminated to obtain HRTFs estimates comparable to ones acquired in an anechoic setup. This paper proposes a sub-band frequency-dependent processing method for reflection suppression in non-anechoic HRTF signals. Array processing techniques based on Plane Wave Decomposition (PWD) are adopted as an essential part of the solution for low frequency ranges, whereas the higher frequencies are easily handled by means of time-crop windowing methods. The formulation of the model, extraction of parameters and evaluation of the method are described in detail. In addition, a validation case study is presented showing the suppression of reflections from an HRTF measured in a real system. The results confirm that the method allows to obtain processed HRTFs comparable to those acquired in anechoic conditions. [ABSTRACT FROM AUTHOR]

To date, traditional visual-based event-related potential brain-computer interface (ERP-BCI) systems continue to dominate the mainstream BCI research. However, these conventional BCIs are unsuitable for the individuals who have partly or completely lost their vision. Considering the poor performance of gaze independent ERP-BCIs, it is necessary to study techniques to improve the performance of these BCI systems. In this paper, we developed a novel 36-class bimodal ERP-BCI system based on tactile and auditory stimuli, in which six-virtual-direction audio files produced via head related transfer functions (HRTF) were delivered through headphones and location-congruent electro-tactile stimuli were simultaneously delivered to the corresponding position using electrodes placed on the abdomen and waist. We selected the eight best channels, trained a Bayesian linear discriminant analysis (BLDA) classifier and acquired the optimal trial number for target selection in online process. The average online information transfer rate (ITR) of the bimodal ERP-BCI reached 11.66 bit/min, improvements of 35.11% and 36.69% compared to the auditory (8.63 bit/min) and tactile approaches (8.53 bit/min), respectively. The results demonstrate the performance of the bimodal system is superior to each unimodal system. These facts indicate that the proposed bimodal system has potential utility as a gaze-independent BCI in future real-world applications. [ABSTRACT FROM AUTHOR]

In response to renewed interest in virtual and augmented reality, the need for high-quality spatial audio systems has emerged. The reproduction of immersive and realistic virtual sound requires high resolution individualized head-related transfer function (HRTF) sets. In order to acquire an individualized HRTF, a large number of spatial measurements are needed. However, such a measurement process requires expensive and specialized equipment, which motivates the use of sparsely measured HRTFs. Previous studies have demonstrated that spherical harmonics (SH) can be used to reconstruct the HRTFs from a relatively small number of spatial samples, but reducing the number of samples may produce spatial aliasing error. Furthermore, by measuring the HRTF on a sparse grid the SH representation will be order-limited, leading to constrained spatial resolution. In this paper, the effect of sparse measurement grids on the reproduced binaural signal is studied by analyzing both aliasing and truncation errors. The expected effect of these errors on the perceived loudness stability of the virtual sound source is studied theoretically, as well as perceptually by an experimental investigation. Results indicate a substantial effect of truncation error on the loudness stability, while the added aliasing seems to significantly reduce this effect. [ABSTRACT FROM AUTHOR]