A Splicing Interpolation Method for Head-Related Transfer Function

이 연구는 중앙면 상에서 주성분 분석법을 이용하여 시간 및 주파수 영역에서 머리전달함수의 모형화 기법들을 다룬다. 시간영역의 머리전달함수, 복소수 값의 머리전달함수, 확장된 머리전달함수, 로그 크기의 머리전달함수에 기반하여 각각 주성분 분석법을 수행하여 얻은 네 가지 머리전달함수 모형들에 대해서 최소자승오차 관점에서 모형화 성능을 비교하고, 모형들간의 이론적인 관계를 살펴보는 것이 이 연구의 목적이다. 모형화에 사용되는 기저함수의 수가 동일하다면, 시간영역에서의 머리전달함수 혹은 확장된 머리전달함수에 기반한 모형이 복소수 값의 머리전달함수에 기반한 모형보다 최소자승오차 관점에서 더 효율적인 모형화 성능을 지닌다. 시간영역에서의 머리전달함수에 기반한 모형과 확장된 머리전달함수에 기반한 모형은 이론적으로 동일한 모형이며 서로 푸리에 변환 관계가 있다. 로그 크기의 머리전달함수에 기반한 모형은 다른 모형들과 모형화 성능 및 이론적인 관계를 비교할 수가 없는데, 이는 로그 크기의 머리전달함수에 기반한 모형은 머리전달함수의 크기 정보만을 로그 크기로 다루는 반면에 다른 모형들은 선형 크기로 머리전달함수의 크기와 위상정보를 모두 다루기 때문이다. This study deals with modeling of head-related transfer functions(HRTFs) using principal components analysis(PCA) in the time and frequency domains. Four PCA models based on head-related impulse responses(HRIRs), complex-valued HRTFs, augmented HRTFs, and log-magnitudes of HRTFs are investigated. The objective of this study is to compare modeling performances of the PCA models in the least-squares sense and to show the theoretical relationship between the PCA models. In terms of the number of principal components needed for modeling, the PCA model based on HRIR or augmented HRTFs showed more efficient modeling performance than the PCA model based on complex-valued HRTFs. The PCA model based on HRIRs in the time domain and that based on augmented HRTFs in the frequency domain are shown to be theoretically equivalent. Modeling performance of the PCA model based on log-magnitudes of HRTFs cannot be compared with that of other PCA models because the PCA model deals with log-scaled magnitude components only, whereas the other PCA models consider both magnitude and phase components in linear scale.

A complex-valued head-related transfer function (HRTF) can be represented as a real-valued head-related impulse response (HRIR). The interaural time and level cues of HRIRs are extracted to derive the binaural model and also to normalize each measured HRIR. Using the Karhunen-Loeve expansion, normalized HRIRs are modeled as a weighted combination of a set of basis functions in a low-dimensional subspace. The basis functions and the space samples of the weights are obtained from the measured HRIR. A simple linear interpolation algorithm is employed to obtain the modeled binaural HRIRs. The modeled HRIRs are nearly identical to the measured HRIRs from an anesthetized live cat. Typical mean-square errors and cross-correlation coefficients between the 1816 measured and modeled HRIRs are 1% and 0.99, respectively. The real-valued operations and linear interpolating in the model are very effective for speeding up the model computation in real-time implementation. This approach has made it possible to simulate real free-field signals at the two eardrums of a cat via earphones and to study the neuronal responses to such a virtual acoustic space (VAR).

3D audio real-time rendering is of great importance for virtual reality (VR) application, especially on mobile devices. However, the limited computational power makes it hard to implement fast generation of spatial sound using head-related transfer function (HRTF). To accelerate the procedure of head-related impulse response (HRIR) convolution, we propose an efficient rendering method using the parameterized HRTF. The HRIRs are preprocessed into the parameterized HRTFs with a delayed parameter, so as to realize the fast convolutions in 3D audio synthesis. We found our method could reduce the calculation time of 3D audio rendering significantly. The results were 0.9 times and 0.68 times on average the play duration of the MPEG standard sequences, with Qualcomm Snapdragon 821 and Samsung Exynos 7420. And the subjective test showed that the real-time rendered sounds had the similar audio quality and location perception to the 3D audio rendered with the raw HRIRs.

Currently, to obtain maximum fidelity 3D audio, an intended listener is required to undergo time consuming measurements using highly specialized and expensive equipment. Customizable Head-Related Impulse Responses (HRIRs) would remove this limitation. This paper reports our progress in the first stage of the development of customizable HRIRs. Our approach is to develop compact functional models that could be equivalent to empirically measured HRIRs but require a much smaller number of parameters, which could eventually be derived from the anatomical characteristics of a prospective listener. For this first step, HRIRs must be decomposed into multiple delayed and scaled damped sinusoids which, in turn, reveal the parameters (delay and magnitude) necessary to create an instance of the structural model equivalent to the HRIR under analysis. Previously this type of HRIR decomposition has been accomplished through an exhaustive search of the model parameters. A new method that approaches the decomposition simultaneously in the frequency (Z) and time domains is reported here.

Known errors exist in loudspeaker array processing techniques, often degrading source localization and timbre. The goal of the present study was to use virtual loudspeaker arrays to investigate how treatment of the interaural time delay (ITD) cue from each loudspeaker impacts these errors. Virtual loudspeaker arrays rendered over headphones using head-related impulse responses (HRIRs) allow flexible control of array size. Here, three HRIR delay treatment strategies were evaluated using minimum-phase loudspeaker HRIRs: reapplying the original HRIR delays, applying the relative ITD to the contralateral ear, or separately applying the HRIR delays prior to virtual array processing. Seven array sizes were simulated, and panning techniques were used to estimate HRIRs from 3000 directions using higher-order Ambisonics, vector-base amplitude panning, and the closest loudspeaker technique. Compared to a traditional, physical array, the prior HRIR delay treatment strategy produced similar errors with a 95% reduction in the required array size. When compared to direct spherical harmonic (SH) fitting of head-related transfer functions (HRTFs), the prior delays strategy reduced errors in reconstruction accuracy of timbral and directional psychoacoustic cues. This result suggests that delay optimization can greatly reduce the number of virtual loudspeakers required for accurate rendering of acoustic scenes without SH-based HRTF representation.

