Download Intensity Discrimination and Binaural Interaction

Technical University of Denmark
Intensity Discrimination and Binaural
Interaction
2nd semester project
DTU Electrical Engineering
Acoustic Technology
Spring semester 2008
Group 5
Troels Schmidt Lindgreen – s073081
David Pelegrin Garcia – s070610
Eleftheria Georganti – s073203
Instructor
Sébastien Santurette
Technical University of Denmark
DTU Electrical Engineering
Ørsteds Plads, Building 348
2800 Lyngby
Denmark
Telephone +45 4525 3800
http://www.elektro.dtu.dk
Title:
Intensity Discrimination and Binaural Interaction
Course:
31236 Auditory Signal Processing
and Perception
Synopsis:
Spring semester 2008
This report deals with intensity discrim-
Project group:
5
ination and binaural interaction of the
auditory system. Measurements concerning difference limen took place.
Participants:
Troels Schmidt Lindgreen
The existence of a binaural processor
David Pelegrin Garcia
in the human auditory system is inves-
Eleftheria Georganti
tigated and the effects of the interaural
level differences (ILD) and the interaural
Supervisor:
Torsten Dau
Instructor:
Sébastien Santurette
Date of exercise: April 10th
time differences (ITD) are discussed.
Test results show that humans have a
kind of binaural processor and that it is
possible to change the perception of the
position of the source image by modifying
the values of ITD and ILD.
Pages: 23
Copies: 4
No part of this report may be published in any form without the consent of the writers.
Introduction
This exercise deals with the intensity discrimination and binaural interaction of the auditory system. Various measurements, namely the intensity discrimination, the timeintensity trading and the binaural masking level difference experiments, are carried out.
Monaural intensity discrimination ability is investigated. The intensity Just Noticeable
Difference (JND) is determined and corresponds to the smallest intensity difference that
the human auditory system can detect. The results are compared to the ones predicted
by Weber’s law for broadband noise stimuli.
The existence of a binaural processor in the auditory system is examined by carrying
out an intensity discrimination experiment. The results obtained empirically are compared to the ones using only monaural detection cues.
In addition, an experiment that examines the effect of the interaural level differences,
the interaural time differences, and the connection between them is performed. The different cues are investigated and their role in sound localization is discussed.
Finally, the phenomenon of Binaural Masking Level Difference (BMLD) is investigated.
The BMLD effect implying that the masking thresholds may be decreased if a specific
binaural presentation is applied to the test subject is observed and discussed.
Technical University of Denmark, April 21, 2008
Troels Schmidt Lindgreen
David Pelegrin Garcia
Eleftheria Georganti
Contents
1 Theory
1
1.1
Intensity discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Just noticeable interaural level difference . . . . . . . . . . . . . . . . . . . .
2
1.3
Interaural time difference . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3
1.4
Time-intensity trading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
1.5
Binaural masking level difference (BMLD) . . . . . . . . . . . . . . . . . . .
5
2 Results
9
2.1
Intensity discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
Time-intensity trading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.3
Binaural Masking Level Difference . . . . . . . . . . . . . . . . . . . . . . . 13
3 Discussion
9
17
3.1
Interaural level discrimination . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2
Time-intensity trading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3
Binaural masking level difference . . . . . . . . . . . . . . . . . . . . . . . . 19
4 Conclusion
21
Bibliography
23
A Matlab code
A1
April 2008
Chapter
Chapter 1. Theory
1
Theory
In general terms, Just Noticeable Difference (JND) is the smallest difference in a specified
modality of sensory input that is detectable by a human being. It is also known as the
difference limen or the differential threshold.
1.1
Intensity discrimination
The smallest intensity difference a listener can detect is called intensity JND. Weber’s law
states that intensity JND (∆I) is proportional to the intensity (I) of a sound. This is called
the Weber fraction:
∆I
=c
I
[Dau et al., 2008, p.3]
(1.1)
Where:
∆I is intensity JND.
I is the intensity.
c is a constant.
Intensity JND can be expressed as a change in level at threshold (∆L):
∆L = 10 · log10
I + ∆I
I
!
[Dau et al., 2008, p. 3]
(1.2)
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Chapter 1. Theory
Technical University of Denmark
Assuming the Weber fraction, (1.1), the threshold is equal for all levels:
∆I
∆L = 10 · log10 1 +
I
= 10 · log10 (1 + c)
!
= k
(1.3)
(1.4)
Where:
k is a constant.
