Signal Processing - May 2017 - 50

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Matrix
Output

Input

Tone Correction
Filter

Output Gains
Vector

Delays and
Absorption Filters

Input Gains
Vector

Direct Path Gain

FIGURE 11. A conceptual block diagram of the modified FDN reverberator as proposed by Jot and Chaigne [86].

digital waveguides (the digital equivalent of analog propagation lines, formed of two opposite delay lines of equal length)
connected at lossless scattering junctions (see Figure 12). Each
scattering junction carries out a simple matrix multiplication to
scatter the incoming signals on digital waveguides from each of
its neighbors to generate outgoing signals to be distributed back
to the same digital waveguides in the opposite direction. A signal reverberated using a DWN can be obtained by summing all
the outgoing signals of one of the scattering nodes. DWNs have
appealing stability properties and significant design flexibility
owing to the different possible network graphs, types of lossless
scattering, and lengths of the digital waveguides. While both
Jot's reverberator and DWNs are capable of producing responses with a high perceptual quality, the parameters of these models are not explicitly linked to the physical characteristics of a
particular room.
Artificial reverberators that are more tightly linked to room
acoustics also exist. One of the earlier designs proposed by Kendall et al. [92] was based on recirculating delay elements whose

Output

Lossless
DWN

37 ms
479

p4- (n

1,0
51
m

57 ms

p4+

157

p5+ (
4 n)

157 ms

Input

)
z -0.16F

lengths were determined by using an image-source model of
a rectangular room. A similar approach was also used in [93].
Karjalainen et al. proposed a class of DWNs designed to simulate early reflections and axial modes of rectangular rooms [94].
A drawback of their algorithm is that many of the algorithm's
internal parameters still require hand tuning to achieve a satisfactory reverberation.
An artificial reverberator that inherits all its parameters from
the physical characteristics of the room it simulates was recently
proposed [12]. This reverberator, termed the scattering delay
network (SDN), is a modified DWN where the length of the digital waveguides and the topology of the network, as illustrated
conceptually in Figure 13, are derived directly from the geometry of the simulated space. In particular, the SDN is a minimal
network connecting as many scattering nodes as there are walls
in the room, and where each scattering node is positioned at the
point where first-order reflections impinge on the wall.
This design ensures that first-order reflections are rendered
exactly, while second- and higher-order reflections are simulated

5 (n

)

z -0.16F

p5-

4 (n

S5
)

Fs = 44.1 kHz
713

FIGURE 12. A conceptual depiction of a DWN. The figure shows a DWN with five nodes (indicated as circles) connected via bidirectional delay lines
(curves with double arrows). To maximize the reflection density, the delay lengths are chosen to be coprime numbers. The input signal can be fed and the
output can be obtained from any node. The inset shows the connection between two nodes where incoming and outgoing signals and the individual delay
elements are clearly visible. (Figure adapted from [91].)
50

IEEE Signal Processing Magazine

May 2017

Table of Contents for the Digital Edition of Signal Processing - May 2017