Numerical simulations of near-field head-related transfer functions: Magnitude verification and validation with laser spark sources.

Despite possessing an increased perceptual significance, near-field head-related transfer functions (nf-HRTFs) are more difficult to acquire compared to far-field head-related transfer functions. If properly validated, numerical simulations could be employed to estimate nf-HRTFs: the present study aims to validate the usage of wave-based simulations in the near-field. A thorough validation study is designed where various sources of error are investigated and controlled. The present work proposes the usage of a highly-omnidirectional laser-induced breakdown (LIB) of air as an acoustic point source in nf-HRTF measurements. Despite observed departures from the linear regime of the LIB pressure pulse, the validation results show that asymptotically-estimated solutions to a lossless model (wave-equation and rigid boundaries) agree in magnitude with the LIB-measured nf-HRTF of a rigid head replica approximately within 1-2 dB up to about 17 kHz. Except a decreased reliability in notch estimation, no significant shortcoming of the continuous model is found relative to the measurements below 17 kHz. The study also shows the difficulty in obtaining accurate surface boundary impedance values for accurate validation studies.

Pinna-related transfer functions and lossless wave equation using finite-difference methods: Validation with measurements.

Nowadays, wave-based simulations of head-related transfer functions (HRTFs) lack strong justifications to replace HRTF measurements. The main cause is the complex interactions between uncertainties and biases in both simulated and measured HRTFs. This paper deals with the validation of pinna-related high-frequency information in the ipsilateral directions-of-arrival, computed by lossless wave-based simulations with finite-difference models. A simpler yet related problem is given by the pinna-related transfer function (PRTF), which encodes the acoustical effects of only the external ear. Results stress that PRTF measurements are generally highly repeatable but not necessarily easily reproducible, leading to critical issues in terms of reliability for any ground truth condition. On the other hand, PRTF simulations exhibit an increasing uncertainty with frequency and grid-dependent frequency changes, which are here quantified analyzing the benefits in the use of a unique asymptotic solution. In this validation study, the employed finite-difference model accurately and reliably predict the PRTF magnitude mostly within ±1 dB up to ≈8 kHz and a space- and frequency-averaged spectral distortion within about 2 dB up to ≈ 18 kHz.

Pinna-related transfer functions and lossless wave equation using finite-difference methods: Verification and asymptotic solution.

A common approach when employing discrete mathematical models is to assess the reliability and credibility of the computation of interest through a process known as solution verification. Present-day computed head-related transfer functions (HRTFs) seem to lack robust and reliable assessments of the numerical errors embedded in the results which makes validation of wave-based models difficult. This process requires a good understanding of the involved sources of error which are systematically reviewed here. The current work aims to quantify the pinna-related high-frequency computational errors in the context of HRTFs and wave-based simulations with finite-difference models. As a prerequisite for solution verification, code verification assesses the reliability of the proposed implementation. In this paper, known and manufactured formal solutions are used and tailored for the wave equation and frequency-independent boundary conditions inside a rectangular room of uniform acoustic wall-impedance. Asymptotic estimates for pinna acoustics are predicted in the frequency domain based on regression models and a convergence study on sub-millimeter grids. Results show an increasing uncertainty with frequency and a significant frequency-dependent change among computations on different grids.

Boundary absorption approximation in the spatial high-frequency extrapolation method for parametric room impulse response synthesis.

The spatial high-frequency extrapolation method extrapolates low-frequency band-limited spatial room impulse responses (SRIRs) to higher frequencies based on a frame-by-frame time/frequency analysis that determines directional reflected components within the SRIR. Such extrapolation can be used to extend finite-difference time domain (FDTD) wave propagation simulations, limited to only relatively low frequencies, to the full audio band. For this bandwidth extrapolation, a boundary absorption weighting function is proposed based on a parametric approximation of the energy decay relief of the SRIR used as the input to the algorithm. Results using examples of both measured and FDTD simulated impulse responses demonstrate that this approach can be applied successfully to a range of acoustic spaces. Objective measures show a close approximation to reverberation time and acceptable early decay time values. Results are verified through accompanying auralizations that demonstrate the plausibility of this approach when compared to the original reference case.

Audibility of dispersion error in room acoustic finite-difference time-domain simulation in the presence of a single early reflection.

