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Perceptual Assessment of Sound Field Synthesis

This repository provides the following PhD thesis, together with errata and the software you need to reproduce the thesis.

Hagen Wierstorf - Perceptual Assessment of Sound Field Synthesis, PhD thesis, TU Berlin, 2014, (doi), (pdf).

The software is spread in different directories named after the chapter and figure numbers. In order to run the code you will need the external toolboxes mentioned below and Matlab or Octave. Some of the code runs only in Octave at the moment, but it should be easily adoptable to Matlab. Those cases are indicated in the README in the corresponding figure directories.

Errata and Updates

Updates of Figures

With release 2.4 of the Sound Field Synthesis Toolbox for Matlab many numerical issues of the time-domain NFC-HOA have been solved.

The following table provides links to all figures, for which essential updates are available. On the figure pages itself you will see thumbnails of the original version as well as of the corrected one.

Updated Figure Description
Fig. 3.13 Improved numerical stability for NFC-HOA
Fig. 3.14 Improved numerical stability for NFC-HOA
Fig. 3.15 Improved numerical stability for NFC-HOA
Fig. 3.17 Improved numerical stability for NFC-HOA
Fig. 5.8 Corrected frequency response by fractional delay filter
Fig. 5.9 Corrected frequency response by fractional delay filter
Fig. 5.10 Coloration listening test with corrected stimuli

2. Theory of Sound Field Synthesis

Chapter 2 was transferred to an online version at https://sfs.readthedocs.io and is further developed and corrected there. This errata mentions only important changes and corrections to the content as presented in the thesis.

2.1 Solution for Special Geometries: Near-Field Compensated Higher Order Ambisonics and Spectral Division Method

The expansion in basis functions was sloppy formulated as (2.2), (2.3), (2.4) are only correct for compact spaces and their summation is infinite and does not stop at a particular N. Changed accordingly they should read

G(\mathbf{x}-\mathbf{x}_0,\omega) = \sum_n \tilde{G}_n(\omega)\Psi^*_n(\mathfb{x}_0)\Psi_n(\mathbf{x})

D(\mathbf{x}_0,\omega) = \sum_n \tilde{D}_n(\omega)\Psi_n(\mathbf{x}_0)

S(\mathbf{x},\omega) = \sum_n \tilde{S}_n(\omega)\Psi_n(\mathbf{x})

and are accompanied for non-compact spaces with these equations

 G(\mathbf{x}-\mathbf{x}_0,\omega) = \int \tilde{G}(\mu,\omega)\Psi^*(\mu,\mathbf{x}_0)\Psi_n(\mu,\mathbf{x}) d\mu

D(\mathbf{x}_0,\omega) = \int \tilde{D}(\mu,\omega)\Psi(\mu,\mathbf{x}_0) d\mu

S(\mathbf{x},\omega) = \int \tilde{S}(\mu,\omega)\Psi(\mu,\mathbf{x}) d\mu

where μ is the measure in the underlying space.

For a discussion see: sfstoolbox/theory#9

2.5 Driving functions

Several of the driving functions for WFS presented in 2.5.2 are now updated after the discussion presented in Schultz (2016), see the WFS driving function chapter on https://sfs.readthedocs.io for more details. The remaining discussion in this section focusses only on corrections of the driving functions as presented in the thesis.

The WFS driving functions for a focused source (2.71) and (2.72) have the wrong direction in time. The equations should read

D(\mathbf{x}_0,\omega) = \frac{1}{2\pi} A(\omega) w(\mathbf{x}_0) \left(i\frac{\omega}{c} + \frac{1}{|\mathbf{x}_0-\mathbf{x}_\text{s}|} \right) \frac{(\mathbf{x}_0-\mathbf{x}_\text{s})\mathbf{n}_{\mathbf{x}_0}} {|\mathbf{x}_0-\mathbf{x}_\text{s}|^2} e^{i\frac{\omega}{c} |\mathbf{x}_0-\mathbf{x}_\text{s}|}

