AND INCOHERENT DIFFUSION
Arthur M. Noxon
Acoustic Sciences Corp.
Eugene, OR 97402 U.S.A.
Coherent and incoherent reflections are very different, both in
physical and psychoacoustic properties. Perception effects such
as imaging and musicality are very sensitive to the type and tuning
of reflections off nearby surfaces. Coherent reflections can have
strong correlation coefficients and add information to the direct
signal. Incoherent reflections with random phase signals are weak
in correlation and provide strong masking effects.
Diffusion is the process of mixing up sound. In a 100% diffuse
sound field, there is no sense of acoustic direction, sound comes
equally from all directions. Diffusion may be at times a desirable
condition for acoustic energy. It is created by a sequence of diffusing
reflections. A sound reflection can be either coherent or incoherent.
This quality is very important to be specified because the coherence
of a reflection has a significant sound masking effect on perception.
A device that helps to develop the state of diffusion
by increasing the scattering of sound is called a sound diffuser.
There are four types of sound diffusion mechanisms.
1. Diffraction (sound bends around corners)
2. Refraction (turns by changing wave speeds)
3. Reflection (changing direction upon impact)
4. Resonance (resonant storage and reradiation)
The first three sound turning mechanisms are pretty well known.
They change the direction of sound but not the time wise evolution
of the waveform itself. The scattered sound has the same sonic signature
as the incident sound, they are highly correlated and therefore
a coherent diffusion process takes place.
The last process, resonance, is not usually considered to be a
sound diffuser. Incident sound on a resonator will stimulate the
build up and decay of sound in the resonator. Resonant discharges
are often practically point sources and so the reradiated sound
is well distributed in space. The sound of a ringing, resonant decay
has its own time wise evolution. The incident wavetrain will have
a pressure vs. time signature that is not followed by the sound
of the ensuing resonant decay. Correlation between the incident
waveform and the resonant discharge is very low. Resonance forms
the basis for an incoherent class of sound reflections.
TIME DELAYED REFLECTIONS AND PERCEPTION
There are distinct time periods that relate to the
various properties of perception. Reflections within the first few
milliseconds following the direct sound belong to localization,
i.e. the perception as to where sound is coming from. Reflections
within the next 30 to 50 ms belong to fusion, the develop- ment
of sound tone recognition. Reflections outside of 60 ms develop
the impression of echo and ambience. The coherency of reflections
with respect to the direct signal may well effect the quality of
perception differently in each of these three time regions. Once
this relationship is known, it can be utilized by recording engineers
and acoustic designers to better achieve desired performance.
Reflections of sound that follow the direct signal
within 50 ms are not distinctly heard but are blended together,
fused into a composite sound. If only one reflection is heard, the
phase add and cancel comb filter coloration effects will be heard.
If there are many reflections, randomly off set in time, the phase
add effect averages out to zero and the composite sounds just like
the direct signal. Whenever reflections do not sound like the direct
signal, the composite also does not sound like the direct signal.
The goal of this paper to introduce and measure coherent and incoherent
reflections and then to subjectively evaluate the impact of each
when audited within the 50 ms sound fusion time window. It will
be shown that incoherent reflections, which may be acceptable in
the 60 ms plus time period as ambience or echo signals, are degrading
to musical quality if perceived during the 50 ms sound fusion period.
This summation or coloration of signals smeared together within
the 50 ms perception window is a distinct aspect of tone recognition
but not the whole picture for listening. It does not account for
the consequence of variations in the time ordered detail of the
harmonic structure in the attack transient. The accuracy of musical
quality belongs to the 20 ms attack transient. It is the only event
in which the timing and the phase alignment of the overtones in
complex signals is detectable. Over the last few years speaker manufacturers
have recognized and accommodated both tune and phase alignment in
the design of speakers. It is no longer sufficient to know how the
sound level of each of each partial varies with time, we must also
have correct time alignment and phase of the partials. One technique
that measures in this area of psychoacoustic perception is the correlation
is a measure of how similar one signal is to another. If a direct
signal (Figure la) causes a simple time delayed reflection (Figure
Ib) the correlation factor between the two signals (Figure Ic) is
zero everywhere in time except at the time delay and then their
correlation is 100%.
