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C00009 00003	INTRODUCTION TO ARTIFICIAL REVERBERATION TECHNIQUES
C00018 00004	CURRENT RESEARCH
C00032 00005	PROPOSED RESEARCH
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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.
The discussion which follows will be divided into two main topics:
the  simulation  of  realistic sounding artificial
reverberation which  can be  controlled via  perceptually  meaningful
parameters by the user; and efforts to maximize  the area in
which  listeners receive  convincing  illusions of  localized sources
that are at apparent positions specified by the user.
An ongoing consideration of this research is that the simulations
must be accomplished  with the minimal number of
speaker-channels (independently controlled loudspeakers)
and  an optimization of computer resources.

The  construction of  algorithms for  the  simulation of  reverberant
spaces is aided  by the quantity of research which has been performed
in the field of room and architectural acoustics. From this rich field
of theory Schroeder (1961) produced a model for the purpose of simulation
of realistic sounding room reverberation using loudspeakers.
The significance of  this contribution is that 
it overcomes the most objectionable perceptual qualities of all previous
attempts at artificial reverberation, and its computer implementation
is both simple and economical.  We will  first  describe the  fundamental
algorithms  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.
Proposed
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.  Perceptual scaling  techniques will  be
enlisted  to determine  the perceptual  distinctiveness and  relative
importances of various features of reverberation  networks, both 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.
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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 implementation
of cues for localization  is next discussed, including
azimuth or angular displacement, distance, and altitude.
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1.  SIMULATION OF REVERBERANT SPACES

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INTRODUCTION TO ARTIFICIAL REVERBERATION TECHNIQUES
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We use three forms of the delayed feedback loop, the basic tool of
artificial reverberation. The first and simplest is the comb filter,
where the frequency response is periodic or comblike.
Figure 14 shows a block diagram of the comb filter with its impulse
response and frequency response.
The second form
is a simplification of the all-pass network of Schroeder (1961), so-called
because, unlike the comb filter, it passes all frequencies equally well.
Figure 15 shows the all-pass network and its impulse response.
The third form is an oscillatory version of the all-pass which, while still
passing all frequencies equally well, has an impulse response of a damped
sinusoid.
Figure 16 shows the oscillatory all-pass network and its impulse response.
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%5the comb filter
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The form of comb filter we use for artificial reverberation
is identical to that discussed by Schroeder (1961), a delayed
and attenuated feedback loop, Figure 14.
The impulse response of the comb filter is a pulse train with
exponentially decaying amplitude. The frequency response resembles
a comb, i.e., peaks at integer multiples of the reciprocal of the delay time.
This and other forms of the comb filter are described in Appendix C.
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%5all-pass unit reverberators
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A particularly useful unit of artificial reverberation is the all-pass network.
We use two different forms:
(1) a first order unit of which the impulse response is a pulse train with
exponentially decaying amplitude, and (2) a second order unit
of which the impulse response is a pulse train of which the amplitude is
a damped sinusoid. These unit reverberators are shown in Figures 15 and 16,
and described in full in Appendix D. We will introduce them briefly here.

The relationship between the input waveform to the first order unit
and the resulting output waveform is formulated in the following
recurrence relation:
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%3
(8)	Y%8n%3 = GX%8n%3+X%8n-m%3-GY%8n-m%3
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This unit reverberator, as with all linear digital filters, consists
of a weighted sum of delayed input samples added to a weighted sum of
delayed output samples. The recurrence relation shows how the next
output sample is to be computed.
X%8n%1 is the n%2th%1 sample of the input waveform and Y%8n%1 is the n%2th%1
sample in the output waveform.  (It is helpful to recall that the digital
resentation of a waveform is a series of samples, or the instantaneous
numerical values of that wave at sampled points in time.  The n%2th%1 
sample is the value of the waveform at time nh, where h is the time between
successive samplings.) X%8n-m%1 is that sample in the input waveform which
occurred m samples before X%8n%1, i.e. the value of the waveform delayed m
samples with respect to X%8n%1 with delay time mh.  This same delay
relationship holds for the output samples Y%8n-m%1 and Y%8n%1.
Finally, as the gain, G, approaches unity, the impulse response of the reverberator
decays more and more slowly.
Essentially, this is the all-pass unit reverberator used by Schroeder (1961),
except that we have realized it in the canonical form, thus saving one
multiplication over the form previously used.
A block diagram of this unit and a plot of a typical
impulse response are shown in Figure 15.
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There is one important generalization of the all-pass network,
the oscillatory all-pass. The recurrence relation for this second
order unit is as follows:
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%3
(9)	Y%8n%3 = G%81%3X%8n%3+G%82%3X%8n-m%3+X%8n-2m%3-G%82%3Y%8n-m%3-G%81%3Y%8n-2m%3

