03-09-2012, 12:55 PM
SPATIAL ENCODING AND DECODING OF FOCUSED VIRTUAL SOUND SOURCES
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Abstract:
Spatial encoding refers to the representation of a sound field which allows storage and transmission of the
latter. In the Ambisonics context, sound fields can be spatially encoded when their spherical wave spectrum is bandlimited.
The process of deriving appropriate loudspeaker driving signals in order to reproduce an encoded sound field
is known as spatial decoding. Care has to be taken when virtual sound sources are positioned such that they appear
inside a given loudspeaker setup for which they are decoded. The properties of the mathematical formulation make
the reproduced sound field deviate strongly from the desired one in certain receiver positions. In this contribution we
demonstrate by means of a two-dimensional scenario how the concept of focused virtual sound sources can be applied in
order to optimize the reproduction accuracy.
INTRODUCTION
Sound field reproduction techniques like higher order Ambisonics
and wave field synthesis employ a large number of
loudspeakers to physically reproduce a desired sound field
over an extended listening area. Theoretically, these methods
are only capable of reproducing virtual sound sources
which are positioned outside of the listening area (“behind
the loudspeakers”). By reproducing a sound field which
converges in one half-space towards a focus point and diverges
in the other half-space, the target half-space, the perception
of virtual sound sources inside the listening area can
be elicited for listeners in the diverging part of the sound
field. Such a situation is referred to as reproduction of a focused
virtual sound source.
While being an established technique in wave field synthesis,
e.g. [1, 2], focused sources have received far less attention
in higher order Ambisonics and related approaches.
To our awareness, publicly available work is restricted
to [3, 4, 5].
In this contribution,we revisit the published approaches and
present a comparison of properties and restrictions. We concentrate
on the peculiaritieswhich arise in the spatial encoding
and decoding procedures which are widely employed in
the Ambisonics-like approaches.
SOUND FIELD REPRODUCTION
In this section, we briefly review the general approach presented
by the authors in [7, 8]. Its physical fundament is
the so-called simple source approach and it can be seen as
an analytical formulation of what is known as higher order
Ambisonics (see e.g. [9]). The simple source approach for
interior problems states that the acoustic field generated by
events outside a volume can also be generated by a continuous
distribution of secondary simple sources enclosing the
respective volume [6].
As stated in section 2, we limit our derivations to twodimensional
reproduction for convenience. Furthermore,
we assume the distribution of secondary sources to be circular.
In order to fulfill the requirements of the simple source
approach and therefore for artifact-free reproduction, the
sound fields emitted by the secondary sources have to be
two-dimensional. We thus have to assume a continuous
circular distribution of secondary line sources positioned
perpendicular to the target plane (the receiver plane) [6].
Our approach is therefore not directly implementable since
loudspeakers exhibiting the properties of line sources are
commonly not available. Real-world implementations usually
employ loudspeakerswith closed cabinets as secondary
sources. The properties of these loudspeakers are more accurately
modeled by point sources.
Focused virtual sources by angular weighting
The results presented in this section have partly been derived
in [3] whereby the investigation was driven by aspects
of implementation. In personal correspondence the author
of [5] announced the outline of an approach employing a
modification of the encoding procedure in order to avoid
excessive energy components in the decoded signals leading
to similar properties of the reproduced sound field. The
latter approach will focus on filter design aspects in order to
achieve an efficient implementation.
In this section, we revisit the subject of [3, 5] and treat it
from a physical perspective in order to illustrate the basic
properties of the reproduced sound field.
A closer look at the properties of (12) for r > rs shows
that it is actually the higher orders which introduce a high
amount of energy at low frequencies into the driving function
[14]. Compare Fig. 2(b) and Fig. 3(b).
CONCLUSIONS
We have presented an investigation of the reproduction of
focused virtual sound sources in the Ambisonics context.
Two approaches can be employed in order to model a focused
source: 1) manipulation (angular weighting) of the
interior spatial expansion of a sound source in order to extend
the region of physical validity, or 2) the explicit modeling
of a sound field diverging from a focus point into the
target half-space.