The Modulation Transfer Function (MTF) is
used in room acoustics as a descriptor of the effectiveness of transmission
down the signal path, between the speaker and listener. A major
application for this has been speech intelligibility. Basis for
MTF analysis is the signal to noise ratio. Noise can be any sound
masking effect, steady state noise, transient noise of reverberation
or apparent noise due to adjacent octave sound levels.
Narrow band MTF is used in the present work.
This is in contrast to the octave band methods common to traditional
speech intelligibility. Here, pure tone modulation used to develop
spectral response detail. A rapidly gated, slow sine sweep is the
test signal for the articulation response curve. This technique
allows blurred transmission bands to be specifically identified.
These narrow ranges of poor articulation are both audible to the
listener and visible in hard copy data. Changes to the room acoustic
are also easily documented. The responsiveness of this test to room
acoustics in addition to the fine grain spectral information in
the articulation response curve suggests that this system be used
as a diagnostic tool. Although originally developed to demonstrate
small room acoustics in the lower registers, it has found use in
the full range of room sizes from the amphitheater and auditorium
right through to recording studio vocal booth.
I ARTICULATION
RESPONSE CURVE (ARC)
A. RATIONALE
The Modulation Transfer Function (MTF) is
used in room acoustics as the descriptor of effective signal transmission
between speaker and listener. A popular application of the MTF is
for speech intelligibility. Here we look at an application of MTF
developed for precision playback environments such as the hi-end,
hi-fi listening room and the recording studio. The suitability of
the standard Speech Transmission Index (STI) approach falls short
on numerous points in these smaller spaces that have high musical
articulation requirements.
The spectrum segment useful for STI prediction
or measurement starts at the 125 Hz band and each octave band is
weighted for significance in speech recognition. Music occupies
two octaves lower than the range used for STI work, half the keyboard
is below Middle C 2 5 2 . The weighting of these and other octaves
in a calculation is not yet established. The musical spectrum and
the relative significance of each octave band may well not be the
same as for speech. The Music Transmission Index (MTI) may be convertible
to STI, but the converse may not be possible. This would be due
to the relative lack of full bandwidth information in the STI. Clearly,
research remains to be done in this area.
The STI joins the group of single index acoustic
descriptors, such as NRC, dB, A, IIC, RT60, et. al. Architectural
specifications can be satisfied with a single index indicator. Acoustical
engineers and consultants engaged in diagnosis and remedy have always
required spectral detail and the subject of intelligibility is no
different.
Measured STI only needs the signal to noise
ratio to be detected. Tracking octave band decay rates is one method
used and monitoring modulated octave band noise levels is another.
Both use selected octave bandwidths and yield a single intelligibility
rating. The approach contributes little to the diagnosis of room
acoustics. The present technique provides narrow band spectral articulation
information. This facilitates diagnostic efforts and evaluation
of STC.
The predictive side of MTF analysis requires
the ability to accurately estimate the signal to noise ratio. The
noise level is due to the reflections in the room and due to its
reverberation. Predictive methods that use room reverberation decay
rates have the prerequisite imposed that the room sound field is
instantaneously diffuse and has an exponential decay rate.
A non-linear method of predicting noise levels
is to use ray tracing of the first 30 reflections. This method better
correlates with measured STI. Complex room geometry limits this
method. Neither linear acoustics nor ray tracing can be used for
predicting in small rooms dominated by room resonant mode decays.
The musical line is characterized as a rapid
staccato of complex tone bursts. Music then is a set of musical
lines, overlaid and intertwining one another. The basic element
of this woven fabric of music is the tone burst. The acoustic descriptor
that relates to musical articulation may well be the tone burst,
indeed a rapid staccato of bursts. Such a signal has been used for
harmonic distortion analysis room acoustic transmission path. Here
we only desire measurement of the signal envelope and the faithfulness
of its modulated transmission. Wave form reproduction, although
important, is not the issue addressed.
A synthesis of these constraints and requirements
is embodied in the present approach to MTF. The Articulation Frequency
Response Curve (AFC) is a relatively simple, direct physical measurement.
