Signal Processing - May 2017 - 47

loudspeakers. The other optimization procedure involves finding
the filter coefficients to be used for beamforming.
Figure 9 illustrates the problem of off-center listening and
loudspeaker directivity patterns implemented to counteract
this problem using a loudspeaker array with two drivers. It may
be observed that when the listener moves to the left of the ideal
listening position, the signal from the left loudspeaker will
arrive earlier and at a higher level than the right loudspeaker,
shifting the perceived direction of the virtual source toward
the left. This problem can be compensated for by adjusting the
right loudspeaker to have a higher level than the left loudspeaker at the corresponding direction, effectively shifting the virtual source back. The loudspeaker directivity patterns shown
in the figure were designed to achieve this and thus to allow the
listening area to be enlarged. Rodenas et al. [59] report results
of an informal listening test with a system realized using loudspeaker arrays with two tweeter and two midrange drivers each
and state that the proposed approach widens the sweet spot for
standard stereophonic material.
While designing loudspeaker directivity patterns for robust
stereophony is a promising idea, technical difficulties such as
the equalization of drivers, compensation for diffraction from the
edges of the loudspeaker cabinets, and the required number of
loudspeakers used in the design may limit its practical use. These
techniques, along with the generalization of the design approach
to multichannel systems and combination with other technologies
such as PSR, are interesting directions for future research.

Perceptually motivated room auralization
In cases where an acoustic scene actually exists, as in a live
concert or a tennis match, the scene is recorded and reproduced
by the techniques reviewed above. These techniques also capture the acoustics of the environment in which these recordings
are made. However, there are applications where such scenes
exist only virtually, as in computer games or VR. In such cases,
the acoustics of the environment that contains the scene to be
rendered need to be synthesized. Auralization is the process of
making the acoustics of a real or virtual environment such as a
room or a concert hall audible [8].
Rooms are multipath environments where the recording of a
source by a microphone will include not only the direct path but also
early reflections, reverberation tail, and diffraction components. Many
different models have been proposed in the past 50 years to simulate
room acoustics. A recent review article provides a summary of the
research on room acoustics modeling [60] and divides algorithms into
three classes: 1) convolutional algorithms, 2) delay networks, and 3)
computational acoustics models. Convolutional algorithms involve
measuring the impulse response of an actual room and convolving it
with a desired input signal. Delay networks, which will be discussed in
more detail in the "Perceptually Motivated Artificial Reverberation"
section, are algorithms where the input is filtered and fed back along
a number of delay paths designed according to desired reverberation
characteristics. Computational acoustics models aim to simulate the
propagation of sound waves in the modeled space.
Among computational acoustics models, there are geometric models, which use geometric arguments to calculate

Stereophonic
Image

Left
Loudspeaker
Array

-10 dB

60°

0 dB
10 dB
0°

Right
Loudspeaker
Array

30°

0 dB
10 dB
0°

FIGURE 9. A conceptual depiction of position-independent stereo with
optimal loudspeaker directivity patterns. When the listener moves toward
the left or right of the stereophonic sweet spot, the directivity pattern
of the loudspeaker array compensates for the resulting delay, and the
direction of the virtual source remains unchanged. (Figure adapted from
[59]. Reprinted with permission. Copyright 2003, Acoustical Society
of America.)

the room impulse response. These include the image-source
method (ISM) [61], [62] and ray tracing [63] or beam tracing [64] and its variants [65]. Other computational acoustics
models such as finite-difference methods [66], digital waveguide mesh [67], FEMs [68], and BEMs [69] are based on the
time- and space-discretized solutions of the wave equation;
hence, individual reflections are not rendered explicitly, but
their effects are merged into the overall simulated wave fields.
Computational acoustics models are capable of providing very
accurate results (at least for certain frequency ranges) and are
therefore used in architectural acoustics. However, their physical accuracy comes at a very high computational cost. While
some computation can be carried out offline, auralization will
typically require real-time operation at interactive rates-for
instance, to allow a user to explore a virtual environment. The
main computational bottleneck that this entails is associated
with the different filtering operations involved in calculating
and synthesizing reflections and edge diffraction components
for each source.
Despite their high computational complexity, extremely accurate room auralization methods will always be in demand for
applications such as architectural acoustics. However, they are
not suitable for applications such as immersive games and VR,
where a low computational cost is paramount. Such applications
warrant the simplification of the model to the lowest possible
number of components and sources to be rendered, which is typically achieved by removing perceptually irrelevant content.

Simplification of room acoustics models
The lack of a comprehensive mathematical model of the precedence effect, analogous to models of monaural masking, has,

IEEE Signal Processing Magazine

May 2017

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