Signal Processing - May 2017 - 49

Boundaries of the Enclosure
and the Enclosed Planes
Material Properties
Reverberation Characteristics
Source Directivity Patterns

Modeling

A 3-D Geometric Model
of the Enclosure
Listener and Source
Positions and Look
Directions

L1
L2

L3
150°

-10 dB

120°

Calculate Valid and
Visible Image Sources
and Diffraction Terms

Auralization

HRTF Filters

-120°

-90°

90°

-60°

60°
30°

Anechoic Signal

±180° 10 dB
-150°
0 dB

θ = 0°

-30°

Direct Path,
Early
Reflections,
and Edge
Diffraction
Components

HRTF Filter
Interpolation

Material
Filters

Air
Absorption
Filters

Artificial
Reverberation

Head Position
and Direction

FIGURE 10. Typical processing stages in a binaural room auralization system using the image-source method to model the room acoustics.

reverberator consisting of a recursive structure using comb and
all-pass filters.
The choice of artificial reverberation in a room auralization system is dictated not only by perceptual considerations
but also by computational cost, and the holy grail in artificial
reverberator design is an algorithm that can achieve good perceptual quality at a reasonable computational cost. The earliest
digital artificial reverberators were proposed by Schroeder in
the 1960s and consisted of comb filters connected in parallel
to simulate the frequency modes of a room and all-pass filters
to simulate a dense reverberation tail [84]. The original designs
by Schroeder sometimes produced a metallic-sounding reverberation, and various improvements were subsequently proposed [9], [85]. These improvements, however, did not provide
any means to explicitly or easily control the characteristics of
the synthesized reverberation.
Feedback delay networks (FDNs) were developed as a multichannel extension of the Schroeder reverberator [87], [88]. The
FDN is a recursive delay network that can generate reverberation
for a number of input channels, such as individual audio channels
of a four-channel (i.e., quadrophonic) system. Each of the input

channels is delayed, fed back recursively through a feedback loop,
attenuated, and mixed with the incoming channels. The delay
lines are designed to have incommensurate lengths, and the feedback loop consists of multiplication with a unitary matrix.
Jot and Chaigne extended the FDN design and proposed a
simple and structured procedure to design good-quality reverberators with a desired frequency-dependent reverberation
time [86]. They also introduced the design principle that to
avoid isolated ringing modes that tend to sound metallic, all the
structure modes should decay at the same rate. A conceptual
block diagram of Jot's reverberator is shown in Figure 11. Notice
the absorption filters in the feedforward path that allow controlling the decay rate at different frequencies, and a tonal correction filter that is used to equalize the reverberator frequency
response so that the generated reverberation sounds more natural. The original design uses a Householder matrix for the
feedback path, but other unitary matrices can also be used [89].
These matrices can also be time varying, resulting in improved
perceptual characteristics [90].
Equivalent to a wide class of FDNs are the digital waveguide
networks (DWNs) [91], [98]. A DWN consists of a number of

IEEE Signal Processing Magazine

May 2017

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