Equally important is the subjective aspect. The auditor in a precision
listening setting can play the test signal over headphones and hear
the rapid, clean staccato of tone bursts whose frequency is slowly
varied. The auditor expects the room acoustic to play this signal
accurately. By removing the headphones and listening to the same
signal in the playback room, defects in the transmission path become
quite audible. In a small room, articulation dramatically varies
with frequency. Typically, there are tenth-octave bands of totally
garbled transmission adjoining similar sized bands of quite intelligible
transmission. The Articulation Response Curve is a fine-grained
quantification of the “fast tracking” ability of a listening
room.
II
COMPARISON WITH TRADITION
A.
DEFINITION OF STANDARD TERMS
1. Signal Intensity (I)
Standard MTF format assumes the sound intensity envelope is a modulated
cosine with a DC offset.
The mean signal intensity (Io) is modulated
by the modulation amplitude (mIo).
2. Modulation Index (m)
The modulation index is defined as the ratio of the intensity of
the modulation to the mean intensity of the signal, modulation plus
noise.
It is also expressed in terms of the signal
level Is = mIo and the noise level IN
= Io - mIo.
3. Modulation Transfer (MT)
This is the attenuation in dB of the modulated signal. It is a function
of the modulation index.
MT = 20 log m
4. Signal to Noise Ratio (SNR)
The signal to noise ratio is the level of difference between the
signal and the noise (LS/N).
It can also be expressed in terms of the
modulation index.
5.
Transmission Index (TI)
The transmission index is the SNR measured in dB and expressed in
percent. To do this the SNR is offset to a practical zero % level
and then proportioned to the range of effective SNR. These are subjectively
determined constants that relate the perceived threshold of modulation
to the maximum value of modulation.
The offset is 12 dB and the range is 30 dB.
6. Speech Transmission Index (STI)
This is compiled as the sum of the weighted TI for each of the 7
octave bands and expressed in percent.
The weighting factors (WK) normalize
to 1.
7. Octave Masking Effect (mO)
This occurs when the lower octave is louder than the measured one.
0.3% of the lower octave intensity is considered noise acting on
the test signal.
The impact of simultaneous independent masking
effects is carried by multiplying their independent modulation indices
together.
m = m1 x m2
B.
MTF IN PRESENTLY MEASURED TERMS
1. Signal Modulation Level (La)
Separated signal and noise levels are not directly measured in the
present test method. The articulation response curve is the timewise
evolution of the received sound levels. This easily allows measurement
of La, the fluctuation in dB of the test signal.
2. Modulation Index m(La)
The modulation level (La) can be expressed in terms of
modulation index by rewriting its definition.
Upon rearrangement, the modulation index
is resolved solely in terms of measured level fluctuation (La).
3. Modulation Transfer (MT)
The reduction in modulation can be related to the modulation level
at the receiver La.
4. Signal to Noise Ratio (SNR)
The signal to noise ratio is developed by using the new expression
of the modulation index.
5. Transmission Index (TI)
The transmission index remains except as the SNR term is above has
been modified.
6. Mean Transmission Index
(TI)
The concept is to sum the various TI values similar to that as done
with the STI. Data collected here is not from octave bands but from
small bandwidths of tones having similar modulation levels.
The STI octave band weighting factor (WK)
here is undefined. It will be carried in the form of (Wi) to suggest
that a listener based preference fit option still remains open.
The octave bandwidth weighting actor in STI
appears here as a “log frequency” term in the averaged
5.
7. Octave Masking Index (mo)
This effect is left out of the current presentation. However, it
should be thoroughly investigated and ultimately included. It clearly
is an operative with small room acoustics. It is easy to find bandwidths
with low level articulation and low mean sound level that are just
upfrequency from a loud and strongly fluctuating signal.
A given mean intensity level is given by
the mean sound level (L)
Assume,
for example, equal octave fraction band widths for a low frequency
75 dB level followed by a weaker 65 dB level
This single level shift is of small consequence
but cumulative effects can occur due to a very rough response curve
loaded with room resonances. Only 4 such 10 dB shifts would produce
a 90% masking index.
III APPLICATIONS
A.
THE TEST SIGNAL
1. The Burst
The MTF (Modulation Transfer Function) method of testing for articulation
uses a gated audio signal. For musical playback in listening rooms,
a pure tone is gated 8 times per second. Shown in the figure is
one burst, it lasts about 60 ms. The sweeping frequency changes
about 1 Hz during each burst. This particular burst started at 183
Hz and over 60 ms has shifted to 184 Hz.
