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
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
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.
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
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 test.
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 reflecting strips.
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 coherent.
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.
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
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.
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 bounce.
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
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.
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
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 fundamental.
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
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.