Interaural cross correlation in a sound field represented by spherical harmonics

The head-related transfer function(HRTF) is an essential part of spatial auditory display systems. In recent years, numerous HRTF databases are established to include human subjects' measurements, which enabled data-driven research projects such as HRTF prediction and personalization. However, in most cases, each HRTF database has its own unique measuring standard and source direction grid set. It's difficult to merge and efficiently represent the global HRTF information across multiple HRTF databases. Current presentation methods, such as principle component analysis (PCA) and spherical harmonics transform (SHT), are constrained by the source grid layout and regularization errors, which lays burdens for common feature extraction from different sets of HRTF measurements. In this work, we propose a novel approach for the global compact representation of HRTFs across different measuring standards, using hemispherical harmonics (HSH) and conformal mapping. The method takes into account the spatial domain covered by the typical HRTF measurements and proves to be less contained by the source direction grids. Both numerical and auditory model experiments are performed, to examine the representation error and consistency when including multiple HRTF databases with different measuring standards and grid layouts. In continuing work, we are using this method as a pre-processing approach for HRTF personalization utilizing multiple HRTF databases.

The area of sound field synthesis has significantly advanced in the past decade, facilitated by the development of high-quality sound-field capturing and re-synthesis systems. Spherical microphone arrays are among the most recently developed systems for sound field capturing, enabling processing and analysis of three-dimensional sound fields in the spherical harmonics domain. In spite of these developments, a clear relation between sound fields recorded by spherical microphone arrays and their perception with a re-synthesis system has not yet been established, although some relation to scalar measures of spatial perception was recently presented. This paper presents an experimental study of spatial sound perception with the use of a spherical microphone array for sound recording and headphone-based binaural sound synthesis. Sound field analysis and processing is performed in the spherical harmonics domain with the use of head-related transfer functions and simulated enclosed sound fields. The effect of several factors, such as spherical harmonics order, frequency bandwidth, and spatial sampling, are investigated by applying the repertory grid technique to the results of the experiment, forming a clearer relation between sound-field capture with a spherical microphone array and its perception using binaural synthesis regarding space, frequency, and additional artifacts. The experimental study clearly shows that a source will be perceived more spatially sharp and more externalized when represented by a binaural stimuli reconstructed with a higher spherical harmonics order. This effect is apparent from low spherical harmonics orders. Spatial aliasing, as a result of sound field capturing with a finite number of microphones, introduces unpleasant artifacts which increased with the degree of aliasing error.

The spherical harmonic decomposition can be applied to present realistically localized sound sources over headphones. The acoustic field, measured by a spherical microphone array, is first decomposed into a weighted sum of spherical harmonics evaluated at the microphone positions. The resulting decomposition is used to generate a set of virtual sources at various angles. The virtual sources are thus binaurally presented by applying the corresponding head-related transfer functions (HRTF). Reproduction accuracy is heavily dependent on the spatial distribution of microphones and virtual sources. Nearly-uniform sphere samplings are used in positioning the microphones so as to improve spatial accuracy. However, no previous studies have looked into the optimal arrangement for the virtual sources. We evaluate the effects of the virtual source distribution on the accuracy of the synthesized HRTF. Furthermore, our study considers the impact of spatial aliasing for a 252-channel spherical microphone array. The microphone's body is modeled as a human-head-sized rigid sphere. We evaluate the synthesis error by comparison with the target HRTF using the logarithmic spectral distance. Our study finds that 362 virtual sources, distributed on an icosahedral grid, can synthesize the HRTF in the horizontal plane up to 9 kHz with a log-spectral distance below 5 dB.

Several approaches to data-based binaural synthesis have been published that process the sound field captured by a spherical microphone array. The captured sound field is typically decomposed into plane waves which are then auralized using head-related transfer functions. The decomposition into plane waves is often based upon modal beamforming techniques which represent the sound field with respect to surface spherical harmonics. The achievable spatial bandwidth is limited due to practical considerations. This paper investigates the perceptual implications of these limitations in the context of data-based binaural synthesis.