2. Duty Cycle
Each tone burst is separated by a dwell time. We use here a 50%
duty cycle: 60 ms on and 60 ms off. During the silent period the
signal generator continues to change frequency. The next burst after
the 184 Hz signal would start at about 185 Hz and slide upwards
to 186. Here we show three distinct tone bursts spread out over
a 4/10 second time window. These bursts are clearly 60 ms long followed
by a 60 ms dwell.
The burst has a square wave modulation. Typical
MTF bursts are sine wave modulated, either amplitude or level. Here
the square wave modulation has ringing in it, visible in both the
on and the off parts of the duty cycle. A ramped attack and decay
would reduce the ringing effect. Although the pure tone quality
of each burst is degraded by the low level ringing, this coloration
provided unique cues for the subjective perception of attack transients.
At about 2 dB articulation level, the LF ringing loses audibility—this
may suggest a method to evaluate perception thresholds of tonal
transients.
3.
Frequency Range
The tone generator is set to be a linear ramp. The signal starts
at about 20 Hz and sweeps with a rate of 20 Hz/sec up to 800 Hz
and back down to 20 Hz. This symmetrical format has proven easy
to read. The ramp up frequencies are not identical to those on the
ramp down. This method also serves as a check on the repeatability
and accuracy of the test.
4.
Signal Intensity
Next is shown the test signal as seen by a dB meter. If each burst
is clean and each dwell period quiet, the dB meter output will alternate
between loud and quiet levels. The signal rises in the presence
of a burst and falls during the dwell time. There are 2 seconds
shown and the 16 sound burst level peaks due to the 8 bursts/second
test rate. The actual electric signal level shifts some 50 dB. The
damping factors in the analyzer circuitry limit the level swing
to only 17 dB. However, this seems to be more range than adequate
for the analysis of most rooms.
5. The Complete Test
The entire test lasts about 75 seconds. The frequency from 20 Hz
through 800 Hz and back down to 20 Hz again. The full test is shown.
The level swing of each successive tone burst is clearly visible
in this display. The burst’s tone raises steadily to the 800
Hz peak frequency and then drops back down during the second half
of the test. By listening to this signal on headphones, an articulate
audition of the test tone is available.
B. THE RECEIVED SIGNAL
1. The Test Setup
The gated set of tone bursts is played into the room. This allows
the distinct features of playback articulation to be observed. A
good way to record the effect is with an omni mic and tape recorder
without AGC (automatic gain control). Once the listener’s
signal is captured on tape, it can be played back through an analyzer
circuit at a later date.
2. Articulation Response Printouts
The articulation response curve is developed by plotting the recorded
sound level vs. time. This is most directly accomplished by running
the signal into a chart level recorder. Another method uses the
dB level output from a meter to feed the vertical sweep of a storage
scope set at very slow horizontal sweep and a printout on an x-y
plotter.
3.
Burst Sequence
A closeup of consecutive tone bursts shows substantial acoustic
energy can occupy the dwell period. There are 4 bursts in this 8/10
second display. Notice how the burst is deformed. What used to be
a sharp attack, flat sustain and abrupt decay has been turned into
a pulse that has lost distinctive features.
Ramps, both up and down take the place of
the sharp attack and decay of the articulate signal. The sustain
does not hold flat, it is foreshortened by the ramping transitions.
In this inarticulate space, the room mumbles, slurs and often will
“double-tongue” the rapidly gated signal.
4. Articulation Response Curve
Here is what a typical hi-fi demo room does to the fully articulate
signal. The signal received by the listener will display some ranges
of articulation but most of the test data looks very thin. When
the vertical strokes are short, the articulation is weak. There
will be little sound level difference between successive tone bursts
and dwells. The only way to improve articulation is to “clear
the air” between bursts by adding acoustic control.
IV ANALOG
TRANSMISSION INDEX
A. APPROXIMATION TO TI
1. Fitted Curve
The STI or as generalized here the TI is an equation based on clear
definitions. The weighting factor feature (WI) can be
set and prorated to bandwidths used to convert the TI into the STI.