If the specular reflection is splintered, scattered out in time,
correlation will still exist, but spread out over the range of time
over which the multiple reflections take place. Two types of splintered
reflection systems were tested and both show correlation to exist
over a longer time period than that of the single flat wall bounce.
In Figure 2a is shown a reflection/absorption diffusion grid that
is composed of alternating depth of reflecting surfaces interspersed
with sound absorbing segments. In this system, every other reflector
is curved to backscatter over a wider angle than the adjacent flat
The Figure 2b shows the ETC for the reflection of 400 to 20K. The
multiple reflections are spread over a 2 ms time period. The correlation
measurement between the direct signal and the reflection (Figure
2c) also shows a 2 ms wide correlation. Each of the time delayed,
scattered reflections is specular, a coherent and faithful reproduction
of the direct signal.
A different type of diffuser is composed of a set of troughs
at various depths, shown in Figure 3a. High frequency sound entering
these wells ricochet some number of times depending on the angle
of incidence and the well depth. The ETC of Figure 3b shows a spread
in time of the reflected signal of about 5 ms. The correlation for
this diffuser using 1/3 octave noise at 3K is (Figure 3c) also spread
over a 5 ms period of time. This short wavelength reflection is
Zero correlation occurs when the reflected signal bears little
to no resemblance to the direct signal. This can occur when the
reflected signal has no amplitude because it was absorbed. Incident
sound onto 2" of medium density fiberglass does not reflect
1/3 octave noise at 3K. Figure 4a shows the ETC of this absorbed
"reflection". The correlation test in Figure 4b shows
"zero" because the silent reflection bears no resemblance
to time wise signature of the direct signal.
There is zero correlation if the reflecting signal is not really
reflected at all but instead is an independent sound. A whistle
tone at 1K was played while the direct 1/3 octave noise at 3K was
tested. The tone bears no resemblance to the direct signal and Figure
5 shows zero correlation.
A series of correlation tests were run on each of
three types of reflecting surfaces. The signal used was 1/3 octave
bandwidth noise on 1/3 octave centers between 125 Hz and 3 KHz.
The correlation between the direct signal and the reflection was
made for flat wall bounces, for the absorption/reflection diffuser
and for the multidepth trough diffuser. For the higher frequencies
the correlation of all three reflectors is strong with the time
window being spread out according to the degree of multi-reflections
The test set up for this sequence (Figure 1) uses an incident angle
of 45° and picks up the reflection also about 45°. There
are two data collecting runs. The first one (Figures 6 through 12)
ranges in 1/3 octave increments from 125 Hz to 500 Hz using 1/3
octave pink noise. The analyzer steps 0.2 ms, just over 100 times
to draw out the correlation curve. The correlation time window is
just over 20 ms and is time delayed sufficient to catch the leading
edge of the reflecting wavefront.
Because narrow band noise is used, the correlation
signature will appear as a sine wave of the frequency that is the
center frequency of the 1/3 octave noise. The amplitude of the correlation
measurement depends on the amplitude of the received signal and
how similar it is to the direct signal. The absorption/reflection
diffuser should provide some attenuation of the correlation signal
due to reduced reflecting signal strength. The random well depth
diffuser has no absorption and any loss in correlation amplitude
can be related to either an off axis concentration of reflected
sound (lobe beaming) or a signal correlation problem.
The 125 Hz through 500 Hz survey shows the absorption/reflection
diffuser to mimic the bare wall bounce faithfully except for a full
bandwidth amplitude reduction due to absorption. The random well
depth diffuser has a thinning of correlation in the 200 Hz 1/3 octave
band (Figure 8c) and again at 500 Hz (Figure 12c). The 200 Hz incoherent
reflection is attributable to wood panel resonance and the 500 Hz
problem belongs to the 1/4 wavelength resonance of the deepest wells.