Finite-difference time-domain method has gained increasing interest for room acoustic prediction use. A well-known limitation of the method is a frequency- and direction-dependent dispersion error. In this study, the audibility of dispersion error in the presence of a single surface reflection is measured. The threshold is measured for three different distance conditions with a fixed reflection arrival azimuth angle of 54.7°. The error is placed either in the direct path, or in the reflection path. Additionally a qualitative follow-up experiment to evaluate how the measured thresholds reflect the audibility of error in short room responses is carried out. The results indicate that the threshold varies depending whether the error is in the direct path or in the reflection path. For transient signals the threshold is higher when the error is located in the direct path, whereas for speech signal, the threshold is higher when it is located in the reflection path. Evidence is found that the error is detectable in rendered room responses at the measured threshold levels.

Introduction to the Special Issue on Room Acoustic Modeling and Auralization.

This Special Issue on Room Acoustic Modeling and Auralization contains nineteen research papers. A majority of the papers focus on various room acoustic simulation techniques, while the remaining ones concentrate on auralization of either simulation or measurement results. Using room acoustic simulation, the last paper in this issue presents a case study of the historic venue, Palais du Trocadero in Paris, France.

Spatial analysis of modal time evolution in room acoustics.

Time-domain simulation methods allow the observation of the state of the simulation domain at each discrete time step. In this work an approach to analyze the progress of the sound field in the simulation domain using time-windowing and spectrum analysis is presented. The method makes it possible to analyze the effect of geometric structures into the spatiotemporal distribution of energy in the domain at a frequency range of interest. Several examples are presented.

Memory cost of absorbing conditions for the finite-difference time-domain method.

Three absorbing layers are investigated using standard rectilinear finite-difference schemes. The perfectly matched layer (PML) is compared with basic lossy layers terminated by two types of absorbing boundary conditions, all simulated using equivalent memory consumption. Lossy layers present the advantage of being scalar schemes, whereas the PML relies on a staggered scheme where both velocity and pressure are split. Although the PML gives the lowest reflection magnitudes over all frequencies and incidence angles, the most efficient lossy layer gives reflection magnitudes of the same order as the PML from mid- to high-frequency and for restricted incidence angles.

Influence of voxelization on finite difference time domain simulations of head-related transfer functions.

The scattering around the human pinna that is captured by the Head-Related Transfer Functions (HRTFs) is a complex problem that creates uncertainties in both acoustical measurements and simulations. Within the simulation framework of Finite Difference Time Domain (FDTD) with axis-aligned staircase boundaries resulting from a voxelization process, the voxelization-based uncertainty propagating in the HRTF-captured sound field is quantified for one solid and two surface voxelization algorithms. Simulated results utilizing a laser-scanned mesh of Knowles Electronics Manikin for Acoustic Research (KEMAR) show that in the context of complex geometries with local topology comparable to grid spacing such as the human pinna, the voxelization-related uncertainties in simulations emerge at lower frequencies than the generally used accuracy bandwidths. Numerical simulations show that the voxelization process induces both random error and algorithm-dependent bias in the simulated HRTF spectral features. Frequencies fr below which the random error is bounded by various dB thresholds are estimated and predicted. Particular shortcomings of the used voxelization algorithms are identified and the influence of the surface impedance on the induced errors is studied. Simulations are also validated against measurements.

Audibility of dispersion error in room acoustic finite-difference time-domain simulation as a function of simulation distance.

Finite-difference time-domain (FDTD) simulation has been a popular area of research in room acoustics due to its capability to simulate wave phenomena in a wide bandwidth directly in the time-domain. A downside of the method is that it introduces a direction and frequency dependent error to the simulated sound field due to the non-linear dispersion relation of the discrete system. In this study, the perceptual threshold of the dispersion error is measured in three-dimensional FDTD schemes as a function of simulation distance. Dispersion error is evaluated for three different explicit, non-staggered FDTD schemes using the numerical wavenumber in the direction of the worst-case error of each scheme. It is found that the thresholds for the different schemes do not vary significantly when the phase velocity error level is fixed. The thresholds are found to vary significantly between the different sound samples. The measured threshold for the audibility of dispersion error at the probability level of 82% correct discrimination for three-alternative forced choice is found to be 9.1 m of propagation in a free field, that leads to a maximum group delay error of 1.8 ms at 20 kHz with the chosen phase velocity error level of 2%.

Audibility of dispersion error in room acoustic finite-difference time-domain simulation in the presence of absorption of air.

The finite-difference time-domain method has gained increasing interest for room acoustic prediction use. A well-known limitation of the method is a frequency and direction dependent dispersion error. In this study, the audibility of dispersion error in the presence of air absorption is measured. The results indicate that the dispersion error in the worst-case direction of the studied scheme gets masked by the air absorption at a phase velocity error percentage of 0.28% at the frequency of 20 kHz.

Overview of geometrical room acoustic modeling techniques.

