Spatial interpolation of head-related transfer functions using enhanced generative adversarial networks

Head-related transfer function (HRTF) interpolation plays an important role for implementation of 3D sound system because it can not only reduce the number of measurements for HRTFs, but also reduce the data of HRTFs for seamless binaural synthesis. This paper addresses the problem of accurately realizing the interpolation of HRTF for synthesis of virtual auditory space, and proposes a HRTF interpolation method based on principal component analysis. Firstly, the HRTF is decomposed into principal components and corresponding principal component weights, where principal components are direction-independent and principal component weights are direction- dependent; then the directional variation of the principal component weight is multivariate polynomial fitted with a bivariate function of two spatial angulus (azimuth and elevation). Moreover, a sphere- partitioning optimization scheme is employed to improve the approximation precision. Experiment results demonstrate that HRTFs in the entire sphere surface can be interpolated by the proposed method with small distortion, and the proposed method performs better than conventional methods. Therefore the proposed method gives a promising way for HRTF interpolation.

Head-Related Transfer Function (HRTF) representation and interpolation is an important problem in spatial audio. We present a kernel regression method based on Gaussian process (GP) modeling of the joint spatial-frequency relationship between HRTF measurements and obtain a smooth non-linear representation based on data measured over both arbitrary and structured spherical measurement grids. This representation is further extended to the problem of extracting spectral extrema (notches and peaks). We perform HRTF interpolation and spectral extrema extraction using freely available CIPIC HRTF data. Experimental results are shown.

Head related transfer function HRTF is the main technique of binaural synthesis, which is used to reconstruct spatial sound image, and the HRTF data only can be obtained by measurement. A high resolution HRTF database contains too many HRTFs, the workload of measurement is too huge to be finished. As a solution, in order to calculate new HRTF by measured HRTFs, many researchers concentrate on the interpolation of HRTF. But, before interpolating, HRTFs should be aligned because there is time delay between different HRTFs. Some researchers try to implement aligning operation based on phase, but the method is not appropriate since the periodicity of phase. Another idea to align HRTFs is by detecting method, however, the time difference is too tiny to detect exactly. None of the methods can provide a good and stable performance. In this paper, we propose a new method to align HRTFs based on correlation. And the experiments show that the proposed aligning method improves the accuracy index SDR 18.5i¾?dB for the most, furthermore, the proposed method could improve the accuracy for all positions.

A high voltage damped oscillating wave generator with variable frequency has been developed using power devices (IGBT), photo devices, a designed noncore transformer and a function-generator in order to diagnose insulating materials as power apparatus (transformer, cable), enameled wires, printed circuit board (PCB), wire-harness in automobiles. The generated maximum voltage (2.5 kV) and the frequency dependency (0.01-2 kHz) were confirmed in output tests.

Urban metro cross-section flow is the passenger flow that travels through a metro section. Its volume is a critical parameter for planning operation diagrams and improving the service quality of urban subway systems. This makes it possible to better plan the drive for the sustainable development of a city. This paper proposes an improved model for predicting urban metro section flow, combining time series decomposition and a generative adversarial network. First, an urban metro section flow sequence is decomposed using EMD (Empirical Mode Decomposition) into several IMFs (Intrinsic Mode Functions) and a trend function. The sum of all the IMF components is treated as the periodic component, and the trend function is considered the trend component, which are fitted by Fourier series function and spline interpolation, respectively. By subtracting the sum of the periodic and trend components from the urban metro section flow sequence, the error is regarded as the residual component. Finally, a GAN (generative adversarial network) based on the fusion graph convolutional neural network is used to predict the new residual component, which considers the spatial correlation between different sites of urban metro sections. The Chengdu urban metro system data in China show that the proposed model, through incorporating EMD and a generative adversarial network, achieves a 15–20% improvement in prediction accuracy at the cost of a 10% increase in the calculation time, meaning it demonstrates good prediction accuracy and reliability.