However the data taken must be converted into a computer and processed
to calculate the STI. An analog electronic circuit approximation
to this equation is desired.
The
key is the TI term. Within the range of desired values a simple
expression has been found to closely match within a few percent.
Also note the expression is in terms of La, the presently
measured modulation variable.
2. Circuit Diagram for Measurement
The circuit diagram for the analog approximation equation is shown.
The first stage develops the level of modulation (La).
The second stage develops the dB level of the modulation (Log La).
These two frequency dependant parts are properly ratioed and added
to a DC offset then integrated against log frequency. Regardless
of the reference level of either term, the DC offset can be scaled
to fit.
If the frequency sweep is a log sweep instead
of linear, then log frequency weighting will be maintained by integrating
over time. Substantial signal conditioning has been left out of
this circuit to retain a sense of propriety integrity but the basic
elements are presented.
B. DISCUSSION OF La
AND Log La
1. Modulation Level (La, dB)
Articulation is measured here in terms of the modulation level in
acoustic dB’s. The weighting scale dB,A or dB,C doesn’t
affect articulation. Articulation is merely a difference in sound
levels.
It is semantically possible to propose that
an effect of negative articulation could exist and not be detected
by the present circuit. This occurs whenever sound levels in the
dwell period exceed levels, attained during the burst. This seems
to be able to happen at a frequency for which sound cancellation
occurs. The modulation transfer function is not defined in this
situation of negative modulation level.
Negative modulation is physically improbable.
It takes time for resonant conditions, strong enough to cancel a
direct signal, to be developed inside the room. The direct signal
will exceed reverb levels during this initial energy buildup period
in the room. During this transition period, the direct signal will
be heard. Energy is always split between the burst and dwell periods.
2. Articulation Level (10 Log La,
dB)
This is also measured in dB and the scale
is adjusted so that 1.0 dB articulation is equal to zero articulation
level (Ref, 1dB). This is really mathematically arbitrary but set
here with considerations. The listener’s minimum perceived
level change is 0.4 to 0.5 dB for any tone. For the practical purpose
of signal burst reproduction 1 dB level differences though audible
have little to no perceived value for depicting quality music transition
detail. Therefore, it was chosen as zero dB. Regardless, this is
an empirical curve fitting arrangement and a different reference
here would be reflected in a different DC offset constant than 0.08
above.
C.
L, La AND Log La OF TEST SIGNAL
1. Constant Modulation Test Signal
The test signal has a constant signal to noise ratio of at least
45 dB or the full dynamic range of the test cassette tape. The corresponding
articulation level shows as the solid, slightly fluctuating dark
line. It is overlaid against the back drop of its gated sweep response
curve (La).
Two curves are shown here. The sound L(t)
level vs. time articulation response curve is the wide4 fluctuating
line. Overlaid on it is a solid, slowly changing and relatively
flat line, the Modulation Level, La(t).
2. Upper Limits to Sound Level
The sound level curve is not fully accurate because of the ballistics
in the electronic detection circuits. For this data run the upper
limit is about 20 dB. The real 40 dB signal modulation does not
show. This is of no practical concern because 15 dB to 20 dB differences
between peaks and valleys in the modulation envelope are subjectively
quite adequate. Most of the data is often on the order of a 5 dB
to 10 dB articulation level (La).
3. Calibration
In future work a 1K test tone should be modulated at zero, 1, 5,
10, 15 and 20 dB modulation levels. This will allow calibration
of testing circuits. An alternative to this is to step the 1K tone
level (zero modulation) to develop calibration at the above -1,
-5, -10, -15, -20 levels.
D.
L, La AND Log La OF RECEIVED SIGNAL
1. Modulated Sweep Response Curve
This shows the signal to noise ratio spectral response of the room
to the rapidly gated tone sweep. The actual received signal level
L(t) is the wide, rapid fluctuating line.
The overlaid solid line is the transmission
index vs. frequency at the 8 Hz gated modulation rate. The mean
TI would be the averaged value of this curve.
2. This curve is a linear frequency sweep
and the mean TI requires log frequency weighting. If a log frequency
sweep was used instead of linear, then straight integration of the
TI in time would produce the mean TI.
