Image Processing Reference
In-Depth Information
in (
11.6
) is valid for a source generated both inside and outside the domain
D
. A key
advantage in this approach over earlier studies on methodologies based on WFS
[
13
,
14
] is that it requires only one equation for both focused and non-focused
sources. The single general equation is very useful for real-time applications related
with both focused and non-focused sources. For example when an audio object is
continuously moving from outside a domain, including movement through the
loudspeaker array which corresponds to the boundary
S
in Fig.
11.1
.
In order to validate the solution provided by (
11.6
), we analyse some typical
results obtained in the following numerical simulations. Figure
11.2
shows results
taken from an array of 16 loudspeakers mounted on one side of a given space. The
problem domain where the solution is valid is defined in anechoic conditions in this
simulation. The geometry can be given to reflect the actual physical boundary
conditions of the studio where the actual WFS system takes place. When the
solution of (
11.6
) is applied to the space, the combination of all the individual
wave fronts produces a unified wave field.
In the simulation a single point source is virtually situated outside the listening
room (
ʸ
~
r
¼
ʸ
~
r
¼
1) in Fig.
11.2b
. A display
screen can be mounted in front of the loudspeaker array (
c.f.
Fig.
11.1
) and is
assumed acoustically transparent. Even though this is generated by a reduced
number of drivers, instead of a contentious ideal line source, the reproduced wave
field is equivalent to the original sound sources wave front in the most of the given
domain in Fig.
11.2
. Near the boundary, e.g. on the left in Fig.
11.2a
, some artefacts
can occur. However the artefacts are not uncommon in many other multi-channel
surround audio techniques, such as ambisonics, 5.1 and 7.1 channel audio [
15
]. This
can happen largely due to truncated secondary source array which can cause
aliasing tails on the reconstructed wave front
0) in Fig.
11.2a
, and also inside (
s truncated regions [
9
,
10
,
15
,
16
]. Overall, the output results show wave field validity within the viewing angle,
as indicated in Fig.
11.2b
. It confirms that the general WFS solution based on the
driving function in (
11.6
) can be used for both cases using sources created outside
(Fig.
11.2a
) and also inside (Fig.
11.2b
) the domain. The general solution (
11.6
)is
applicable in 2D and also in general 3D cases.
'
11.3
Implementation of WFS
11.3.1 General System Design
In implementation of WFS, ideally, the entire listening space should be surrounded
by a continuous line-source. However, in practice the secondary source can be
replaced with a series of discrete drivers as shown in Fig.
11.3
[
9
].
The control PC where the WFS algorithm is implemented is equipped with
multi-channel audio interface cards, e.g. HDSP MADI interface card [
17
]. From
here the signals are then fed via coaxial cables into AD/DA converters. In a studio a
