Psychoacoustic experiments have shown that directional properties of the direct sound, salient reflections, and the late reverberation of an acoustic room response can have a distinct influence on the auditory perception of a given room. Spatial room impulse responses (SRIRs) capture those properties and thus are used for direction-dependent room acoustic analysis and virtual acoustic rendering. This work proposes a subspace method that decomposes SRIRs into a direct part, which comprises the direct sound and the salient reflections, and a residual, to facilitate enhanced analysis and rendering methods by providing individual access to these components. The proposed method is based on the generalized singular value decomposition and interprets the residual as noise that is to be separated from the other components of the reverberation. Large generalized singular values are attributed to the direct part, which is then obtained as a low-rank approximation of the SRIR. By advancing from the end of the SRIR toward the beginning while iteratively updating the residual estimate, the method adapts to spatio-temporal variations of the residual. The method is evaluated using a spatio-spectral error measure and simulated SRIRs of different rooms, microphone arrays, and ratios of direct sound to residual energy. The proposed method creates lower errors than existing approaches in all tested scenarios, including a scenario with two simultaneous reflections. A case study with measured SRIRs shows the applicability of the method under real-world acoustic conditions. A reference implementation is provided.

Spherical harmonic (SH) representations of sound fields are usually obtained from microphone arrays with rigid spherical baffles whereby the microphones are distributed over the entire surface of the baffle. We present a method that overcomes the requirement for the baffle to be spherical. Furthermore, the microphones can be placed along a circumferential contour around the baffle. This greatly reduces the required number of microphones for a given spatial resolution compared to conventional spherical arrays. Our method is based on the analytical solution for SH decomposition based on observations along the equator of a rigid sphere that we presented recently. It incorporates a calibration stage in which the microphone signals due to a suitable set of calibration sound fields are projected onto the SH decomposition of those same sound fields on the surface of a notional rigid sphere by means of a linear filtering operation. The filter coefficients are computed from the calibration data via a least/squares fit. We present an evaluation of the method based on the application of binaural rendering of the SH decomposition of the signals from an 18/element array that uses a human head as the baffle and that provides 8th ambisonic order. We analyse the accuracy and robustness of our method based on simulated data as well as based on measured data from a prototype.

We present a method for obtaining a spherical harmonic representation of a sound field based on a microphone array along the equator of a rigid spherical scatterer. The two-dimensional plane wave de-composition of the incoming sound field is computed from the microphone signals. The influence of the scatterer is removed under the assumption of distant sound sources, and the result is converted to a spherical harmonic (SH) representation, which in turn can be rendered binaurally. The approach requires an order of magnitude fewer microphones compared to conventional spherical arrays that operate at the same SH order at the expense of not being able to accurately represent non-horizontally-propagating sound fields. Although the scattering removal is not perfect at high frequencies at low harmonic orders, numerical evaluation demonstrates the effectiveness of the approach.

The measurement of directivity for sound sources that are not electroacoustic transducers is fundamentally limited because the source cannot be driven with arbitrary signals. A consequence is that directivity can only be measured at a sparse set of frequencies-for example, at the stable partial oscillations of a steady tone played by a musical instrument or from the human voice. This limitation prevents the data from being used in certain applications such as time-domain room acoustic simulations where the directivity needs to be available at all frequencies in the frequency range of interest. We demonstrate in this article that imposing the signature of the directivity that is obtained at a given distance on a spherical wave allows for all interpolation that is required for obtaining a complete spherical harmonic representation of the source's directivity, i.e., a representation that is viable at any frequency, in any direction, and at any distance. Our approach is inspired by the far-field signature of exterior sound fields. It is not capable of incorporating the phase of the directivity directly. We argue based on directivity measurement data of musical instruments that the phase of such measurement data is too unreliable or too ambiguous to be useful. We incorporate numerically-derived directivity into the example application of finite difference time domain simulation of the acoustic field, which has not been possible previously.

