A recent development in artificial reverberation technology is the Scattering Delay Network (SDN) [,237]. An SDN can be considered a computationally efficient approximation to geometric ray tracing using a small digital-waveguide network. It thus classifies as both a delay network and approximate physical room model.
![]() |
Figure illustrates the image method
[11,] for determining acoustic
reflections between two parallel walls. The method can be visualized
by imagining the walls of the acoustic space to be mirrored.
Then the acoustic ray paths from the source
to the listener
can be found by drawing a straight line from each source image to the
listener. The length of this line determines propagation delay and
filtering due to air absorption, and the wall traversals going from
room-image to room-image indicate the actual reflection planes, where
further absorption and dispersion can be applied. In Fig.
,
only the left and right wall reflections are considered, yielding a
simplified series of room images along one dimension.
![]() |
Figure shows a Scattering Delay Network (SDN) model for
the configuration of Fig.
. In an SDN, the second-order
(and all higher-order) image sources are constrained to follow the
same path segments as the first-order reflections. The direct path
and first-order reflections
and
are modeled precisely
(correct propagation delays and filtering--filtering not shown)
because the locations of the two waveguide junctions along the walls
are chosen to yield correct first-order reflections. The second-order
reflections
and
are constrained to use the same
waveguides, yielding the modified path images shown in dotted lines.
The path of each second-order reflection is altered as shown, forcing
it to reuse acoustic path segments of the first-order reflections
while introducing a new path segment which connects the two scattering
junctions. Only the second-order reflections make use of the
waveguide bidirectionality in this simple example. We can see, for
example, that the modified paths are always somewhat longer than the
straight lines-of-sight from source-image to listener
. In
particular, a ray emitted from a source-image aims for the
listener-image in the adjacent room image (correct for a first-order
reflection) instead of directly for the real listening-point L.
Higher order reflections are thus lengthened by a non-diverging
factor, and this lengthening disappears as the source and listener
approach any line orthogonal to the walls.
Since only the left-right wall reflections are considered in
Fig., it can be considered a 1D example (virtual room
images are laid out along only one dimension). The 2D case would
introduce two more scattering junctions and support image sources from
all directions in the 2D plane. The 3D case requires six scattering
junctions and
digital waveguides. There is no reason not to
consider dimensions higher than
.
The filtering and arrival times in an SDN model are therefore well preserved qualitatively, and the SDN can achieve a high degree of perceptual accuracy for its computational cost. However, since the details of the reflection pattern are modified after the first-order reflections, the early texture of the impulse response should be checked for "flutter" and any other textural defects. As discussed in [], perceptually adequate mode densities are achieved for cuboid reverberant spaces larger than on the order of ten cubic meters.
Figure depicts a complete 2D Scattering Delay Network
(SDN), adding now the reflections from the other two walls. Note that
the scattering junctions are fully connected. This is necessary to
support image sources along any diagonal. (A pair of junctions on
opposite walls only support room images along the axis orthogonal to
those walls.) The diagonal waveguides are needed when the best path
from a source image needs to enter a room image from the north or
south, say, but exit to the east or west.