    where  G%81%3 = C%83%3/C%81%3
           G%82%3 = C%82%3/C%81%3
	   C%81%3 = h%22%3(%4w%80%22%3+%4s%22%3)+4%4s%3h+4
           C%82%3 = 2h%22(%4w%80%22%3+%4s%22%3)-8
           C%83%3 = h%22%3(%4w%80%22%3+%4s%22%3)-4%4s%3h+4
	   %4w%80%3/m is the frequency of the oscillation
	   7m/%4s%3 is the reverberation time, as in the first-order unit

%1
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A block diagram of this unit and a plot of a typical
impulse response are shown in Figure 16.
At first glance, the sinusoidal property of
the second order unit might seem to be undesirable 
because one might perceive the frequency of the
sinusoid as a spurious tone. We have found conditions, however,
which suggest that this oscillatory characteristic may be used to advantage.

The parameters of both all-pass unit reverberators (equations (8) and (9))
and the comb filter are:
delay time (pulse spacing), gain, and reverberation time (the time it takes
for the reverberant signal to decay by 60dB, or approximately 7m/%4s%1).
Only two of the three parameters are independent, i.e. the value of
any one of the parameters may be expressed as a function of the other two.
This construction is useful when linking unit reverberators to form a
compound reverberator, discussed below.
The second order all-pass unit has as an additional parameter, the frequency
of the sinusoid.
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CURRENT RESEARCH
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While the quality of reverberation of rooms is to some
degree a matter of taste, there are some general attributes which all
`good' rooms seem to have: 1) an amplitude-frequency response which has no strong
coloration, i.e. resonances or apparent periodicities, 2) an echo density which
is sufficiently high that individual echos are not resolved by the ear,
and 3) an echo response which is free from periodicities or flutter.
Our goal, then, is to combine unit reverberators to form reverberation networks
which preserve maximum similarity to the reverberation of real rooms.
As with much that is described here, the strategies we use for combination of
several comb filters and/or all-pass units in parallel and/or series are based
on the work of Schroeder.

The most useful implementation is, perhaps, the combination of all-pass units
in series. This network meets the above mentioned criteria of real rooms in the
following ways:
1) the frequency response of the network is, by definition, flat, since each of
of the units is flat, 2) the delay time of each of the units
decreases exponentially, which increases the echo density to
a point where individual echos can not be resolved by the ear, and
3) the delay times are set to be incommensurate with each other, which
eliminates the possibility of periodicity or flutter in the echo response.
Due to its flat frequency response, this network does not add its own 
`color' to the reverberation; it is therefore called `colorless' reverberation.