It is obvious that (1.4) cannot hold for all levels. Low levels [Sone] and the level of
pain sets limits for (1.4). It should be noted that Weber’s law holds for wide-band noise
above 20 dB SL, but not for a 1 kHz tone. The observation that Weber’s law does not
hold for tones is often called the ”near-miss” to Weber’s law. [Moore, 2004, p. 145]
1.2
Just noticeable interaural level difference
Interaural Level Difference (ILD) is the difference in the sound pressure level of the signals arriving at both ears, which can provide sound localization cues. The effect of head
diffraction and shadow on the ILD is sketched in figure 1.1 and is most pronounced for
frequencies above 1500 Hz. Head and pinna diffraction attenuates sound at the far ear,
while boosting the sound at near ear.
Figure 1.1: Effect of head shadow on the ILD. Sound waves are emitted from a loudspeaker.
Monaural intensity JND can be measured as described in section 2.1.1. Assuming that
intensity JND is identical for both ears and in the hypothetic case that humans have no
gain in intensity JND from binaural hearing, the value of intensity JND is the same for
monaural intensity JND and binaural intensity JND. If there is any gain by using both
ears, the binaural intensity JND is less than for monaural intensity JND.
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Intensity Discrimination and Binaural Interaction
April 2008
Chapter 1. Theory
Whether humans benefit from binaural hearing regarding intensity JND can be investigated by presenting a stimuli in both ears where the sound level is lowered by half ILD
in one ear and raised with half ILD in the other ear, as shown in figure 1.2. Assuming no
benefit from binaural hearing regarding intensity JND, the intensity JND will be twice as
high as the monaural intensity discrimination. This is because the ILD effect is divided
to both ears and therefore the level change has to be twice as high in order to reach the
same level change for each ear compared to receiving all the energy monaurally.
x
x
x
?
65 dB SPL
Intensity JND = x
65 dB SPL + ILD/2
65 dB SPL - ILD/2
If there is no improvement from binaural hearing: ILD = 2·x
If there is an improvement from binaural hearing: ILD > 2·x
Figure 1.2: Just noticeable monaural intensity discrimination and just noticeable interaural level difference.
Taking the value of intensity JND for monaural intensity discrimination as 1, the value
of intensity JND for binaural intensity discrimination should be 2 if there is no benefit of
binaural hearing regarding intensity JND. On the other hand, if humans have some kind
of binaural processor, there would benefits from binaural and the intensity JND will be
lower.
1.3
Interaural time difference
As commented in section 1.2, the level difference between the two ears (or interaural level
difference, ILD) provides cues for localization of sounds in the horizontal plane. Another
cue for localization is the interaural time difference (ITD), i.e. the delay existing between
the signals arriving at the two ears, produced by a path difference between them, as can
be observed in figure 1.3. Modeling the human head as a sphere of radius r, this delay can
be described as a function of the angle of incidence θ using equation (1.5).
ITD =
rθ + r sin θ
c
(1.5)
Where:
c is the propagation speed of sound in the air.
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Chapter 1. Theory
Technical University of Denmark
Figure 1.3: Sound arriving from a direction
θ. Modeling the human head as a sphere
of radius r, the path difference between the
sound arriving at both ears can be described
as d = rθ + r sin θ [Dau, 2008, p. 23].
1.4
Time-intensity trading
In the previous sections, it has been stated that small differences in level or delay of the
signals at both ears make it possible to detect the incidence direction of the sound, i.e. the
sound image is shifted from the median plane. This effect is also known as lateralization.
However, if the same signal is presented to both ears (diotic stimulus), the sound appears to come from the center of the head. If the level of the signal at one ear is rised, the
sound image shifts towards that side. It is also possible to shift the sound image by making
one of the signals lead the other. In this case, the sound image shifts to the side where the
signal is leading. Thus, it is possible to design an experiment where the sound image shift
produced by level cues is compensated by interaural time delays in the opposite direction,
so the sound appears to come from the median plane. This kind of experiment is called a
“trading” experiment.
The result of this experiment is the ratio between ITD and ILD, called “compensation
factor” or “trading ratio”, i.e. the amount of delay that it is necessary to compensate
(bring the sound image back to the center) for a level difference of 1 dB. The trading ratio
depends on the presentation level, and usually less ITD is necessary to compensate ILD
at higher presentation levels [David et al., 1959], as shown in figure 1.4.
There is one hypothesis (called “Latency theory”) which states that intensity differences
might be transformed into time differences at a certain stage of neural processing. However, some of the effects observed in this experiment, such as increase of spaciousness or
perception of separate images, prove that both cues, ITD and ILD, are not equivalent at
all [Dau et al., 2008].
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Chapter 1. Theory
Figure 1.4: Trading curves of a typical subject for broadband clicks at various levels. The curves drawn
through the plots were obtained using third-degree polynomial fits [David et al., 1959].
1.5
Binaural masking level difference (BMLD)
The changes in interaural level and time differences that were examined in the previous
section offer valuable cues to improve sound localization. Another interesting aspect of
binaural process is that of the Binaural Masking Level Difference (BMLD). This process
implies that a test subject will have remarkably lower masking threshold when he/she
makes use of binaural information, than when making use of monaural information cues,
at certain presentation conditions. An interesting example showing this is that of a listener
detecting sounds in a noisy environment (low SNR) by making use of binaural interactions.
