Being curious about numerical simulations in acoustics using the Finite Element Method (FEM), we started to compile a series of jupyter notebooks providing some insight into the theory, implementation as well as simulation results. The notebooks are available on Github https://github.com/spatialaudio/computational_acoustics.
If you just want to take a brief look, follow the ‘view it on nbviewer’ links in the Readme for a non-interactive view on the notebooks. We are planning to add notebooks on other methods of computational acoustics in the future.
Firtha, G.; Fiala, P.; Schultz, F.; Spors, S. (2018): “On the General Relation of Wave Field Synthesis and Spectral Division Method for Linear Arrays.” In: IEEE/ACM Trans. Audio Speech Language Process., 26(12):2393-2403 https://doi.org/10.1109/TASLP.2018.2865091
was recently published. The topic is also covered in Gergely Firtha’s dissertation in chapter 4, please see his open access project https://github.com/gfirtha/gfirtha_phd_thesis
Sound field synthesis aims at the reproduction of an arbitrary target sound field over an extended listening area applying a densely spaced loudspeaker ensemble. Two basic analytic methodologies—the explicit and the implicit—exist in order to derive the required loudspeaker driving functions. The explicit solution aims at the direct solution of the involved integral equation describing the general sound field synthesis problem, resulting in driving functions in the form of a spectral integral. The implicit solution extracts the driving function from an appropriate boundary integral representation of the target sound field. So far the relationship between two approaches was investigated for target field specific synthesis scenarios. For linear arrays this paper introduces a high-frequency approximation for the explicit solution resulting in a novel, purely spatial domain formulation of the direct approach. The presented driving functions allow the synthesis of an arbitrary virtual sound field, optimizing the reproduction on an arbitrary reference line. It is furthermore shown that for an arbitrary virtual sound field, the implicit solution constitutes a high-frequency approximation of the explicit method.
Winter, F.; Wierstorf, H.; Hold C.; Krüger, F.; Raake A.; Spors, S. (2018), “Colouration in Local Wave Field Synthesis,” In: IEEE/ACM Transactions on Audio, Speech, and Language Processing, vol. 26, no. 10
Abstract: Sound Field Synthesis techniques including Wave Field Synthesis and Near-Field-Compensated Higher Order Ambisonics aim at a physically accurate reproduction of a desired sound field inside an extended listening area. This area is surrounded by loudspeakers individually driven by their respective driving signals. The latter have to be chosen such that the superposition of all emitted sound fields coincides with the desired one. Due to practical limitations, artefacts impair the synthesis accuracy resulting in a perceivable change in timbre. Recently, two approaches to so-called Local Wave Field Synthesis were published which enhance the reproduction accuracy in a limited region while allowing stronger artefacts outside. This work reports on two listening experiments comparing conventional techniques for Sound Field Synthesis with the mentioned approaches. Furthermore, the influence of different parametrisations for Local Wave Field Synthesis is investigated. The results show that the enhanced reproduction accuracy in Local Wave Field Synthesis leads to a reduction of perceived colouration, if a suitable parametrisation is chosen.
Winter, F.; Ahrens, J.; Spors, S. (2018): “A Geometric Model for Spatial Aliasing in Wave Field Synthesis.” In: German Annual Conference on Acoustics (DAGA).
The poster and additional material can be found here.
Abstract: Wave Field Synthesis aims at a physically accurate synthesis of a desired sound field inside a target region. Typically, the region is surrounded by a finite number of discrete loudspeakers. For practical loudspeaker setups, this spatial sampling causes spatial aliasing artefacts and does not allow for an accurate synthesis over the entire audible frequency range. In the past, different theoretical treatises of the spatial sampling process for simple loudspeaker geometries, e.g. lines and circles, led to anti-aliasing criteria independent of listener’s position inside a target region. However, no inference about the spatial phenotype of the aliasing artefacts could be made by this models. This work presents a geometrical model based on high-frequency approximations of the underlying theory to describe the spatial occurrence and the propagation direction of the additional wave fronts caused by spatial aliasing. Combined with a ray-tracing algorithm, it can be used to predict position-dependent spatial aliasing artefacts for any convex loudspeaker geometry.
Winter, F.; Hold, C.; Wierstorf, H.;Raake A.; Spors, S. (2017): “Colouration in 2.5D local wave field synthesis using spatial bandwidth-limitation.” In: 2017 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA).
The poster and additional material can be found here.
Abstract: Sound Field Synthesis techniques, such as Wave Field Synthesis aim at a physically accurate reproduction of a desired sound field inside an extended listening area. This area is surrounded by loudspeakers individually driven by their respective driving signals. Due to practical limitations, artefacts impair the synthesis accuracy resulting in a perceivable change in timbre compared to the desired sound field. Recently, an approach for so-called Local Wave Field Synthesis was published which enhances the reproduction accuracy in a limited region by applying a spatial bandwidth limitation in the circular/spherical harmonics domain to the desired sound field. This paper reports on a listening experiment comparing conventional Sound Field Synthesis techniques with the mentioned approach. Also the influence of the different parametrisations for Local Wave Field Synthesis is investigated. The results show that the enhanced reproduction accuracy in Local Wave Field Synthesis leads to an improvement with regard to the perceived colouration.
A new version of our Sound Field Synthesis Toolbox for Matlab/Octave is available. This is a minor update fixing some bugs and adding support for mono-frequent simulations of local Wave Field Synthesis (LWFS) using spatial bandwidth-limitation.
- add monochromatic implementation of LWFS using spatial bandwidth-limitation
- add monochromatic circular expansion functions for ps and pw
- add function for conversion from circular to plane wave expansion
- add freq_response_* and time_response_* for all LWFS methods
- add optional message arg to progress_bar()
- fix missing conf.N in freq_response_nfchoa()
- fix auralize_ir() for local files
Winter, F.; Hahn, N; Spors, S. (2017): “Time-Domain Realisation of Model-Based Rendering for 2.5D Local Wave Field Synthesis Using Spatial Bandwidth-Limitation.” In: Proc. of the 25th European Signal Processing Conference (EUSIPCO), 2017.
The slides and additional material can be found here.
Abstract: Wave Field Synthesis aims at a physically accurate synthesis of a desired sound field inside an extended listening area. This area is surrounded by loudspeakers individually driven by their respective driving signal. Recently, the authors have published an approach for so-called Local Wave Field Synthesis which enhances the reproduction accuracy in a limited region by applying a spatial bandwidth limitation in the circular/spherical harmonics domain to the desired sound field. This paper presents an efficient time-domain realisation of the mentioned approach for 2.5-dimensional synthesis scenarios. It focuses on the model-based rendering of virtual plane waves and point sources. As an outcome, the parametric representation of the driving signals for both source types allows for the reproduction of time-varying acoustic scenarios. This also includes an adaptation to the tracked position of a moving listener. The realisation is compared with conventional Wave Field Synthesis regarding the spatial structure and spectral properties of the reproduced sound field. The results confirm the findings of the prior publication, that the reproduction accuracy can be locally improved with Local Wave Field Synthesis.