Linear sweep is often used in low frequency
room measurements. It is said the ear hears quasi-linear frequency
scale below 200 Hz. The log sweep spends ¾ of the time below
170 Hz about ¼ of the frequency range to be explored. The
remainder ¼ test time packs the remaining ¾ frequency
range (200 to 800 Hz). Although log frequency sweep accommodates
a simple integration scheme for the mean TI, it most likely is not
sampling sufficiently the room articulation. A more sophisticated
integration must be used.
V
SAMPLE TESTS
A. ROOM SEQUENCE
A listening room, 8’ x 14’ x 18’ with double
sheetrocked walls and concrete floor is tested at various stages
of acoustic treatment. Fundamental, is the use of corner-loaded
bass traps. The mic is placed at the hi-fi listener’s position
and two speakers, in phase are located at the opposite end of
the room in a stereo setup.
1.
Bare Room Response
To read this type of printout, we focus on the percentage of the
test frequency sweep that has a wide (10 dB) swing, peak to peak.
Marginally acceptable is a medium swing (5 dB). Real garbling
occurs with less than a 2 dB swing. Note also the irregular “median
line.” It is the average about which jitters the articulation
signal. The terrain looks like a lot of steep hills and valleys
covered with very little articulation.
2. Absorption Added in Stages
a. Here, a simple Tx6 set has been added to the front of the
room behind the speakers. Already a substantial pattern of low
level articulation is established throughout the entire test.
The hills and valleys have grown less severe and are covered better
with a wider articulation band. Note also the overall flatness,
the room is being acoustically EQ’d.
b. The next setup adds traps (16x3 plus 11x3 pair stacks) at
the back of the room. Again, the frequency bands of improved articulation
widen. The severity of the peaks and valleys is more reduced.
A few peak/valley patterns have even disappeared.
The softening of the peak/valley profiles means the “Q”
of the room, the sharpness of its resonance responses, have been
lowered. As the room resonances are damped, the peaks drop, the
valleys rise and there is an overall softening effect to the room
response curve.
c.
Next is added a side wall treatment, 4 sets of 9” x 5’
½ Rounds. This controls stage width and imaging, lateral
flutter and cross talk. It develops overall a much deeper articulation.
It produces wide bands of continuously full articulation, some 200
Hz wide between 400 and 600 Hz. Yet, curiously there seems to be
some areas of thinning, reduced articulation around 150 Hz.
d. The head wall traps are the next to be set, 6-11x5 ½
Rounds plus a single column of 11x6 Full rounds in the center. This
develops stage depth, clarity and imaging detail. Dramatic articulation
improvement is seen broadband, the peak/valley terrain flattens
substantially. The width of the articulation patterns have grown
quite wide and improvement is seen in the mid-bass. The front/rear
energy storage system of the room has been dampened to make this
marked improvement.
e. Finally we have added the rear wall. A 16x3 + 11x5 center column
and 4 sets of 11x5 ½ Rounds with one more pair on the front
wall. The result is a very wide and steady articulation pattern
that extends even into the deepest bass. Peaks and valleys now even
more are soft, rounded. The room still retains a strong, comfortable
ambience.
If you compare the overall before and after room articulation signatures,
you will see that the sound levels below 100 Hz have not changed
and those above 100 Hz are depressed by about 5 dB. In addition,
we see that below 400 cycles the articulation signature increases
from 2 to 8 dB and above 400 from 10 to 18 dB.
3.
Equalizer Added
The effects of equalizing the signal were explored. The effort was
made to get the trapped, articulate room to have an over flutter
response. A 1/3 octave equalizer was set with pink noise and headphones.
The following articulation test results. For better results, a parametric
equalizer could be used. With this equalizer a noticeable ringing
effect occurs, most likely not desirable in quality audio. Nonetheless,
the response curve has been flattened, peaks lowered, valleys raised.
Notice however, that there is “zero effect” on articulation.
Electronic EQ only adjusts levels, not articulation.