Computerized room acoustics modeling has been practiced for almost 50 years up to date. These modeling techniques play an important role in room acoustic design nowadays, often including auralization, but can also help in the construction of virtual environments for such applications as computer games, cognitive research, and training. This overview describes the main principles, landmarks in the development, and state-of-the-art for techniques that are based on geometrical acoustics principles. A focus is given to their capabilities to model the different aspects of sound propagation: specular vs diffuse reflections, and diffraction.

Extension of a spectral time-stepping domain decomposition method for dispersive and dissipative wave propagation.

For time-domain modeling based on the acoustic wave equation, spectral methods have recently demonstrated promise. This letter presents an extension of a spectral domain decomposition approach, previously used to solve the lossless linear wave equation, which accommodates frequency-dependent atmospheric attenuation and assignment of arbitrary dispersion relations. Frequency-dependence is straightforward to assign when time-stepping is done in the spectral domain, so combined losses from molecular relaxation, thermal conductivity, and viscosity can be approximated with little extra computation or storage. A mode update free from numerical dispersion is derived, and the model is confirmed with a numerical experiment.

Optimization of absorption placement using geometrical acoustic models and least squares.

Given a geometrical model of a space, the problem of optimally placing absorption in a space to match a desired impulse response is in general nonlinear. This has led some to use costly optimization procedures. This letter reformulates absorption assignment as a constrained linear least-squares problem. Regularized solutions result in direct distribution of absorption in the room and can accommodate multiple frequency bands, multiple sources and receivers, and constraints on geometrical placement of absorption. The method is demonstrated using a beam tracing model, resulting in the optimal absorption placement on the walls and ceiling of a classroom.

Effects of sources on time-domain finite difference models.

Recent work on excitation mechanisms in acoustic finite difference models focuses primarily on physical interpretations of observed phenomena. This paper offers an alternative view by examining the properties of models from the perspectives of linear algebra and signal processing. Interpretation of a simulation as matrix exponentiation clarifies the separate roles of sources as boundaries and signals. Boundary conditions modify the matrix and thus its modal structure, and initial conditions or source signals shape the solution, but not the modal structure. Low-frequency artifacts are shown to follow from eigenvalues and eigenvectors of the matrix, and previously reported artifacts are predicted from eigenvalue estimates. The role of source signals is also briefly discussed.

Acoustic visualizations using surface mapping.

Sound visualizations have been an integral part of room acoustics studies for more than a century. As acoustic measurement techniques and knowledge of hearing evolve, acousticians need more intuitive ways to represent increasingly complex data. Microphone array processing now allows accurate measurement of spatio-temporal acoustic properties. However, the multidimensional data can be a challenge to display coherently. This letter details a method of mapping visual representations of acoustic reflections from a receiver position to the surfaces from which the reflections originated. The resulting animations are presented as a spatial acoustic analysis tool.

Modeling incoherent reflections from rough room surfaces with image sources.

Reflections at rough surfaces change the temporal structure of the reflected signal. This paper shows how to incorporate this temporal behavior in geometric room acoustics modeling. Specifically, a beam tracer is used for calculating the image sources and reflection paths. The roughness of the surfaces is taken into account in post-processing. A single reflection is assumed to distribute the energy according to an exponential function in time based on Biot's rough surface modeling theory. Multiple reflections are modeled with convolutions of exponential functions which are approximated as gamma functions.

Engaging concert hall acoustics is made up of temporal envelope preserving reflections.

Strong, exciting, and engaging sound is perceived in the best concert halls. Here, it is shown that wideband early reflections that preserve the temporal envelope of sound contribute to the clear and open acoustics with strong bass. Such reflections are fused with the direct sound due to the precedence effect. In contrast, reflections that distort the temporal envelope render the sound weak and muddy because they partially break down the precedence. The presented findings are based on the earlier psychoacoustics research, and confirmed by a perceptual evaluation with six simulated concert halls that have same monaural room acoustical parameter values according to ISO3382-1.

The room acoustic rendering equation.

An integral equation generalizing a variety of known geometrical room acoustics modeling algorithms is presented. The formulation of the room acoustic rendering equation is adopted from computer graphics. Based on the room acoustic rendering equation, an acoustic radiance transfer method, which can handle both diffuse and nondiffuse reflections, is derived. In a case study, the method is used to predict several acoustic parameters of a room model. The results are compared to measured data of the actual room and to the results given by other acoustics prediction software. It is concluded that the method can predict most acoustic parameters reliably and provides results as accurate as current commercial room acoustic prediction software. Although the presented acoustic radiance transfer method relies on geometrical acoustics, it can be extended to model diffraction and transmission through materials in future.