A higher frequency series (Figure 13 through 15)
shows the same test except the step in 50 ms, four times faster
than before. The full test window now is 5 ms. The wave form appears
to be longer but only because the time scale is shorter. The weak
correlation for random well depth diffusers still exists at 1000
Hz (Figure 13) but by the 2K octave and above both diffusing systems
have full and adequate correlation except that the random depth
wells have additional multiple reflections (Figure 15) that stretch
out over the 5 ms window.
The ETC for the random depth well diffuser was
taken with the mic in the bottom of one of the deep wells for frequencies
between 200 Hz and 20K Hz. The only indication of possible resonance
effects is (Figure 16) the rapid drop of initial reflections followed
by a resurgence of energy discharge between 4 and 7 ms after the
initial reflection. The waterfall (Figure 17) was taken to try to
identify the resonance. It ranges from 50 to 500 Hz over a time
period of almost 100 ms. By using the heavy time averaging window
of 40 ms, the structural resonance effects below 250 and the 1/4
wavelength at 375 Hz become evident.
There seems to be low correlation when the reflected signal is
involved with resonance even though the energy of the reflection
is high. The resonant discharge produces a tone that has its own
time wise identity, not a simple time delayed and coherent reflection
of the direct signal.
INCOHERENT REFLECTIONS AND PERCEPTION
There is a subjective aspect to incoherent reflections.
The demonstration of this effect was first performed in a respected
hi end audio manufacturer's demo room at the 1988 CES, Las Vegas.
The audio playback system had random depth well diffuser panels
behind and between the speakers, set up to diffuse the front wall
A CD track was played that had solo classical guitar work. The
perceived musical quality of a plucked low E guitar string was radically
affected by the reflections out of the random well depth diffuser.
All 15 people in attendance simultaneously could repeatedly witness
this effect. Its characteristic was identified as being a "colorless
note". The fundamental string tone was present but its expected
rich harmonic structure seemed to be obscured.
When the random depth well diffuser panel was covered over with
a blanket and the musical section was replayed; the easily recognized
and all so familiar sound of a plucked acoustic guitar string returned.
High frequency string sounds did not seem to have this "colorless"
quality, only the lower frequencies, those with substantial transient
partials in the middle octaves, 250 to 750 Hz.
ATTACK TRANSIENT FIDELITY
Correlation of continuous sound is a straight-forward
statistical sampling process. Trying to do correlation on the attack
transient of a plucked guitar string is more difficult because of
the short time period of the attack and the long time period of
the sustain. A study of the attack transient wave form itself does
show the effects of different types of reflecting surfaces.
The signal out of a plucked electric guitar string is shown (Figure
18) with rapid harmonic detail changes in the first 50 ms for a
125 Hz note. The overall long term spectrum for this pluck (Figure
19) shows strong and regular upper partials. The signal was recorded
and played back over a small, average speaker. Its sound was reflected
off of the three types of surfaces and captured by a mic and storage
scope. The first 40 ms of each bounce shows the evolution of the
attack transient into the sustain wave form.
The first pluck (Figure 20) series shows a substantial
initial 10 ms transient difference between the random well depth
diffuser and the other two. Beyond the attack transient is seen
a wave form change. With the random well depth diffuser there is
strong third harmonic detail added to the positive peaks of the
A second pluck at 125 Hz was recorded, this time with more harmonic
detail due to a shifted finger position. Again the specular/absorptive
reflection is very similar (Figure 21) to the wall reflected signal
except for reduced amplitude. The random depth well reflector shows
again the first 10 ms attack transient distortion. It also shows
harmonic distortion in the sustain particularly with accentuated
rise times in the positive part of each fundamental peak.
The persistent upper partial distortion in the 3
to 400 Hz region out of the random depth diffuser led to another
test, this time at 400 Hz. Again, serious distortion (Figure 22)
in the first 50 ms of the attack transient is observed. Also in
the sustain is seen more than simple reduction of levels as with
the specular/absorptive diffuser. Here, every other cycle is louder
and sharper peaked while adjoining pulses are quieter and more grounded
than the other two reflecting surfaces.
© 2009 Acoustic Sciences Corporation.
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