We proposed a new head-related transfer function (HRTF) interpolation method based on splicing. The sound spreads from sound source to listener’s ears, the wave of head-related impulse response (HRIR) clearly indicates time delay which can be symbolized by the sample number of the first obvious peak and the signal filtered by the diffraction and reflection properties of the torso, head, and pinna. Based on this feature and the importance of the time delay in interpolation, we split the measured HRIR into three parts according to the first obvious peak of the wave and the length of the useful signal. First, we used radial basis function neural network to construct regression forecast models using spatial parameters (i.e., azimuth, elevation, and distance) and the HRIRs sample number of the first obvious peak. Then, we used the tetrahedral interpolation with barycentric weights to calculate the second part of the HRIR. Finally, we spliced the forecast information and the useful signal in terms of the sample number of the first obvious peak. For an unknown position in three-dimensional space of near-field, we interpolated its HRIR by the proposed method. The Signal-to-Deviation ratio (SDR) increased 5 dB compared with the tetrahedron interpolation in the time domain.

Today, there exists a growing number of HRTF datasets available with each set often proposing a unique variation on the spatial discretization measurement grid. These differing grids, typically determined by the mechanical system employed, result in datasets, which are not directly comparable or exploitable. To alleviate the limitation of incompatible grids and assist in the adaptation of measurements performed on one grid to another, facilitating the inter-exchange of HRTF sets, a fixed radius HRTF interpolation method is proposed. The approach is based on decomposition of the sound field using spherical harmonics, allowing for a global spatial recomposition. The frequency domain HRTF is separated into its complex components and interpolations are performed independently before reconstitution. Spherical harmonic truncation order is chosen to provide a system which is roughly square, improving matrix inversion with Tikhonov regularization. A high spatial density HRTF was used as a test case for evaluating the interpolation method. A series of measures are employed to quantitatively compare the quality of the interpolation as compared to traditional interpolation methods in both the time and frequency domains.

Accurate head-related transfer functions (HRTFs) are essential for delivering realistic 3D audio experiences. However, obtaining personalized, high-resolution HRTFs for individual users is a time-consuming and costly process, typically requiring extensive acoustic measurements. To address this, spatial upsampling techniques have been developed to estimate high-resolution HRTFs from sparse, low-resolution acoustic measurements. This paper presents a novel approach that leverages the spherical harmonic domain and an autoencoder generative adversarial network to tackle the HRTF upsampling problem. Comprehensive evaluations are conducted using both perceptual models and objective spectral metrics to validate the accuracy and realism of the upsampled HRTFs. The results show that the proposed approach outperforms traditional barycentric interpolation in terms of log-spectral distortion, particularly in extreme sparsity scenarios involving fewer than 12 measurements. These results go some way to justifying that the proposed autoencoder generative adversarial network approach is able to create high-quality, high-resolution HRTFs from only a few acoustic measurements, helping pave the way for more accessible personalized spatial audio across a range of applications.

Head-Related Transfer Function (HRTF) plays a critical role in how the auditory system perceives spatial information. The spectral cues embedded in HRTF are vital for accurately determining the elevation of sound sources. In existing approaches, deep neural networks (DNNs) have been utilized to predict the magnitude spectra of HRTF from images of the pinna, typically employing the HRTF log-magnitude as the output during training. However, HRTF encompasses the acoustic characteristics of both the head and torso, exhibiting direction-dependent patterns that pose challenges in reconstructing its spectral cues. To address this complexity, we propose an innovative method for HRTF individualization. Our model uses Pinna-Related Transfer Function (PRTF) as the output during training, which helps alleviate the impact of sound reflections from the head and torso in the head-related impulse response (HRIR). Our experimental findings, based on an HRTF dataset, illustrate that our proposed model excels in reconstructing the first and second spectral cues. Furthermore, it outperforms previous deep learning models in terms of log spectral distortion (LSD).

Head related transfer function (HRTF) is a continuous function of spatial direction. In practice, only HRTFs at discrete directions can be measured. In order to obtain HRTFs at unmeasured directions, a continuous reconstruction (or interpolation) procedure is needed. In this paper, a method for continuous reconstruction of HRTF based on optimal-degree spherical harmonics expansion is developed. Expansion coefficients were derived by using the pseudo-inverse method. To address the ill-posed problem in inverse calculation, the expansion degree for each frequency bin was optimized by a heuristic method. This method searches the minimum-norm errors of the reconstructed HRTFs with respect to measured ones which were not used to derive the coefficients. The KEMAR HRTF at 710 directions and a human HRTF at 493 directions were employed in reconstruction. Measured HRTFs from KEMAR or human subject were dived into three groups according to directions, in which the first group of 2/5, the second group of 2/5, and the third group of 1/5 data were used to calculate the expansion coefficients, determine the optimal expansion degree, and evaluate the reconstruction performance, respectively. Compared with the expansion methods using a constant degree for all frequency, the reconstruction performance of the current method is prior.

