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B. SIMULATION OF REVERBERANT SPACES
AND LOCALIZED SOUND SOURCES
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In this part  of the proposal we  will discuss our approaches  to the
computer  simulation   of  reverberant  spaces  and  localized  sound
sources.  The  goal of our  research is  the development of  computer
algorithms which can  simulate a wide variety  of natural reverberant
spaces,  and which are  able to project arbitrary  sound sources into
such spaces at any  localized stationary position or upon  any moving
path.  One  or  our   concerns  is  the  simulation  of  high-quality
reverberation which  can be  controlled via  perceptually  meaningful
parameters by the user.   Another concern is to maximize  the area in
which  listeners receive  convincing  illusions of  localized sources
that are at apparent positions specified by the user.  Both  of these
fundamental concerns must be accomplished  with the minimal number of
speaker-channels and  an optimization of computer resources.  This is
one of the central problems for our research efforts.

The discussion which  follows will be  divided into two  main topics:
the simulation of  reverberant spaces and the simulation of localized
sound sources.    We will  first  describe the  fundamental  computer
algorithems  for the  generation of  reverberation, and  indicate the
perceptual   correlates  to   the  parameters   which  control  these
algorithms.   We will  then discuss  the approaches  which have  been
taken to utilize these basic algorithms in compound and multi-channel
reverberation systems.  Coloration of timbre, the qualitative  effect
of  reverberation on  the  source  signal,  will be  discussed  as  a
consideration  in  designing  complex  reverberation systems.  Future
research concerns are then presented.   One matter of concern is  the
ability to  acoustically `tune'  the simulated space,  using spectral
shaping  techniques, to  increase user-control over  the qualities of
the resultant reverberant  environment.  An  extended concern is  the
simulation of a virtual space, a complex and naturalistic reverberant
environment  which  provides  the   listener  with  the   qualitative
perceptual cues  of the  user-specified real-world  situaltion.   One
important  matter  with  respect to  this  extended  concern  is  the
development   of  optimization  techniques  for   the  production  of
uncorrelated reverberation.   Perceptual scaling  techniques will  be
enlisted  to determine  the perceptual  distinctiveness and  relative
importances of various features of reverberation  networks, as an aid
to the development  of optimal reverberation systems and as a test of
the adequacy  of particular systems.  We will  conclude this  section
with a  discussion of our  plans for the development  of higher-order
algorithms  for the  simulation of  reverberant spaces, based  on the
above  research,   which  give  the   user  perceptually   meaningful
parametric controls.

The next section will present a discussion of our approach to the
simulation of localized sound sources, projected within a reverberant space
at user-specified stationary positions or paths of motion.  We begin
with a description of the features of a computer algorithm which we
have designed for this simulation using four loudspeakers.
Several perceptual cues for localization are controlled in parallel, 
using empirically-based functions to specify quantitative parameters
of sound to the speakers. Future research includes a rigorous investigation
of these functions by perceptual scaling techniques.  Especially of
interest are questions of optimization:  maximization of the area for
viable listening positions and minimization of the number of independent
speaker-channels needed.  The further investigation of cues for
localization is next discussed, including cues for azimuth, distance,
and altitude.
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