Additive noise produced by the recording hardware will contribute to streamed signals from spherical microphone arrays under practical conditions. For the application of binaural reproduction and under the assumption that the noise is uncorrelated between the array channels, the spectral properties and the overall level of the rendered noise in the ear signals have been shown to be strongly influenced by the configuration of the array as well as of the processing pipeline. In a previous investigation, we determined the audibility thresholds for changes in the rendered noise due to listener head rotations as a function of the differences in noise level of individual array channels. In this article, we calibrate the instrumental metric of Composite Loudness Level to the perceptual data and predict audibility of changes in the additive noise due to head rotations for a broad set of array configurations and distributions of the noise levels across array channels. We demonstrate that some types of microphone layouts can produce audible variations even if the noise level is equal in all channels. This is particularly the case for sampling grids that exhibit negative quadrature weights such as the Lebedev and Fliege-Maier grids for some spherical harmonic orders. The analysis of configurations with unevenly distributed noise contributions show that the influence of the noise from individual array channels is determined by the proximity of their virtual location to the relative trajectory of the ears.

Approaches for incorporating sound source directivity into wave-based room acoustic simulations using a spherical harmonic representation have been presented recently. Normally, the directivity is measured or prescribed on a spherical surface centered at the nominal source position. In wave-based simulations, this directivity can be represented through a locally-defined driving term acting at the source location. In practice, the directivity of real-world sound sources like musical instruments or industrial machinery can only be measured approximately in terms of spatial resolution and accuracy. We show that the measurement data can be augmented such that the impairments due to the limitations of the measurement accuracy are mitigated. We revisit the previously proposed approach of only using the angle-dependent magnitude of the measured directivity together with a spherical-wave propagation model and demonstrate its potential by means of numerical simulations based on two case studies.

Spherical microphone arrays are used to capture spatial sound fields, which can then be rendered via headphones. We use the Real-Time Spherical Array Renderer (ReTiSAR) to analyze and auralize the propagation of sensor self-noise through the processing pipeline. An instrumental evaluation confirms a strong global influence of different array and rendering parameters on the spectral balance and the overall level of the rendered noise. The character of the noise is direction independent in the case of spatially uniformly distributed noise. However, timbre of the rendered self-noise changes with head orientation in the case of spatially non-uniform noise. We determine audibility thresholds of the coloration artifact during head rotations for different array configurations in a perceptual user study.

The spatial decomposition method decomposes acoustic room impulse responses into a pressure signal and a direction of arrival for each time instant of the pressure signal. An acoustic space can be auralized by distributing the pressure signal over the available loudspeakers or head-related transfer functions so that the required instantaneous propagation direction is recreated. We present a user study that demonstrates based on binaural auralization that the arrival directions can be synthesized from random data such that the auralization is nearly indistinguishable from the auralization of the original data. The presented concept constitutes the fundament of a highly scalable spatialization method for omnidirectional room impulse responses.

We propose and evaluate an acoustic crosstalk canceler for binaural sound presentation based on an 8-channel linear loudspeaker array. The system uses traditional LSFI beamforming and path estimation in the mid and low frequency range, respectively. Simulations show a channel separation of around 40 dB over the vast part of the considered frequency range. The channel separation in a real-world implementation was measured to be 10 dB – 25 dB over a broadband spectrum of 250 Hz – 9000 Hz. When comparing localization precision of virtual binaural signals to ground-truth presentation with headphones, a 21 subject study revealed significantly higher localization precision (F(1) = 23.56; p0.001); task difficulty, timbre and spaciousness where rated the same accross both presentation methods. Robustness of the method was high and no fixation of the subjects' heads was applied.

Self-bending wave fields exhibit an envelope that seemingly bends in space under free-field conditions. They are created by wave fronts that fold along a caustic. In this paper, we invert the concept by exploiting the reciprocity principle of the Helmholtz equation in order to create a linear sensor array whose sensitivity seemingly bends in free space in the nearfield of the array. The sensor array therefore allows for listening around a distracting source, a jammer, or a physical object as sensitivity nulls can be placed at a defined distance. We illustrate the operating range and the robustness ofthe solution based on numerical simulations. For the presented scenario, an attenuation of more than 50 dB in a controllable region in space is achieved in a frequency range of more than two octaves.

