## Jupyter Notebooks on Finite Element Method in Acoustics

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.

## Article: On the General Relation of Wave Field Synthesis and Spectral Division Method for Linear Arrays

The article
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

Abstract:
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.

## Article: Colouration in Local Wave Field Synthesis

In the IEEE/ACM Transactions on Audio, Speech, and Language Processing we published

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

The paper can be found here.

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.

## Paper: A Geometric Model for Spatial Aliasing in Wave Field Synthesis

At the 44th German Annual Conference on Acoustics (DAGA) we presented the contribution:

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.

## Paper: Colouration in 2.5D local wave field synthesis using spatial bandwidth-limitation.

At the 2017 IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA) we presented the contribution:

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.

## New Releases of the Sound Field Synthesis Toolbox for Python and Matlab/Octave

New versions of our Sound Field Synthesis Toolbox are available for Matlab/Octave and Python.

Matlab
This release fixes small bugs, removes obsolete local WFS functions and introduces optional logarithmic spacing of linear secondary sources. For documentation see http://matlab.sfstoolbox.org/en/2.4.2. Download SFS Toolbox 2.4.2 for Matlab.

NEWS (SFS Toolbox for Matlab 2.4.2)

• extend signal_from_spectrum and spectrum_from_signal to N-dim matrices
• remove obsolete *_localwfs functions
• add optional logarithmic spacing for linear secondary sources

Python
This release introduces WFS driving functions in the time domain and an image source model for a point source in the frequency domain. For documentation see http://python.sfstoolbox.org/en/0.4.0.
You can install the toolbox via pip install sfs, see https://pypi.python.org/pypi/sfs/0.4.0.

NEWS (SFS Toolbox for Python 0.4.0)

• Driving functions in time domain for a plane wave, point source, and focused source
• Image source model for a point source in a rectangular room
• DelayedSignal class and as_delayed_signal()
• Spherical Hankel function as util.spherical_hn2
• Use spherical_jn, spherical_yn from scipy.special instead of sph_jnyn
• Generalization of the modal order argument in mono.source.point_modal()
• Rename util.normal_vector() to util.normalize_vector()
• Add parameter max_order to NFCHOA driving functions
• Add beta parameter to Kaiser tapering window

## Release 2.4.1 of the Sound Field Synthesis Toolbox for Matlab/Octave

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.

NEWS (2.4.1)
 - 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 

## Paper: Dynamic Measurement of Binaural Room Impulse Responses Using an Optical Tracking System

The paper

Hahn, N.; Hahne, W.; Spors, S. (2017): “Dynamic Measurement of Binaural Room Impulse Responses Using an Optical Tracking System” In: Proc. Int. Conf. Spatial Audio (ICSA), Graz, Austria.

was presented at the 4th International Conference on Spatial Audio. The slides can be found here

 Static Dynamic ($\Omega=0.5^\circ/\text{s}$) Dynamic ($\Omega=8^\circ/\text{s}$) castanets ($\varphi=-45^\circ$) speech ($\varphi=+45^\circ$)

## Paper: Synthesis of a Spatially Band-Limited Plane Wave in the Time-Domain Using Wave Field Synthesis

The paper

Hahn, N.; Winter, F.; Spors, S. (2017): “Synthesis of a Spatially Band-Limited Plane Wave in the Time-Domain Using Wave Field Synthesis” In: Proc. Eur. Sig. Process Conf. (EUSIPCO), Kos, Greece.

was presented at the 25th European Signal Processing Conference (EUSIPCO). The slides can be found here.