Spherical microphone arrays (SMAs) are widely used to capture spatial sound fields that can then be rendered in various ways as a virtual acoustic environment (VAE) including headphone-based binaural synthesis. Several practical limitations have a significant impact on the fidelity of the rendered VAE. The finite number of microphones of SMAs leads to spatial undersampling of the captured sound field, which, on the one hand, induces spatial aliasing artifacts and, on the other hand, limits the order of the spherical harmonics (SH) representation. Several approaches have been presented in the literature that aim to mitigate the perceptual impairments due to these limitations. In this article, we present a listening experiment evaluating the perceptual improvements of binaural rendering of undersampled SMA data that can be achieved using state-of-the-art mitigation approaches. In particular, we examined the Magnitude Least-Squares algorithm, the Bandwidth Extraction Algorithm for Microphone Arrays, Spherical Head Filters, SH Tapering, and a newly proposed equalization filter. In the experiment, subjects rated the perceived differences between a dummy head and the corresponding SMA auralization. We found that most mitigation approaches lead to significant perceptual improvements, even though audible differences to the reference remain.

We propose a method to reproduce 3D auditory scenes captured by spherical microphone arrays over headphones. This algorithm employs expansions of the captured sound and the head related transfer function over the sphere and uses the orthonormality of the spherical harmonics. Using a spherical microphone array, we first record the 3D auditory scene, then the recordings are spatially filtered and reproduced through headphones in the orthogonal beam-space of the head related transfer functions (HRTFs). We use the KEMAR HRTF measurements to verify our algorithm. In experiments, we use a hemispherical array for recording. The reproduction results are posted online.

Estimation of the direction of arrival (DOA) of reflections in a room using spherical microphone arrays can be performed using several methods such as plane-wave decomposition, and delay-and-sum beamforming, for which the resolution of the estimation process is usually bounded by the array order, or the number of microphones. In this paper a method for DOA estimation of the reflections in a room using room impulse-response data and spherical microphone arrays is presented, in which only a first order microphone array is required. The proposed method uses signal processing in the spherical harmonics domain, utilizing an analytical dependence of the spherical harmonic coefficients on different acoustics parameters. It is shown that the zero order spherical harmonics coefficients is a function of the time delays and amplitudes of the planes waves composing the sound field, while the first order coefficients are a function of the time delays, amplitudes and the elevation and azimuth components of the wave arrival direction. Using this property leads to the development of an estimator based on the least-squares approach, in which each order is used to estimate a single sound-field parameter.

From the Contents: An Introduction to Binaural Processing.- The Auditory-modeling Toolbox.- Acquisition and Representation of Head-related Transfer Functions.- Binaural Analysis of Complex Listening Environments.- Binaural Scene Analysis with Multi-dimensional Statistical Filters.- Extracting Room and Source-distance Information from Binaural.-Binaural Evaluation of Auditory Scenes Using Head Movements.- Binaural Systems in Robotics.- Binaural Assessment of Multi-channel Reproduction.- Optimization and Assessment of Binaural Algorithms for Hearing.

Subjective preference tests with a simulated single reflection in an anechoic chamber were conducted in order to get a knowledge of the preferred properties of sound fields. The degree of preference in relation to a long-time autocorrelation function of source signal and the interaural cross correlation of the sound field is discussed here. The preferred time delay gap between the direct sound and the first echo can be determined by the coherence of autocorrelation function and the amplitude of the echo. The preferred echo direction to a listener may be obtained by minimizing the interaural cross correlation which relates to the ’’subjective diffuseness.’’ Results of the autocorrelation function, which was measured with an A-weighting filter, and the interaural cross correlation are presented for several music motifs. convection velocity and wavelength. The vortex strength, convection

