Auralization of Simulated Sound Fields 

by Jens Ahrens, Division of Applied Acoustics Chalmers University of Technology, 412 96 Gothenburg  Sweden 

Abstract 

Virtual prototyping and digital twin technologies keep gaining relevance in the design of products and spaces whose acoustic properties are important components of the design goals. Particularly wave-based simulations are becoming more popular in this context, which have the advantage being able to model acoustic phenomena like diffraction that a simpler approach like geometrical acoustics cannot model. Many acoustic properties cannot be measured numerically in a reliable manner so that auralization¹ of a virtual product or space is required so that human listeners can evaluate the signals.  

Spatial auralization of wave-based simulations is not straightforward because many spatial properties of the simulated sound field such as the propagation direction at a given time and location are not accessible in a tangible form. We present the open-source Chalmers Auralization Toolbox that auralizes simulated sound fields binaurally by observing the pressure and particle velocity on a suitable grid of locations to virtually place a human head into the acoustic simulation in post processing. The toolbox has been validated to produce perceptually transparent auralizations, i.e., it produces ear signals that are perceptually indistinguishable from the corresponding ground truth ear signals.  

1. Introduction 

Spatial auralization is very common in geometric room acoustic simulation, and all commercial simulation software packages provide such a functionality. Binaural auralization appears to be most popular format given that only a regular pair of headphones is required for playing back the auralization. 

Geometric acoustic principles make it straightforward to perform auralization as the spatial information like the incidence directions of the direct sound and the wall reflections are known in a tangible form. Binaural auralization, for example, consists essentially in filtering each such sound field component of the simulation with the head-related transfer function (HRTF) that corresponds to the direction of incidence of the component and summing up the result over all components to produce the output signals.  

Wave-based methods like finite element method, boundary element method, and finite-difference time-domain compute a sound pressure and/or particle velocity distribution over space. Wave-based simulations are useful for both for room acoustic simulation as well as for simulating sound radiation off vibrating surfaces in a virtual prototyping scenario. See Fig. 1 for an example of a volumetric simulation of a sound pressure field. Such data require a different approach for auralization compared to the geometric acoustics-based methods outlined above.  

Fig. 1: Example volumetric time-domain simulation of a sound pressure field computed with the discontinuous Galerkin method. Screenshot from COMSOL Multiphysics. Data are from [1].  

When binaural auralization is targeted, an option is to include the listener’s head into the simulation and simply playback the pressure signals over headphones that arise at the ear canal entrances of this virtual listener [2]. This is inconvenient because the simulation has to be computed from scratch for each head orientation that one intends to obtain.  

The alternative is sampling the sound field at a sufficient number of points and applying mathematical transforms that introduce the listener’s head into the sound field in post processing. The listener’s head is represented by HRTFs, and the result of the process is the ear signals that would arise at the listener’s ears if their head were exposed to the simulated sound field. The major advantages of this approach are the circumstances that the sound field needs to be simulated only once, and that the orientation of the listener’s head can be chosen arbitrarily in postprocessing so that the application of head tracking about arbitrary rotation axes is straightforward. The downside of this approach is that the acoustic scattering off the virtual listener is not present in the acoustic simulation. This circumstance appears to be tolerable in most situations. 

Such sampling-based auralization methods have been investigated in the academic community since about the middle of the 2000s. Examples for early works are [3,4,5], but it was not until recently that the relevant simulation methods had become so capable that auralization became relevant.  

2. The Chalmers Auralization Toolbox 

We created the Chalmers Auralization Toolbox to support research on the matter. It comprises MATLAB implementions of all previously published (and more) methods for sampling-based auralization of sound fields. It also comes with a variety of binaural audio examples. The methods that the toolbox provides can perform auralization based on three different geometries of the sampling grid, which are depicted in Fig. 2. 

Fig. 2: Example sampling grids: Volumetric (343 points), cubical surface (150 pairs of points), and spherical surface (100 pairs of points). The blue dots denote pressure sampling points, and the orange dots denote coincident particle velocity sampling points. Surface sampling can also be performed using two layers of pressure sampling points instead of one layer of pressure and particle velocity. The optimal dimensions for all sampling grid geometries are slightly smaller than those of a human head. 

3. Status of the Work 

The main goal of our work on the Chalmers Auralization Toolbox has been the perceptual validation of the toolbox for signals that cover the entire audible frequency range. We were able to prove that perceptually transparent auralization is indeed possible with the methods that are implemented in the toolbox if the sound pressure and particle velocity are observed at a few hundred locations each in a portion of space that is slightly smaller than a human head [6].  

We want to emphasize that the listening experiment employed a direct comparison between the different stimuli to guarantee that any kind of audible differences would be detectable by the subjects. Such a paradigm may be considered stricter than necessary in many practical applications. For example, the requirements for perceptual transparency appear to be considerably more relaxed if a pause of, say, 1 s is introduced between listening to the ground truth and the auralization. Certain differences that may be perceivable in a direct comparison can turn imperceivable if such a pause is introduced. Similarly, providing perceptual transparency over the entire audible frequency range may not be necessary in many applications because the simulation is carried out only in a limited frequency range, or because the simulation method may introduce uncertainty at high frequencies. Such circumstances reduce the required number of sampling point of the simulated sound field significantly. As an example, the study in [7] auralized car pass-bys in the frequency range below 5 kHz, and the auralization employed 81 sampling points of pressure and particle velocity each. 

The Chalmers Auralization Toolbox automatically computes example auralizations as well as the corresponding ground truth ear signals for each sampling grid that one selects. The user that thereby evaluate the suitability of the auralization for the given purpose straightforwardly. 

4. Final Remarks 

We highlight that the Chalmers Auralization Toolbox is not intended to be a production tool but rather a reference implementation for research and benchmarking. The main output of the toolbox is a set of filters that need to be applied to the sound field data to perform the auralization. It may be worth for users considering integrating this filtering operation into one’s preferred room acoustic simulation framework. This way, the toolbox is only needed once to create the auralization filters. Everything else can then be carried out by the simulation framework. 

5. Resources 

MATLAB implementation:  

https://github.com/AppliedAcousticsChalmers/auralization-toolbox

Binaural audio examples:  

References 

[1] COMSOL Multiphysics application example, “Wave-Based Time-Domain Room Acoustics with Frequency-Dependent Impedance,” https://www.comsol.com/model/wave-based-time-domain-room-acoustics-with-frequency-dependent-impedance-90551 , accessed May 6, 2024. 

[3] B. Støfringsdal and U.P. Svensson, “Conversion of Discretely Sampled Sound Field Data to Aualization Formats,” J. Audio. Eng. Soc. 54(5), pp. 380-400 (May 2006) 

[4] I. Balmages and B. Rafaely, “Open-sphere designs for spherical microphone arrays,” IEEE TASLP, vol. 15, no. 2, pp. 727– 732 (2007) 

[5] M. A. Poletti and U. P. Svensson, “Beamforming Synthesis of Binaural Responses From Computer Simulations of Acoustic Spaces,” J. Acoust. Soc. Am. 124, pp. 301–315 (2008) 

[6] Jens Ahrens, “Perceptually Transparent Binaural Auralization of Simulated Sound Fields”,  https://arxiv.org/abs/2412.05015  

[7] Müller, L. Ahrens, J. & Kropp, W., “Loudspeaker Array-Based Auralization of Electric Vehicle Noise in Living Environments,” Forum Acusticum 2025. (Audio examples are available at https://zenodo.org/records/15102179)