There is a fourth attribute of natural reverberation: its
spatially diffuse character.  In simulation techniques this is of utmost
importance, since it determines the subjective impression of a real space.
In order to simulate this quality it is necessary to produce uncorrelated
reverberant signals from at least two speaker-channels (independently
controlled loudspeakers). The obvious, and our first, implementation 
was to create totally independent but similar reverberation networks for
each of the speaker-channels.  This method has given exceptionally realistic
reverberation, but it is also very expensive.
A more economical method is to use a single reverberator which,
at the final stage, branches to parallel (though not identical) unit reverberators. 
These final unit reverberators may then be connected each to one of the
speaker-channels; or the output of the final unit reverberators may be mixed
in differing proportion for each speaker-channel.
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%5colorless reverberation
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To form the all-pass, or `colorless,' reverberator, several of the first-order
all-pass unit reverberators are cascaded. We adjust the delay and gain of each
unit reverberator until the impulse response of the compound reverberator is
a smoothly decaying exponential with a perceptually relevant increase
of density throughout the entire reverberation time.
Thus far we have had the most success with
delays and gains which decrease exponentially from unit to unit in the series.
The decreasing delays (expressed as the nearest prime number of samples)
produce a smoothly increasing pulse density. With exponentially decreasing gains,
in contrast to constant gains, the contribution of the each successive
unit reverberator
in the series is normalized, insuring that most of the contribution of each
unit reverberator will be above the noise threshold of the system.

We have implemented this reverberation network in digital simulations,
and the simulation is auditioned and tested via loudspeakers
in real rooms. While we know that ultimately, due to the addition of signals
from loudspeakers and the irregular response of the room, the signal cannot 
remain uncolored once it leaves the loudspeaker, it is important
to be able to maintain the flat response at least as far as the loudspeaker.
A coincidental resonance peak or depression between a colored reverberator and
the room would tend to intensify the acoustical problems of both.
There are cases, however, when one might actually want some coloration,
or more likely, some specific coloration.  For example, we may want to
impose some special spectral shape on the output of the reverberator,
and thus shape the room in which a simulated signal occurs. 
In this case, the resultant signal will conform exactly to the contour 
of the shaping filter only if the reverberator is colorless.

In an informal investigation we listened to a digitized violin phrase
without reverberation, with colored reverberation, and with colorless reverberation,
Recorded Example 4.
Although the digitized violin input is the same in all cases, the violin
timbre seems more natural when comparing either of the reverberated signals
to the non-reverberated signal and most natural with colorless reverberation.
This suggests that the accuracy of testing timbral synthesis and data-reduction by
perceptual comparisons would be improved by the use of artificial reverberation
and by the condition that the reverberation is not adding its own spectral character
to the sounds under consideration. Figure 17 shows the long-term discrete
Fourier transform of a single digitized violin note, first without reverberation,
then with colored reverberation, and finally with colorless reverberation.

Schroeder (1962) pointed out the difficulty of maintaining both uncolored
reverberation and exponential decay of the pulse train when mixing the
direct signal and the reverberator output. 
If signals are mixed by addition, then the result is no longer flat.
However, flatness can be maintained by nesting the mixing process inside
yet another all-pass network which, in turn, has the deficiency
of producing non-exponential decay.  Here, the imprecision of perception
seems to be a help, for without
exhaustive searching we have found delay-gain relationships
for both types of mixing where deficiencies are not apparent.
Although we cannot now suggest a theory for 
perceptually valid colorless reverberation, we are convinced that this
is an area worth further investigation.
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%5spatially diffuse reverberation
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We have made extensive use of multi-channel reverberation projection to
achieve a spacially diffuse quality, but using a combination of comb and
all-pass unit reverberators first suggested by Schroeder.  Our implementation
of this reverberator, in l967, was the first outside of Bell Telephone
Laboratories.

The comb/all-pass reverberator takes the output of four parallel
comb filters as the input of two or more cascaded first-order all-pass
units.  The delay and gain parameters follow closely the limits suggested
by Schroeder.  In order to avoid echo cancellation and superposition
each delay is expressed as the prime number of samples
which is the closest approximation of the delay time.
The gains are expressed as a function of the delay time and the desired
reverberation time.
The time gap between the direct signal and the reverberation, the `first
delay,' is determined by the shortest comb filter delay.
In creating a two-channel and then four-channel diffuse projection, the
comb/all-pass reverberator was reproduced once for each channel.
We used incommensurate delay ratios. The gains were expressed as a
function of the delay time and the desired reverberation time.
Experienced listeners have agreed that this method has given surprisingly 
realistic reverberation.

