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C00010 00003	The design of an algorithm for  the computer simulation  of localized
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II. RESEARCH PROPOSAL
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In  this section  we will  present  the details  of  our present  and
proposed future research.  The presentation is divided into two major
parts: (A) the  simulation of music  instrument tones,   and (B)  the
simulation of reverberant  spaces and localized sound  sources.  This
division is  based on the distinction of those active elements of the
auditory environment,  the  actual sound  sources,  from the  passive
space  which surrounds them  and the  cues for their  localization in
that space.  The apparent independence of these two lines of research
serves  our interests  for presentation alone.   However, our unified
goal is the  simulation of any source, located at any position in any 
reverberant environment.  Our realistic two-year goal for the purpose of
this proposal, is the simulation of a number of varied music instrument
tone sources, located in any position in some typical reverberant
environments.  The interdependence of factors can be readily
seen when we consider the influence of the specific environment on the
quality of the sounds within it.  

An important further aspect of our research is presented under
Proposed Facility of section III.  We view the development of
a small, special purpose, real-time digital signal processing
system and the programs as integrally related to, and
as a major product of, the research.

We will begin by giving an overview of the fundamental issues and
concerns of our research.
The fundamental principles of our present research, using a large
general purpose computer, and the proposed research, using a special
purpose processor, lie in sampling theory.  The details
of the theory as applied to acoustical pressure waves are thoroughly
discussed by Mathews (1969). Briefly, the fundamental assumption
is that a complex waveform can be digitally represented by discrete numerical
sampling of the instantaneous amplitude of that wave, and that the
accuracy of this representation increases as the time interval between
the successive samples becomes smaller and as the numerical precision
of each sample is increased.  Using the synthesis
techniques, discussed below, we generate a complex wave by producing
the samples in numerical sequences, which are then passed to digital-to-
analog converters, the voltage outputs of which are recorded on a
multi-channel tape recorder.  Digital synthesis has the obvious
advantage of allowing the generation of a waveform which has been
precisely controlled in frequency and amplitude.
In fact this precision can only be met by means of digital synthesis,
and it will be shown to be of the utmost importance for our research.
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The  main  considerations  and  criteria   in  designing  a  computer
algorithm  for the simulation of  music instrument tones  are: 1) the
optimal use of computer resources, i.e.  storage, efficiency,  2) the
perceived naturalness of the results,  3) the
general  applicability  to the  widest range  of  cases found  in the
repertoire of instrumental timbres,  4) the level of  user-control of
the  algorithm such that  parametric specifications  are perceptually
meaningful, 5) the efficiency with which hypotheses may be verified.
Essential  to  our  work,  therefore,  is  information
concerning the  nature of the  perception of music  instrument tones.
The  measure  of success  of  any proposed  simulation  technique, as
outlined in the  above criteria, infers that  the dimensions of  human
timbre perception will be mapped into  the computer algorithm.  Given the
present lack  of knowledge in auditory theory about the perception of
timbre, we find that a part of our research program is concerned with
uncovering the perceptual dimensions  of instrument tones, which will
suggest optimal structural  representations of  tones  and
parametric  controls  for  simulation.   This  research  particularly
involves rigorous perceptual evaluation and multidimensional scaling 
of the results of  simulation algorithms,  both as  an objective test
of  specific techniques,  and as  a  method for  deriving theoretical
knowledge which  supports our  further development  of more  powerful
algorithms.
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The design of an algorithm for  the computer simulation  of localized
and moving sound sources in a reverberant space have criteria similar
to those enumerated above for the simulation of tones.   Optimization
for this  simulation algorithm also  includes a determination  of the
minimal  number of independent speaker-channels which are necessary
to create high-quality reverberation  and which maximize the  area in
which listeners  receive convincing illusions of  the localization of
stationary and  moving sound  sources.   Research in  the control  of
artificial reverberation  is aimed at  allowing the user  to simulate
any desired set of environmental characteristics.  Examination of the
perceptual cues for room  qualities,  a little-touched subject  in
auditory theory,   is included  in our  effort to formulate  the most
powerful  simulation algorithm.  The perceptual  cues for the angular
localization of sounds, by contrast,  are well-understood in auditory
theory. The problem seen for this area of simulation is in the use of
a small number of speaker-channels at fixed angles to accurately  and
convincingly  produce a  full  range  of  possible angles  of  source
localization  for  the  largest region  of  listener  positions.   In
considering the simulation of the distances of sources and  the paths
of their  motion, theoretical knowledge implicates  specific physical
cues  on sounds, but  empirical quantification is  again necessary in
the designing of a powerful computer algorithm.  
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