1
- .. _chap-theory :
1
+ SFS Toolbox -- Theory
2
+ =====================
3
+
4
+ .. .. image:: img/header.png
5
+
6
+ Sound field synthesis (SFS) includes all methods that try to generate a defined
7
+ sound field in an extended area that is surrounded by loudspeakers. The SFS
8
+ Toolbox focuses on those methods that provide analytical solutions to the
9
+ underlying mathematical problem, namely |WFS |, |NFC-HOA |, and the |SDM |.
10
+
11
+ The Toolbox provides you with the implementation of the underlying
12
+ mathematics. You can make numerical simulations of the resulting sound fields
13
+ and can even create binaural simulations of the same sound fields. This enables
14
+ you to listen to large loudspeaker arrays, even if you don’t have one in your
15
+ laboratory or at home. In addition, you can easily plug-in your own algorithms
16
+ in order to test or compare them.
17
+
18
+ The Toolbox is structured in the following three projects.
19
+
20
+ Theory:
21
+ http://sfstoolbox.org/ (current page)
22
+
23
+ SFS Toolbox for Matlab/Octave:
24
+ http://matlab.sfstoolbox.org
25
+
26
+ SFS Toolbox for Python:
27
+ http://python.sfstoolbox.org
2
28
3
- Theory of sound field synthesis
4
- ===============================
5
29
6
30
.. Latex macros definitions used in this document
7
31
.. container :: hidden
@@ -17,10 +41,10 @@ Theory of sound field synthesis
17
41
\def \twohalfD {{2.5 \text {D}}\, }
18
42
\def \threeD {{3 \text {D}}\, }
19
43
20
- Most of the figures in this chapter are directly created by the python variant
21
- of the | SFS Toolbox | . All of them display the corresponding code for creating
22
- them directly before the actual figure. In order to recreate them, you have to
23
- execute the following code first:
44
+ Most of the figures in this page are directly created by the SFS Toolbox for
45
+ Python . All of them display the corresponding code for creating them directly
46
+ before the actual figure. In order to recreate them, you have to execute the
47
+ following code first:
24
48
25
49
.. Common plotting settings
26
50
.. plot ::
@@ -476,7 +500,7 @@ into :eq:`D_wfs` as
476
500
\underbrace {-2 w(\x _0 ) \partial _\n S(\x _0 ,\omega )}_{D(\x _0 ,\omega )} \;
477
501
{\mathop {\mathrm {d}{A}}}(\x _0 ).
478
502
479
- In the | SFS Toolbox | we assume convex secondary source distributions, which
503
+ In the SFS Toolbox we assume convex secondary source distributions, which
480
504
allows to formulate the window function by a scalar product with the normal
481
505
vector of the secondary source distribution. In general, also non-convex
482
506
secondary source distributions can be used with |WFS | – compare the appendix in
@@ -635,7 +659,7 @@ This document will consider only model-based rendering.
635
659
636
660
Frequently applied models in model-based rendering are plane waves, point
637
661
sources, or sources with a prescribed complex directivity. In the following the
638
- models used within the | SFS Toolbox | are presented.
662
+ models used within the SFS Toolbox are presented.
639
663
640
664
.. _sec-plane-wave :
641
665
@@ -1156,7 +1180,7 @@ they can easily be omitted. For corresponding driving functions for focused
1156
1180
sources without the evanescent part of the sound field see [SporsAhrens2010 ]_
1157
1181
for |SDM | and [AhrensSpors2009b ]_ for |NFC-HOA |.
1158
1182
1159
- In the | SFS Toolbox | only focused sources in |WFS | are considered at the moment.
1183
+ In the SFS Toolbox only focused sources in |WFS | are considered at the moment.
1160
1184
1161
1185
1162
1186
.. _sec-driving-functions-wfs :
@@ -1337,7 +1361,7 @@ which is the traditional formulation of a point source in |WFS| as given by eq.
1337
1361
(2.22a) in [Verheijen1997 ]_ [#F6 ]_ for the 2.5D. It has the advantage that its
1338
1362
temporal domain version could again be implemented as a simple weighting- and
1339
1363
delaying-mechanism. This is the default driving function for a point source in
1340
- the | SFS Toolbox | .
1364
+ the SFS Toolbox.
1341
1365
1342
1366
Transfered to the temporal domain via an inverse Fourier transform :eq: `ifft ` it
1343
1367
follows
@@ -1529,7 +1553,7 @@ or by using an approximated point source as
1529
1553
{\mathrm {e}}^{{\mathrm {i}}\frac {\omega }{c}|\x _0 -\xs |}.
1530
1554
1531
1555
As before for other source types, the approximated versions are the default
1532
- driving functions for a focused source used in the | SFS Toolbox |.
1556
+ driving functions for a focused source used in the SFS Toolbox|.
1533
1557
1534
1558
Transfered to the temporal domain via an inverse Fourier transform :eq: `ifft ` it
1535
1559
follows
0 commit comments