In order to derive a definition for the BMLD an example is given. One can consider the
situation that is shown in figure 1.5, where a masker and a tone signal are presented to
a test subject via earphones. In figure 1.5 (b) white noise from the same sound generator is fed to both ears. Additionally, a pure tone, from the same signal generator is fed
separately to each ear and mixed with the noise. In this point, it is assumed that the
level of the tone is adjusted so that it can be just masked by the noise, and presenting a
level of L0 dB. In this case, the total signals at the two ears are identical and the tone is
inaudible. In figure 1.5 (c) the situation is slightly different. The tone signal at one of the
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Chapter 1. Theory
Technical University of Denmark
Figure 1.5: Illustration of two situations in which binaural masking level differences (BMLD’s) occur.
In situation (a) a tone signal is being presented to the test subject (reference). In condition (b) the
detectability of the tone is poor, while in condition (c), where the interaural relations of the signal and
masker are different, detectability is good [Moore, 2004, p. 258].
ears is inverted, by adding a phase shift of π radians. The tone now becomes audible again.
The tone can be adjusted to a new level Lπ , so that it is once again at its masked threshold.
In this point the definition of BMLD can be introduced, which is the difference between
the two levels, L0 − Lπ [dB]. Its value may be as large as 15 dB at low frequencies (around
500 Hz), decreasing to 2-3 dB for frequencies above 1500 Hz. [Moore, 2004, p.258]
Figure 1.6: Illustration of situations in which binaural masking level differences (BMLD’s) occur. In
condition (a) the detectability of the tone is poor when noise and signal are fed to one ear only. In
condition (b) the same noise is added at the other ear, and the tone becomes audible again. [Moore,
2004, p. 258].
Another interesting example of the effects of BMLD can be seen in figure 1.6, where at
first noise and signal are fed to one ear only (figure 1.6 (a)), and the signal is adjusted
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Intensity Discrimination and Binaural Interaction
April 2008
Chapter 1. Theory
to be at its masked threshold, thus inaudible. Then, if the same noise is added at the
other ear (figure 1.6 (b)), the tone becomes audible again. This implies that by adding
noise at the ear where no signal is present the tone becomes more detectable. This noise,
however should be correlated with the masker at the other ear. Uncorrelated maskers will
not result in BMLD.
It is important to note that BMLD phenomenon is not limited to pure tone signals but it
is also observed for complex signals too (complex tones, clicks and speech sounds).
Over the years, many different models have been proposed to account for the various
aspects of binaural processing [Moore, 2004, p.263]. Durlach presented a rather simple
model that was able to describe the BMLD phenomenon. This model was based on the
Equalization - Cancellation (EC) concept. That is based on the idea that the auditory
system tries to eliminate the masker by manipulating the stimuli between the two ears,
until the masker components are equal (equalization) and then subtracts them so that
they cancel each other (cancellation) [Dau et al., 2008].
The first step of this model (equalization process) involves amplification or attenuation
of the stimuli and shifting in time. This is because the model needs to compensate for
the interaural level differences (ILD) and interaural time differences (ITD). In order to
take into consideration the finite limit of the BMLD phenomenon the model assumes an
imperfect equalization process. This assumption is realized by introducing two sources of
error: jitter in the amplification () and shifting in time (δ). and δ are asummed to
be statistically independent random variables, with zero mean and variances σ2 and σ2δ
respectively. Under those assumptions, Durlach [Dau et al., 2008] was able to show that
the difference between the N0 S 0 and N0 S π condition can be described by the following
equation:


BMLD(N0 S 0 − N0 S π ) = 10 log10 1 +
2e−ω0 σδ
2 2
1 + σ2 − e−ω0 σδ
2 2



(1.6)
where:
ω0 is the center frequency (in radians) of the auditory filter with the stimulus. From
equation (1.6) it is possible to note that for very low frequencies:
limω0 →0 BMLD(N0 S 0 − N0 S π ) = 10 log10
2
1+ 2
σ
!
(1.7)
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Chapter 1. Theory
Technical University of Denmark
Figure 1.7: BMLD (N0 S 0 − N0 S π ) as a function of ω0 . Data points are from 18 different studies. The curve
corresponds to equation (1.6) with σδ = µs and σ = 0.25. [Dau et al., 2008]
and that at very high frequencies:
limω0 →∞ BMLD(N0 S 0 − N0 S π ) = 10 log10 (1) = 0
(1.8)
Equations (1.7) and (1.8) show that at very low frequencies BMLD depends on σ . For
a value of σ = 0.25 , equation (1.7) results in 15 dB of BMLD. Equation (1.8), on the
other hand, implies that at high frequencies the BMLD phenomenon is not observed. The
modeled BMLD curve is better illustrated in figure 1.7, where data points from 18 different
studies are plotted together with the Durlach’s model estimation.