Head related transfer functions (HRTFs) are needed to present virtual spatial sound sources via headphones. Since individually measured HRTFs are very costly and time consuming, in this paper the individualization of the dummyhead's HRTFs will be discussed. Here, the individualization is based on a scalable ellipsoidal head model. From this model the individualization is splitted into the individualization of the interaural time difference (ITD) and the spectral domain. The ellipsoidal modeling of the ITD gives quantitatively good results, considering the individual measurements. The second approach in spectral domain scales the transfer function in frequency. An angle dependent factor is calculated by the head dimensions of the subject. Afterwards, the scaling results are compared and discussed with individual measurements.

Toward orthogonal non-individualised head-related transfer functions for forward and backward directional sound: cluster analysis and an experimental study

Four head-related transfer function (HRTF) data sets were compared to determine the effect of HRTF measurement methodology on the localization of spatialized auditory stimuli. Spatial audio interfaces typically require HRTF data sets to generate the spatialized auditory stimuli. HRTF measurement is accomplished using a variety of techniques that can require several nearly arbitrary decisions about methodology. The effects of these choices upon the resulting spatial audio interface are unclear. Sixteen participants completed a sound localization task that included real-world, broadband stimuli spatialized at eight locations on the horizontal plane. Four different HRTF data sets were utilized to spatialize the stimuli: two publicly available HRTF data sets and two data sets obtained using different in-house measurement systems. All HRTFs were obtained from the Knowles Electronics Mannequin for Acoustics Research. Unsigned localization error and proportion of front/back reversals did not differ significantly across HRTF data sets. Poorest accuracy was observed in locations near the medial (front/back) axis of the listener, mainly because of the relatively large proportions of reversals at these locations. This study suggests that the particular generalized HRTF data set chosen for spatialization is of minimal importance to the localizability of the resulting stimuli. This result will inform the design of many spatial audio interfaces that are based upon generalized HRTFs, including wayfaring devices, communication systems, and virtual reality systems.

In this study, head‐related transfer functions (HRTFs) of a dummy head and human subjects are numerically estimated by using the boundary element method (BEM), and their availability for auralization is discussed from the subjective viewpoints. Geometries of their heads are obtained by a 3‐D laser scanner. The effect of the torso for the estimation of the HRTFs is also examined and discussed via the 3‐D measurement. The estimated HRTFs are compared for each subject with the measured HRTFs in various objective criteria, such as spectral distortion (SD), signal‐to‐distortion ratio (SDR), and interaural time/level differences (ITD/ILD). Availability of the estimated HRTFs for the synthesis of the 3‐D sound image are then evaluated via hearing experiments. In our previous study [Proceedings of WESPAC IX (2006)], the results of the experiment is insufficient since the low‐frequency range of the estimated HRTFs caused the ambiguity in sound localization. In this study, the frequency range of the estimation is extended to as high frequency as possible, and the availability of the estimated HRTFs for auralization is discussed from two viewpoints: the subjective difference between the estimated and measured HRTFs, and some subjective attributes obtained from the hearing of the stimuli convoluted with the estimated HRTFs.

The head-related transfer function (HRTF) defines the acoustic path from a source to the two ears of a listener in a manner that is highly dependent on direction. This directional dependence arises from the highly individual morphology of the pinna, which results in complex reflections and resonances. While this notion is generally accepted, there has been little research on the importance of different structural elements of the pinna on the HRTF. A parametric three-dimensional ear model was used to investigate the changes in shape of the pinna in a systematic manner with a view to determining important contributing morphological parameters that can be used for HRTF individualization. HRTFs were simulated using the boundary element method. The analysis comprised objective comparisons between the directional transfer function and diffuse field component. The mean spectral distortion was used for global evaluation of HRTF similarity across all simulated positions. A perceptual localization model was used to determine correspondences between perceptual cues and objective parameters. A reasonable match was found between the modelled perceptual results and the mean spectral distortion. Modifications to the shape of the concha were found to have an important impact on the HRTF, as did those in proximity to the triangular fossa. Furthermore, parameters that control the relief of the pinna were found to be at least as important as more frequently cited side-facing parameters, highlighting limitations in previous morphological/HRTF studies.