4. Full Acoustics Plus Equalizer
a. The “full on” room has also been tested. This is
not too unlike the typical dedicated Hi-end reference listening
room. Basically, a carpet has been added along with floor bounce
traps. All the traps of the prior setup (#6) have been elongated
from their 5-foot height to a full floor to ceiling length. A major
articulation improvement is noted, especially in the 20 to 400 Hz
range. The natural acoustic #Q is taking a strong control, the low-end
boom below 100 is almost gone.
b. Finally, to this “ultra” system, we degrade its
sonics but add equalizer effects. Again the EQ is set with pink
noise, RTA and 1/3 octave equalizer. The result is pretty flat,
and articulate response. There are a few small band widths with
poor articulation remaining. Even these may well be cleaned up with
additional tweaking. Again the ringing effect of the equalizer is
clearly audible in this test, something undesired in precision audition.
B.
1/3 OCTAVE PINK NOISE, RTA
1. RTA and Room Treatment Sequence
For the entire series of test just described, 1/3 octave RTA was
also taken. Above 40 Hz the overall levels are reduced by 2 dB.
If we overlay and line up the mid-range levels, we see a relative
increase in the lower octaves below 70 Hz by 2 dB. This is the acoustic
EQ effect. This acoustic treatment brought the deep bass 2 dB closer
to the mid bass levels.
Relatively minor corrections towards flattening the spectrum sound
levels with no loss of deep bass sound power is how RTA sees the
effects of the full on acoustics. Clearly RTA doesn’t begin
to suggest the fast tracking ability of the listening room.
2. RTA and Slow Sine Sweep
The narrow band frequency sweep room response curve is compared
to the 1/3 octave pink noise levels. The frequency range is 20 to
800 Hz. The frequency scale is linear, this stretches the 1/3 octave
bandwidths as the frequency goes higher.
The RTA levels are weighted higher with increasing frequency. This
is due to wider bandwidths, more 1 Hz levels being added together.
The equivalent narrow band spectrum can be had by subtracting the
bandwidth weighting term from each bandwidth level.
L = 10log f + 10log 23%
The 1/3 octave has 23% bandwidth. When the two curves are overlaid
the general tendency is seen but the detailed narrow band sweep
cannot be even inferred by the 1/3 octave measurement.
3.
RTA and Articulated Sweep
Not unlike the vague relationship between the frequency response
of the room and the RTA, so it is with the articulated sweep. Overall
trends do track, but the RTA gives no indications by which features
in the articulated sweep response curve can be derived.
For example, 1/3 octave EQ suggests that
the 250 Hz band should be cut some 5 dB. However, the articulated
sweep response shows that the problem high sound level is a 1/3
octave band centered at 180 Hz.
C. SLOW SINE AND MODULATED SWEEPS
Here we compare the slow sine sweep to the
modulated sweep. The sound levels at the listener’s position
are recorded in both cases between 20 and 800
Hz.
1.
Observations and Tendencies
Tendencies are noticed. The trend of the slow sine sweep matches
the trend of the articulated sweep.
a) Articulation levels La of 12
to 15 dB attain peak sound levels equal to that of the slow sine
sweep levels.
b) Articulation levels that are less than
12 dB fall short of the slow sine sweep level by an amount approximately
equal to: 15 - La.
c) Strong articulation is associated with
wide bandwidths of relatively uniform sound level on the slow sine
sweep response curve.
d) The lower the “Q” of sine
sweep response curve the stronger the articulation signal.
e) Very low articulation levels are always
accompanied by a very sharp, high “Q” room resonance
section of the room response curve.
f) Rapid sound level changes in the slow
sine sweep curve mark frequency bands with poor articulation response.
C. ROOM MODES AND “Q”
From the above it is clear that room mode
spacing and the adjustment of room resonance “Q” are
controlling variables in the development of articulation response
in small rooms.
1.
Mode Spacing
To illustrate by contrast, it can be safely concluded that a group
of closely spaced high “Q” resonances will produce stronger
articulation than if that given group was well separated having
well isolated resonance peaks. The tight grouping of some modes
leave more spaces between other modes. The real answer to an articulate
room will be to have a set properly spaced and damped room resonances.
2. Modulation Level La and Room
“Q”
It is straight forward to expect that the higher the “Q”
for a particular room resonance, the lower the articulation levels
would be. For the data presented above in Section V-B, an interesting
curve “Q” vs. La is produced. The room “Q”
has an almost exact inverse relationship with the articulation level
La. The empirical data is found to lie on the curve of:
Q x La = 180
Since the minimum La for acceptable listening
is about 5 dB, the most probable maximum acceptable “Q”
will be about 36. For the very desirable La of 10 dB
we have room resonance “Q” of 18. The “Q”
of a typical room is often 40 to 50 prior to specific acoustic conditioning.