For better efficiency of computation, a variation of this comb/all-pass
was implemented.
We reverse the order of the comb and all-pass units
of the comb/all-pass so that the output of three first-order
all-pass units in series is taken as the input to each of four comb filters
in parallel.  The four comb filters are then added in various phase relationships
(+ - + -, for example) with a different permutation for each loudspeaker.
When the reverberation given by this smaller, more efficient, reverberator
is compared to that of the large reverberator previously discussed, we have
found that, for most applications, there is no loss of quality.
However, the large reverberator is still used in the generation of some of
the more unusual qualities of simulated rooms and localized sound sources.
We have also considered an all-pass multi-channel reverberator, which
will be discussed below.
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PROPOSED RESEARCH
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We will here discuss the proposed research which is centrally concerned
with approaches to our ultimate aim: the development of a general
and easily-controlled algorithm for simulation which is based on a 
perceptual model for reverberant spaces.
We plan to use the second order (oscillatory) all-pass unit reverberator 
to implement the undulatory reverberation characteristic of good music rooms and
determine whether this characteristic will intensify the realism of our simulation.
In support of this enquiry, and also to create colorless and spatially diffuse
reverberation, we will develop all-pass multi-channel reverberators
which include second order units.
Based on analysis of multi-channel recordings of selected rooms we will explore
the degree and nature of inter-channel reverberance differences, the
overall spectral `shape,' and localized resonances.  We will then
include the results of these studies in our simulation,
which, in turn, will be verified by perceptual testing techniques similar
to those already discussed.  Based on these findings, we plan to develop
an algorithm which can be controlled by the user via perceptually
meaningful parameters such as reverberation time of the room, resonances and
their location, reflective qualities, proximity of the walls to the listener,
and the location of obstacles in the room.
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%5applications of the second order all-pass unit reverberator%1
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Preliminary investigation indicates that the second order (oscillatory)
unit reverberator will serve two aspects of our research.
In discussing acoustical attributes of good music rooms, Knudsen
(1963) characterizes the reverberation as having not only a relatively
smooth decay but also a `slightly undulating' characteristic.
As mentioned above, we have produced smoothly decaying and colorless
reverberation. But it is only with the development of this oscillatory unit
that we can consider as an additional characteristic the undulatory quality
of the reverberation.
When this unit reverberator is used as a unit of a compound reverberator
both the frequency and amplitude of its contribution can be controlled.
This suggests that we will be able to determine whether the undulatory
characteristic will intensify the realism of our simulation and also,
perhaps, discover some sort of parametric range of control.

The second application of this unit is for spatially diffuse
reverberation.  The fact that it produces phase relationships which
are of another order of complexity compared to the first-order unit
suggests that it could be used as an important feature of an all-pass
multi-channel reverberator.  For example, the output of three or four 
first order units in series can be taken as the input of a number of
second order units (one for each channel) which have incommensurate
delays and incommensurate periods of oscillation.
It appears that such a reverberator could
produce reverberation which is as diffuse as that of the
all-pass/comb variation, described above, but also colorless.

There is no intuitive way to predict the nature of the complexity
and the effect of the damped oscillation when this unit reverberator
is in series with other like units or with first order units.
We have found, however, that much can be learned from visual and aural
observation of the impulse response of the output as the units are connected.
We are therefore developing a graphic predictive analysis program which both
displays and `plays' the impulse response of any combination of unit
reverberators.  Such experimentation is totally dependent upon the combination
of computer implementation and well trained `ears.'
Recorded Example 4 includes an illustration of an oscillatory single-channel
reverberator (five all-pass units in series, the first of which is an oscillatory
unit): first the impulse response, and then a 440 Hz smoothed sawtooth.
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%5simulation of real rooms
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The problem of simulating a real room is significantly more difficult
than simply producing spatially diffuse reverberation, although the
requirement for multi-channel output is the same.  Multi-channel
recordings made in real rooms preserve, to a large extent, the important
localized resonances and produce the perceptual impression of a physical
space.  The artificial reverberation techniques have not so far produced
an equally strong impression.

