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D. Rocchesso: Sound Processing
artificial reverberation
The formula for the amplitude gain is such that sources within the distance of 1m
from the loudspeaker
will be stuck to unity gain, thus avoiding the asymptotic
divergence in amplitude implied by a point source of spherical waves.
The model is as accurate as the physical system being modeled would per-
mit. A listener within a room would have a spatial perception of the outside
soundscape whose accuracy will increase with the number of windows in the
walls. Therefore, the perception becomes sharper by increasing the number of
holes/loudspeakers. Indeed, some of the holes will be masked by some walls, so
that not all the rays will be effective
(e.g. the rays to loudspeaker 3 in fig. 13).
In practice, the directional clarity of spatialisation is increased if some form of
directional panning is added to the base model, so that loudspeakers opposite
to the direction of the sound source are severely attenuated. With this trick,
it is not necessary to burden the model with an algorithm of ray-wall collision
detection.
The Moore model is suitable to provide consistent and robust spatialization
to extended audiences [60]. A reason for robustness might be found in the fact
that simultaneous level and time differences are applied to the loudspeakers.
This has the effect to increase the lateral displacement [13] even for virtual
sources such that the rays to different loudspeaker have similar lengths. Indeed,
the localization of the sound source gets even sharper if the level control is driven
by laws that roll off more rapidly than the physical 1/d law of spherical waves.
In practical realizations, the best results are obtained by tuning the model after
psychophysical experimentation [54].
An added benefit of the Room within a Room model is that the Doppler
effect is intrinsically implemented. As the virtual sound source is moved in the
outer room the delay lines representing the virtual rays change their lengths,
thus producing the correct pitch shifts. It is true that different transpositions
might affect different loudspeakers, as the variations are different for different
rays, but this is consistent with the physical robustness of the technique.
The model of the Room within a Room works fine if the movements of the
sound source are confined to a virtual space external to the inner room. This
corresponds to an enlargement of the actual listening space and it is often a
highly desirable situation. Moreover, it is natural to model the physical proper-
ties of the outer room, adding reflections at the walls and increasing the number
of rays going from a sound source to the loudspeakers. This configuration, il-
lustrated in fig. 13 with first-order reflections, is a step from spatialization to
reverberation.
3.6.2
Reverberation
Classic reverberation tools
In the second half of the twentieth century, several engineers and acousticians
tried to invent electronic devices capable to simulate the long-term effects of
sound propagation in enclosures [14]. The most important pioneering work in
the field of artificial reverberation has been that of Manfred Schroeder at the
Bell Laboratories in the early sixties [88, 89, 90, 91, 93]. Schroeder introduced
5
This distance is merely conventional.
6
We are neglecting diffraction from this reasoning.