D_\text{2.5D}(\mathbf{x}_0,\omega) = \frac{g_0}{2\pi} A(\omega) w(\mathbf{x}_0) \sqrt{i\frac{\omega}{c}} \left(1 + \frac{c}{i\omega} \frac{1}{|\mathbf{x}_0-\mathbf{x}_\text{s}|} \right) \frac{(\mathbf{x}_0-\mathbf{x}_\text{s}) \mathbf{n}_{\mathbf{x}_0}} {|\mathbf{x}_0-\mathbf{x}_\text{s}|^2} e^{i\frac{\omega}{c} |\mathbf{x}_0-\mathbf{x}_\text{s}|}

3. Sound Field Errors and their Perceptual Relevance

3.3 Spatial Aliasing and Discrete Secondary Source Distributions

Equation (3.5) for the selection of the maximum order of band-limited NFC-HOA has to be slightly changed to

M \le \begin{cases} \frac{N_\text{s}}{2} - 1 & \text{for even } N_\text{s} \\ \frac{(N_\text{s}-1)}{2} & \text{for odd } N_\text{s} \end{cases}

5. Psychoacoustics of Sound Field Synthesis

The impulse responses representing the different WFS systems in the coloration experiment were all created using integer delays. This added a few distortions for high frequencies, which are observable in Fig. 5.8 as the slight ripples in the spectra for the conditions with an inter-loudspeaker distance of 0.5 cm and 0.3 cm. We repeated the experiment by using a fractional delay method and a sampling rate of 48 kHz which ensured that the delay line had a flat frequency response in the region up to 44.1 kHz. Now the frequency response for the WFS system with an inter-loudspeaker distance of 1 cm showed a flat frequency response. The same holds for the results of the listening test presented in Fig. 5.10. In the repeated listening test, the conditions for 1 cm and 2 cm are no longer different from the reference condition. The results of the new listening test are available at: https://doi.org/10.5281/zenodo.164592

Software Requirements

If you want to reproduce the corrected and most up-to-date version of the figures, please have a look at the requirements of the sfs-2.4 branch instead.

Sound Field Synthesis Toolbox for Matlab

From the Sound Field Synthesis Toolbox for Matlab git repository you need to checkout commit 3730bc0, which is identical with the release 1.0.0. Under Linux this can be done the following way:

$ git clone https://github.com/sfstoolbox/sfs-matlab.git
$ cd sfs-matlab
$ git checkout 3730bc0
$ cd ..

Auditory Modelling Toolbox

From my copy of the Auditory Modelling Toolbox git repository you need to checkout commit aed0198. Under Linux this can be done the following way:

$ git clone https://github.com/hagenw/amtoolbox.git
$ cd amtoolbox
$ git checkout aed0198
$ cd ..

The Auditory Modelling Toolbox depends further on the Large Time-Frequency Analysis Toolbox, which you can get in the same way:

$ git clone https://github.com/hagenw/ltfat.git
$ cd ltfat
$ git checkout 3f9af4a
$ cd ..

Setting up Toolboxes in Matlab

After installing both toolboxes you have to start them first in Matlab/Octave in oder to run the scripts provided with this PhD thesis. This can be done by running the following commands from the sfs-matlab/ and amtoolbox/ directory, respectively.

>> cd sfs-matlab
>> SFS_start;
>> cd ../ltfat
>> ltfatstart;
>> cd ../amtoolbox
>> amtstart;

Get additional data

If you don't want to rerun all the numerical simulation, but just want to rerun some of the plotting routines, you can download all the results of the numerical simulations that is not directly included into this repository from http://doi.org/10.5281/zenodo.846561

Now everything is prepared and you can start to reproduce any figure in the thesis.

The scripts presented here were tested with Matlab 8.1.0.604 (R2013a), Octave 4.0.0, gnuplot 5.0 patchlevel 3.

License

Copyright 2015-2018 Hagen Wierstorf

Licensed under the Apache License, Version 2.0 (the "License"); you may not use this file except in compliance with the License. You may obtain a copy of the License at

http://www.apache.org/licenses/LICENSE-2.0

Unless required by applicable law or agreed to in writing, software distributed under the License is distributed on an "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. See the License for the specific language governing permissions and limitations under the License.

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