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		NSF  Proposal

	Computer Simulation of Natural Auditory Signals
		and Reverberant Spaces
I.	Introduction
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story. Is not particularly useful for synthesis and only half the information
needed for instrument building.
******
In recent years there have been significant advances in computer simulation
and analysis of complex auditory signals.  On the one hand, the use of the computer
has demonstrated the extraordinary complexity of natural sounds and insufficiency
of current acoustical theory, and on the other, the computer has provided
the means of implementation of powerful synthesis and analytical techniques.

At the Stanford Artificial Intelligence Laboratory programs and techniques
have been developed for the simulation of moving
sound sources in reverberant spaces and for the analysis and synthesis of 
complex signals, some of which are startlingly simple in implementation and
novel in conception.  While the progress of this research has certainly been enhanced
by the high level of technological expertise at the Artificial Intelligence
Laboratory, it has been equally dependent upon the cross-disciplinary skills
and insights of the researchers themselves.  It is this latter aspect, science/music,
which has given our research its particular character and which circumscribes our
interests.

The Perception of Timbre

Music is based upon, and indeed is dependent upon, signals and environments
which are infinately more complex than those which are commonly used in
psycho-acoustical research.  Yet, it is well-known that trained listeners are
capable of making extraordinarily fine distinctions between complex signals
in complex environments.  In some of the dimensions of acoustical phenomena,
such as pitch, the nature of the distinctions is fairly well understood.
However, in another dimension, timbre (sometimes called tone-color),
there is no coherent theory to explain either the physical characteristics of a
sound to which the ear responds or the mode of organization effected in perceptual
processing.

	Methodology-
We have discovered a technique for synthesis by means of FM [reference] which is capable
of producing for the listener a strong impression of a variety
of natural music-instrument tones.  The spectrum produced by this technique, however,
differs in major and conspicuous ways from the spectrum of a natural tone which
produces a similar impression.  This discrepancy has led us to begin
a rigorous investigation of those physical characteristics of a complex spectrum
which are perceptually salient.  

In order to develop a methodology, another powerful synthesis technique was
created which allows temporal control of phase and amplitude for n partials.
It is capable of synthesizing a tone which includes all of, or a simplification
of, the spectral detail derived from a computer analysis of a natural tone,
therby allowing a systematic reduction in data of a spectrum and comparison
of the audible waveform with the unaltered original.

The two synthesis techniques are applied to the same natural tone of interest.
The FM synthesis data is increased to reach an acceptable simulation,
while the additive synthesis data is decreased to maintain an acceptable
simulation.  Examination of the difference between the resulting spectra provides
the information for another synthesis pass.  The results of this method should
confirm our success at having isolated those physical features of spectra
which correlate to the perception of timbre.

	Testing and Scaling-
Audio signals are generated by a PDP-10 computer which has a 4-channel D-A
converter for analog conversion of the sampled waveform.
The analysis is accomplished by means of an A-D converter which converts
audio input into a sampled wave which is stored on a disk for processing.
The programs forthe synthesis of wave-forms are based on the acoustical
compiler developed by M.V. Mathews at Bell Telephone Laboratories
adapted to the time-sharing, interactive capabilities of the PDP-10 system,
while the wave analysis programs were written by J.A. Moorer of Stanford.