Image Processing Reference
In-Depth Information
11.3.4 Virtual Source Localisation
The physical properties of the output sound field generated by an audio rendering
system can directly be measured by using precise measuring microphones. This is
done to objectively evaluate the accuracy of the acoustic sources being synthesised
by (
11.6
). When the solution (
11.6
) based on the WFS theory is applied to the space,
the combination of all the output wave fronts generated by the drivers produces a
wave front equivalent to the original virtual one in a given domain. The result
shows that the solution Eq. (
11.6
) which is used for a source created outside the
domain is also effective and can be extended to the cases with a focused source. The
position of a virtual source is experimentally determined by measuring the direction
of a wave front
s propagation. In order to identify the position of an acoustic source
created by the rendering system, the perpendicular direction to a wave front is
measured using the two microphone setup mounted at predefined reference posi-
tions. The acoustic measurement technique determines the maximum pressure
gradient at the measuring point.
Figure
11.7
shows a representative example of the experimental results measur-
ing the difference in position between the intended object and the rendered virtual
object, where + denotes the reference position of the intended object. The mea-
surements are taken from a studio with moderately absorptive walls to limit
reverberations. The absorption coefficient
'
= 0.3-0.4, varying with the frequency.
The measuring system is composed of a combination of B&K half-inch free-field
measuring microphones [
20
]. The phase difference between a pair of the micro-
phones was measured using a B&K PULSE Sound & Vibration analyser [
21
]. An
off-centre localisation condition is deliberately chosen in this particular experi-
ment, shown as reference object position + in Fig.
11.7
. This is chosen so that the
result can present the higher limitation of the directional errors. Common artefacts
by any WFS-based systems can usually be found near the ends of a truncated
loudspeaker array [
9
,
10
,
15
,
16
]. When the WFS system is switched on, the main
propagating direction of the wave front is measured at each pair of multiple receiver
positions, e.g.,
A
1
and
B
1
,
A
2
and
B
2
,
ʱ
, and
A
N
and
B
N
, where
N
is the total number
of the measurements. The directional errors
...
are indicated in Fig.
11.7
and can be
generally below 7
in directional accuracy [
12
]. Causes of the errors in the
measurement can be classified largely in two groups, one related to position, and
the other to time. Firstly we consider position, the physical size of the measuring
devices and the gap between two neighbouring loudspeaker drivers cause aliasing
errors while monitoring. The maximum uncertainties at which these errors take
place correspond to about 10
. In addition, time delay and extra phase errors can
occur in DSP and measuring equipment. Therefore, the resulting errors are not
uncommon in real environments. In the context of human hearing, the errors are
acceptable as the directional error is within 10
limit [
22
].
Some artefacts can be found outside the viewing angle which is indicated in
Fig.
11.7
. This is due to the fact that the limited length of the secondary source array
can cause discontinuity of a reconstructed wave front at each end. The spatial
Δ
ˆ