In order to develop our basic data, we plan to make 4-channel recordings of
selected signals in a number of real rooms which fulfill the general requirements
of good reverberation.  Through the use of a high precision 4-channel
analog to digital converter (described in section III, Research
Facilities), we will digitize the signals, analyze the data for frequency
and impulse response, and examine through graphic techniques the
degree and nature of inter-channel differences.

We plan to begin our research in the simulation of real rooms through
processing techniques applied to all-pass networks.  The networks will be
optimized such that four unit reverberators in series will branch to n units
in parallel, where the outputs are passed to the n speaker-channels.

The value of artificial reverberation which has a flat response is that
spectral shaping filters can be arbitrarily applied to the reverberator
output.  Two of the the filters we intend to use are the digital resonator
and anti-resonator, described in Appendix C.
The general synthesis
algorithm is designed to allow operations to be performed on the 
simulated tone and the simulated reverberation independently.  (In the
following section on localization, the need for this control will
be made clear.)  Therefore, resonator and anti-resonator circuits,
having different cues, can be applied to the reverberation of each
of the speaker-channels according to the %5localized%1 resonances of
a real room.  It was pointed out above, that spatially diffuse reverberation
is dependent on uncorrelated signals at the two ears.  Our preliminary
investigations suggest that, in addition to an uncorrelated impulse
response, localized resonances are of considerable perceptual importance
to spatially diffuse reverberation.

Other filters which may be useful are the more traditional high-pass, low-pass,
band-pass, and band-stop filters, as well as more special purpose filters.
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%5perceptual scaling and testing
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We project a special use for formal perceptual scaling and testing of
the  qualitative  differences between  various  simulated reverberant
spaces.   Of  central interest  is  a  determination of  the  optimal
algorithm for  the production  of naturalistic  reverberation, having
good    spatial   diffusion.    The   smallest    total   number   of
unit-reverberators which  can  be used  to  create such  high-quality
reverberation  will  be  a major  concern,  since  this  would be  an
important saving  in  computer  resources. In  this  regard,  we  are
interested  in  the  amount of  apparent  uncorrelation  between  the
speaker-channels  which can  be produced  by  the smallest  number of
independent unit-reverberators per channel.  The related  interest is
in  the smallest  number  of unit-reverberators  needed  for any  one
channel,  given the total  output of all  four channels.   We will in
addition  differentiate  the  usefulness  of  the  various  types  of
unit-reverberators,  in  combinations,  with  respect  to  the  above
concerns.

The ability of  spectral shaping filters  to create convincing  cues
for natural  environments will also  be studied.   We are  especially
interested  in a test  of the importance of  the localized
resonances which can be produced by independent shaping filters in
different speaker-channels for the creation of natural sounding spaces.
An evaluation of the relative efficacy of localized resonances via
spectral shaping filters and uncorrelated speaker-channels via
independent reverberator networks is a central concern.
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%5higher level algorithms
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Following the research in the development of algorithms for the simulation
of real rooms and the evaluation of the results through the use of the
scaling techniques described above, we plan to generalize this data in the
form of interactive algorithms.  Of principle importance will be the
organization of the data required for the simulation techniques into
perceptually appropriate `visible' controls for the user.  

We are currently using an interactive reverberator compiler as is an aid
in exploring the technical aspects of digital artificial reverberation.
The program utilizes the parameters of delay time, gain, reverberation
time, and first delay.  We are currently expanding this program to also
display and play the impulse response of the reverberator as each unit reverberator
is defined. As the next level of control, we plan to develop algorithms
which will allow us to deal with problems of reverberation and the
simulation of reverberant spaces in terms of their perceptual attributes.
Or more specifically, we plan to move beyond considerations of the characteristics
of a particular complex reverberator and describe the room we wish to
simulate in terms such as reverberation time of the room, resonances and
their location, reflective qualities, proximity of the walls to the listener,
and the location of obstacles in the room.
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