D. LINEAR “Q”
VS La
The classic sabine equation uses diffuse
exponent sound fields. The “Q” vs. La relationship
can be predicted, it is seen to not fit the measured relationship.
This is expected because the sound field in small rooms and lower
octaves does not exponentially decay.
1.
“Q” and RT60
There exists a group of “Q” relationships dependant
on a variety of variables. The RT60 is no exception.
The frequency of the resonance (f) part of
the dependant variables.
Q = 1/22 RT60
2.
La and RT60
For linear RT60, the diffuse exponential decay sound
field level drops proportional to time.
The gated tone burst has burst rate (F) and
its dwell period is the time allowed for sound level decay.
An 8 Hz gated frequency yields an equation
relevant to the present test.
3. Linear “Q” and La
By combining the above equations the frequency dependant “Q”
x La relation is developed.
For linear decay the Cis directly proportional
to frequency. This is not what is measured, a constant. Since both
definitions used, “Q” and La assume a linear
acoustic relationship with RT60, neither can be identified
as the non linear term at this point.
DISCUSSION
The goal of this project has been to explore
the Transmission Index of small rooms in the lower octaves. The
rapidly gated slow sine sweep is an effective test signal. Although
envelope shaping of the attack and decay should be explored, the
existing coloration led to the observation that low level coloration
becomes inaudible at a higher modulation level than does the modulation
itself. This suggests that “quality” detection thresholds
may well be much different from “quantity” detection.
Research in perception along the lines of complex signal detection
thresholds needs to be applied to the present work.
The difference between the linear and measured
QLa term stands to illustrate that the prediction of TI in the lower
octaves in small rooms has yet to be accomplished. More empirical
work also needs to be done in this area. The observation presented
here is only based on one data run.
A new, complex test signal and detection
method may be considered to directly measure the masked partial
signal level. A correlation between pure tone modulation levels
at the partially frequency and the masking level of the partial
wherein a complex tone burst ie. Linear, additive effects, may be
fruitful.
The TI equation has been approximated here
by a fitted curve using the same single variable. The only reason
for this is to access the convenience of a relatively simple analog
circuit.
Further work with the exact equation ought
to be completed using analog or computational methods to develop
the TI. There also may be additional terms added to reduce the error
of the approximation curve.
There lies ahead a great opportunity to work
on the theoretical side of the Transmission Index at lower frequencies
in small rooms. The first step aside from large halls in linear
acoustics was the ray tracing method, but this is not applicable
to small room resonant modes.
The relative level effect needs to be factored
into the present TI approach. A room with strong level changes in
a slow sine sweep must be penalized when compared to a room with
a relatively flat response. A method to isolate this effect needs
to be developed and produce an independent modulation index.
In general, standards for speech in small
rooms need to be applied to this work. The performance of STI analyzers
needs to be compared to traditional listening tests in small classrooms
where modes exist in the speech range. In large halls, little emphasis
is given to the lower speech octave, 125 Hz. Small rooms, with their
room modes and typical lack of low frequency absorption, may well
require re-assessment of this weighting.
CONCLUSION
A method that develops spectral response
curves for articulation has been demonstrated. The measure variables
have been written into the equations that define the Modulation
Transfer Function and the corresponding Transmission Index. The
signal to reverberant noise level is directly measured and there
is no conversion of data that requires the assumption of linear
acoustics.
The equipment used to make this test is relatively
common. The source is a pre-recorded cassette test signal. Analysis
will use as little as a sound meter and strip chart recorder. By
adding a circuit for signal processing, the Transmission Index response
curve can be developed. With additional circuits even the STI can
be stated.
The STI is fast becoming a standard specification.
Engineers and consultants require a spectral version of the Transmission
Index in order to remedy the acoustics. Now that this simple and
low cost articulation test method has been shown to produce detailed
spectral information, it is hoped that this technique will be the
forerunner of a new class of sound system analysis.
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(The following were used in the preparation
of the paper)
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