The influence of GL (amplifier gain the low-frequency range below 355 Hz) and IACC on ASW was determined by psychoacoustic experiments with simulated concert-hall sound fields using anechoic symphonic music presented to subjects by multiple loudspeakers. ‘‘Equal ASW curves’’ were determined for 1/1 octave band filtered source signals with mid-frequencies from 125 to 4000 Hz. The ASW’s for the upper four bands are found to be equal for the same IACC and SPL band values, indicating equal importance of those bands in determining overall ASW’s. Combinations of GL’s and IACCE3’s (average of IACC’s in the 500, 1 and 2 kHz bands) for wide-band musical source signals were determined that produced the same ASW’s. The early sound was comprised of 2 to 11 early ‘‘reflections’’ and judgments were made with and without later reverberation. It was found that both larger values of GL and smaller values of IACCE3 result in larger values of the subjectively determined ASW’s. It is shown that GL and IACCE3 jointly are physical measures of spatial impression in a concert hall and that, combined, they cover the frequency range from low to high frequencies.

An apparatus for implementing a 3-dimensional virtual sound and method thereof are disclosed, in which computational and storage complexity are reduced, in which system stability is secured, and by which the 3-dimensional virtual sound can be implemented in such a mobile platform failing to be equipped with expensive instruments for the implementation of the 3-dimensional sound as a mobile communication terminal and the like. The present invention includes a first step of giving an inter-aural time delay (ITD) to at least one input sound signal, a second step of multiplying output signals of the first step by principal component weight, and a third step of filtering result values of the second step by a plurality of low-order approximated IIR filter models of basis vectors extracted from a head related transfer function (HRTF). The basis vectors, extracted from the head related transfer function database are approximated using balanced model approximation technique.

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.

Spherical microphone arrays have been recently studied for sound-field recordings, beamforming, and sound-field analysis which use spherical harmonics in the design. Although the microphone arrays and the associated algorithms were presented, no comprehensive theoretical analysis of performance was provided. This work presents a spherical-harmonics-based design and analysis framework for spherical microphone arrays. In particular, alternative spatial sampling schemes for the positioning of microphones on a sphere are presented, and the errors introduced by finite number of microphones, spatial aliasing, inaccuracies in microphone positioning, and measurement noise are investigated both theoretically and by using simulations. The analysis framework can also provide a useful guide for the design and analysis of more general spherical microphone arrays which do not use spherical harmonics explicitly.

Using spherical microphone arrays to form directed beams is becoming an important technology in sound field analysis, teleconferencing, and surveillance systems. Moreover, in scenarios for capturing musical content, the recording and post-production process could be simplified through flexible beamforming technology. Often, audio engineers favor the use of conventional recording microphones over spherical microphone arrays which might be due to the engineer's preference for distinct spatial and timbral characteristics of different microphone types and brands. We present an approach to create beamforming pattern using a 144 channel spherical microphone array, which aims to match the distinct spatial and timbral characteristics of classic microphones. For this, we first measured the spatial and timbral characteristics of several classic microphones types as well as the characteristics of our spherical microphone array in an anechoic chamber. Using a regularized least-square approach, these data were then used for computing the filters for the spherical microphone array that forms the desired beams. We show the results of several microphone-beam simulations and compare them with the impulse responses of the original classic microphones. Advantages and limitations of our approach will be discussed.

While various methods for sound source localization have been developed, most of them utilize on the time difference of arrival (TDOA) between microphones or the measured head related transfer functions (HRTF). In case of a real robot implementation, the former has a merit of light computation load to estimate the sound direction but can not consider the effect of platform on TDOAs, while the latter can, because characteristics of robot platform are included in HRTF. However, the latter needs large resources for the HRTF database of a specific robot platform. We propose the compensation method which has the light computation load while the effect of platform on TDOA can be taken into account. The proposed method is used with spherical head related transfer function (SHRTF) on the assumption that robot platform, for example a robot head, installed microphones can be modeled to a sphere. We verify that the proposed method decreases the estimation error caused by the robot platform through the simulation.