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).

The interaural time delay (ITD) is a primary cue to lateral sound source direction and can be calculated from a head-related impulse response (HRIR). Although many ITD calculation techniques utilize cross-correlation, recent work suggests that for horizontal plane HRIRs, ITD calculation based on HRIR onset threshold may better match human perception of source location. The goal of the current study is to more comprehensively compare ITD calculation methods across a large sample of HRIRs. 2448 ITD calculation methods were compared using 42 240 HRIRs from the HUTUBS database (440 directions from 96 individuals). Within each method and individual, the calculated ITD function was compared to a spatially smoothed ITD function using a 10th-order spherical harmonic truncation. When large deviations from the smoothed version occurred (>250 μs), the method was tagged as being non-robust to calculation artifacts. Although the robustness of the onset threshold technique was found to be highly dependent upon threshold level and low-pass filter parameters, proper selection of these parameters resulted in little to no calculation artifacts and superior performance to other calculation methods. Improvements in the robustness of ITD calculation may help to optimize virtual auditory displays or HRIR personalization procedures using the minimum-phase plus ITD model.

Head-related transfer functions (HRTFs) describe the acoustical transmission process from a point sound source to two ears in the free field. They are vital to the researches of binaural hearing and virtual auditory display. Measurement is the most important approach to obtain HRTFs, but it is time-consuming. To accurate HRTF measurement, a computer-controlling measurement system is designed. The system consists of multiple sound sources at different elevations with a finest interval of 5° and a horizontal turntable with an azimuthal resolution of 0.1°. It is able to work in non-anechoic environment and suitable for both mannequin and human subject measurement. A practical example indicates that the system allows for measuring far-field HRTFs at 493 source directions within half an hour. By using the system, a super high directional resolution HRTF database for KEMAR mannequin is established. The database includes 3889 pairs of head-related impulse responses (HRIRs, the time domain counterpart of HRTFs) at distance of 1.0 m, elevation interval of 5° (from -45° to 90° ), and azimuthal interval of 2.5°. Each HRIR is 1024-point length at 96 kHz sampling frequency and 24-bit quantization. The database is applicable to the research on binaural hearing and virtual auditory display.

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 functions (HRTFs) vary with both frequency and source position. The near-field HRTFs with source distance less than 1.0 m are particularly complicated due to their distance dependence. Principal component analysis (PCA), which is conventionally carried out in the frequency or time domain, has been widely applied to reduce the dimensionality of far-field HRTF data with source distance greater than 1.0 m. The present work firstly extends the conventional PCA, and then proposes a spatial PCA method in the spatial domain rather than in the frequency or time domain to reduce the dimensionality of near-field HRTF data. An illustrative case indicates that near-field HRTF magnitudes at 9 distances with 493 directions for each distance can be approximately represented by the weighted sum of 15 spectral shape basis functions using the conventional PCA or the weighted sum of 15 spatial basis functions using the spatial PCA. Both representations account for more than 98 % energy variation of the original data, and reduce the dimensionality of the original data to about a quarter. The proposed method is also applicable to the head-related impulse responses in the time domain. Furthermore, the spatial PCA scheme is potentially applicable to simplify near-field HRTF measurement.

An adaptive feedback control scheme and a switching strategy for the output tracking stabilization of switched nonlinear systems with time-delay are presented by using RBF (radial basis function) neural network The RBF neural networks is used to compensate adaptively for the unknown nonlinear parts of switched nonlinear systems, and the approximation errors of RBF neural networks are introduced to the adaptive law in order to improve the tracking quality of the systems. The controller and switching strategy can guarantee asymptotic stability of tracking error for the overall system

In this paper, we propose a joint estimation method of two parameters for phase space reconstruction in chaotic time series, based on radial basis function (RBF) neural networks. And we obtain the best estimation values, according to some objective standards. Furthermore, The single-step and multi-step RBF prediction model is used to estimate the best embedding dimension and delay time, and Lorenz system is selected as an example. Finally, the estimation values are tested in the original model. The simulations show that we can obtain the best estimation values through the method, and the prediction accuracy is significantly improved.

This paper introduces a continuous functional model for head-related transfer functions (HRTFs) in the horizontal auditory scene. The approach uses a separable representation consisting of a Fourier-Bessel series expansion for the spectral components and a conventional Fourier series expansion for the spatial components. Being independent of the data, these two sets of basis functions remain unchanged for all subjects and measurement setups. Hence, the model can transform an individualized HRTF to a subject specific set of coefficients. A continuous functional model is also developed in the time domain. We show the efficient model performance in approximating experimental measurements by using the HRTF measurements from a KEMAR manikin and the synthetic data from the spherical head model. The statistical results are determined from a 50-subject HRTF data set. We also corroborate the predictive capability of the proposed model. The model has near optimal performance, which can be ascertained by comparison with the standard principle component analysis (PCA) and discrete Karhunen-Loeve expansion (KLE) methods at the measurement points and for a given number of parameters.

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.

Aiming at a nonlinear, time variant and time delay temperature control system in beer fermentation process, this paper presents an algorithm using internal model control based on RBF neural network. The internal model and the controller are represented by Radial Basis Function (RBF) neural network respectively. Simulation results show that the proposed algorithm has good properties in terms of robustness and transient.