Local sound field synthesis allows for synthesizing a given desired sound field inside a limited target region such that the field is free of considerable spatial aliasing artifacts. Spatial aliasing artifacts are a consequence of overlaps due to unavoidable repetitions of the space-spectral coefficients of the secondary source driving function. We analyze various conceivable analytic ways of restricting the bandwidth of the spatial spectrum of the driving function such that considerable overlapping is prevented: local spatial bandlimitation (A), spectral windowing (B), and local spatial band-limitation plus spectral windowing (C). While solution B is computationally significantly more efficient than A and C, it provides only limited control over the spatial location around which the aliasing-free region evolves. Solutions A and C provide more flexibility and higher accuracy whereby both achieve largely identical results so that the spectral windowing after the local spatial bandlimitation may be skipped. We present a detailed analysis of the properties of the spatial aliasing artifacts arising in the synthesis of a virtual plane wave. We establish a procedure for predicting the maximum possible size of the aliasing-free target region depending on its location and on the propagation direction of the desired sound field. The results can help reducing regularization in numerical solutions as they represent physical limitations that can be considered in the choice of parameters.

We propose a method for the synthesis of the magnitudes of Head-related Transfer Functions (HRTFs) using a sparse representation of anthropometric features. Our approach treats the HRTF synthesis problem as finding a sparse representation of the subject's anthropometric features w.r.t. the anthropometric features in the training set. The fundamental assumption is that the magnitudes of a given HRTF set can be described by the same sparse combination as the anthropometric data. Thus, we learn a sparse vector that represents the subject's anthropometric features as a linear superposition of the anthropometric features of a small subset of subjects from the training data. Then, we apply the same sparse vector directly on the HRTF tensor data. For evaluation purpose we use a new dataset, containing both anthropometric features and HRTFs. We compare the proposed sparse representation based approach with ridge regression and with the data of a manikin (which was designed based on average anthropometric data), and we simulate the best and the worst possible classifiers to select one of the HRTFs from the dataset. For instrumental evaluation we use log-spectral distortion. Experiments show that our sparse representation outperforms all other evaluated techniques, and that the synthesized HRTFs are almost as good as the best possible HRTF classifier.

Spherical microphone and circular microphone arrays are useful for sampling sound fields that may be resynthesized with loudspeaker arrays. Spherical microphone arrays are desirable because of their ability to capture three-dimensional sound fields, however it is often more practical to construct loudspeaker arrays in the form of a closed circle located in the horizontal plane. This leads to a spatial undersampling as such a circular sampling can only yield a perfect representation of a height-invariant sound field. This paper investigates the consequences of such spatial undersampling by converting between cylindrical and spherical harmonic decompositions of solutions to the wave equation. We show analytically and via numerical simulations that 1) the result of the spatial undersampling is a purely horizontally propagating sound field, and 2) the ratio of travelling and standing components in the undersampled sound field varies depending on the incidence colatitude. The conversion is also used in a beamforming scenario and shows that the beamformer response becomes increasingly omnidirectional as the source moves away from the horizontal plane.

The theory of sound field synthesis methods like Wave Field Synthesis (WFS) and Near-field Compensated Higher Order Ambisonics (NFC-HOA) may be formulated based on the assumption of continuous distributions of secondary sources that enclose the receiver area in the general case. In practice, a finite number of discrete loudspeakers is used, which constitutes a fundamental departure from the theoretical requirements. In this paper, we present a detailed analysis of the consequences of this spatial discretization on the synthesized sound field via an analytical frequency-dependent modal decomposition of the latter for the case of Gaussian sampling. It is shown that the underlying mechanisms are essentially similar to those in the discretization of circular secondary source distributions so that the results obtained in the latter context may be directly applied. The outstanding parallel in the discretization of spherical and circular distributions is the fact that in both cases, repetitions in a given space frequency domain occur. Therefore, the spatial bandwidth of the desired sound field has essential influence on the properties of the evolving artifacts. We propose to categorize sound field synthesis methods into spatially narrowband, wideband, and fullband approaches and show that NFC-HOA constitutes a spatially narrowband method and that WFS constitutes a spatially fullband method.

Methods like Wave Field Synthesis aim at the synthesis of a given desired sound field over a large receiver area. Practical limitations lead to considerable artifacts commonly referred to as spatial aliasing. Above a given frequency these artifacts are apparent anywhere in the receiver area when linear arrays of secondary sources are considered. This paper presents an analytical approach based on the Spectral Division Method which achieves an accuracy of the synthesized sound field which is significantly higher than in conventional approaches in a limited target zone. This local increase in accuracy is achieved via a manipulation of the spatial bandwidth of the secondary source driving function.

Head-related impulse responses (HRIRs), which are measured from an acoustic source to the left and right ear, characterize the acoustic properties of the outer ear. Due to the involved measurement effort, HRIRs are typically available only for source positions on a circle or surface of a sphere. Range extrapolation techniques aim at calculating HRIRs with a different source distance. A number of techniques have been proposed in the past which are based on expansions of HRIRs in terms of surface spherical harmonics. This paper presents an alternative approach which bases on the interpretation of a BRIR dataset as virtual loudspeaker array which is driven by Wave Field Synthesis in order to achieve range extrapolation.

We present an analytical approach targeting the physical reproduction of sound fields by means of linear distributions of loudspeakers. Unlike with conventional analytical approaches like wave field synthesis, the employed loudspeakers are not required to be omnidirectional. The approach does not compensate for loudspeaker properties which deviate from certain assumptions but it rather allows for the explicit consideration of these properties within some limits which are outlined.

In this paper, we consider physical reproduction of sound fields via planar and linear distributions of secondary sources (i.e., loudspeakers). The presented approach employs a formulation of the reproduction equation in spatial frequency domain which is explicitly solved for the secondary source driving signals. Wave field synthesis (WFS), the alternative formulation, can be shown to be equivalent under equal assumptions. Unlike the WFS formulation, the presented approach does not employ a far-field approximation when linear secondary source distributions are considered but provides exact results. We focus on the investigation of the spatial truncation and discretization of the secondary source distribution occurring in real-world implementations and present a rigorous analysis of evanescent and propagating components in the reproduced sound field.

Sound field reproduction methods like higher order Ambisonics which are based on orthogonal expansions always introduce a limitation of the spatial bandwidth of the secondary source driving function. This spatial truncation creates a sweet spot in the center of the secondary source distribution. This spot, or rather area, is ldquosweetrdquo both in terms of spatial aliasing artifacts as well as in terms of accuracy of the desired component of the reproduced wave field. The higher the temporal frequency of the reproduced wave field the smaller is the sweet spot. In this paper we show that the location sweet spot can be moved freely inside the secondary source distribution. The accuracy of the actual reproduced wave field is then significantly higher in the sweet spot than in the same region in the conventional approach.

In this paper, we introduce a direct manipulation tabletop multi-touch user interface for spatial audio scenes. Although spatial audio rendering exists for several decades now, mass market applications have not been developed and the user interfaces still address a small group of expert users. We implemented an easy-to-use direct manipulation interface for multiple users, taking full advantage of the object-based audio rendering mode. Two versions of the user interface have been developed to explore variations in information architecture and will be evaluated in user tests.

In this paper, we present the derivation and investigation of analytical expressions for the loudspeaker driving signals for higher order Ambisonics. The approach relies on the assumption of a continuous distribution of secondary sources on which sampling is performed to yield the actual loudspeaker signals for real-world implementations. For source-free volumes enclosed by the secondary source distribution, this formulation of Ambisonics leads to what is known as simple source approach. Since the simple source approach is theoretically well documented, we will depart from it and concentrate on the special case of a circular distribution of secondary point sources and derive analytical expressions for the driving signals. We furthermore derive a closed-form expression for the actual reproduced wave field for the circular secondary source distribution.

In multi-party teleconferencing, the transport of separate speech streams to a particular user and the subsequent spatial rendering of the different streams enables a more efficient communication. A simple means of spatial presentation at client side is that of binaural rendering and headphone presentation. For downwardcompatibility, e.g. when the transport mechanism does not support multiple parallel downlink streams, a system is proposed that combines an automatic speaker classification mechanism with a spatial rendering of the segregated streams. The combined system aims at a better separability of the speakers than conventional systems. The paper details the two basic components, namely automatic speaker classification, and binaural rendering. Based on a first evaluation of the approach, a proof of concept is provided, and directions for further improvement are discussed.