In figure 1.7 it can be seen that the curve indicating the BMLD level seems to fall to
zero for frequencies around 3 kHz. On the other hand at the same frequency range the
empirical data seem to converge asymptotically to a value around 3 dB. Durlach suggested
that a possible error source for this discrepancy might be due to the various mathematical
operations of the model. For example a calculation that corresponds to ”the averaging
over the equalization errors before forming the SNR at the output of the EC mechanism”
might cause this discrepancy. [Durlach, 1963].
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Chapter
Chapter 2. Results
2
Results
2.1
2.1.1
Intensity discrimination
Monaural intensity discrimination
Monaural intensity JND is measured for three test subjects using bandpass noise from
250 Hz to 4 kHz, in a period of 500 ms at two presentation levels: 65 dB SPL and 75
dB SPL. A Matlab script with an adaptive three-interval, three-alternative, forced-choice
procedure with one-up, two-down tracking rule is used for this experiment. Results are
shown in figure 2.1.
intjnd
dp
3
JND [dB]
eg
tl
2
1
0
65
70
75
level [dB SPL]
Figure 2.1: Monaural intensity discrimination.
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Chapter 2. Results
Technical University of Denmark
The results in figure 2.1 are shown as ∆L as a function of frequency. In figure 2.2 the same
results are shown as the Weber fraction (see (1.1) on page 1) as a function of level. The
results in figure 2.2 are calculated by rearranging equation (1.2) to:
∆I
= 10∆L/10 − 1
I
(2.1)
0.8
dp
eg
tl
0.7
∆I/I
0.6
0.5
0.4
0.3
0.2
0.1
64
66
68
70
72
Level [dB SPL]
74
76
Figure 2.2: Weber fraction calculated from results shown in figure 2.1.
2.1.2
Binaural intensity discrimination
Binaural intensity JND is measured for three test subjects using bandpass noise from 250
Hz to 4 kHz, in a period of 500 ms at 65 dB SPL. The stimulus is presented in both ears
where the sound level is lowered by half ILD in the right ear and raised with half ILD
in the left ear, as shown in figure 1.2. A Matlab script with an adaptive three-interval,
three-alternative, forced-choice procedure with one-up, two-down tracking rule is used for
this experiment. Results are shown in figure 2.3.
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Intensity Discrimination and Binaural Interaction
April 2008
Chapter 2. Results
dp
eg
JND [dB]
4
tl
2
0
60
65
70
reference level [dB SPL]
Figure 2.3: Binaural intensity discrimination.
2.2
Time-intensity trading
A “trading” experiment was performed in order to measure the amount of delay (ITD)
that is necessary to bring the sound image to the center when a level difference (ILD) was
applied to one ear. The method used was an adaptive one-up, one-down rule in combination with a two-interval, two-alternative, forced choice procedure implemented in a Matlab
script. The signals in the two intervals were the same, but the channels were reversed in
the second one (the left channel in the first interval was presented as the right channel in
the second one, and vice versa). The stimulus signal was a binaural click train comprised
of ten five-sample clicks separated 2,200 samples at a sampling frequency of 44.1 kHz. At
one ear, the signal was amplified ILD/2 whereas at the other ear, an attenuation of ILD/2
was applied. Moreover, one channel was advanced half ITD (which was the tracking variable) and the other one was delayed half ITD. At each presentation the test subject had
to say which side the sound image had moved towards.
Three test subjects (DP, EG and TL) took the experiment. The ITD was measured
for seven different ILDs (-10, -7, -4, 0, 4, 7 and 10 dB) at two different presentation levels
(L p ): 45 dB SPL and 60 dB SPL. For each test subject and presentation level, a thirdorder polynomial was used to fit the data. The measured data and the fitted polynomials
for test subjects DP, EG and TL are shown in figures 2.4, 2.5 and 2.6, respectively.
The values of the “trading ratio” and the bias calculated as the first and zero order coefficients of the fitted polynomials fitted from each measurement are shown in table 2.1.
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Chapter 2. Results
2.5
Technical University of Denmark
2.5
Measurements
2
Fitted curve
1
ITD [ms]
1
ITD [ms]
Measurements
2
Fitted curve
0
-1
0
-1
-2
-2
-2.5
-2.5
-10
-5
0
5
10
-10
interaural level difference [dB]
-5
0
5
10
interaural level difference [dB]
(a) L p = 45 dB SPL
(b) L p = 60 dB SPL
Figure 2.4: Results of the time-intensity trade experiment for test subject DP at presentation levels of 45
dB SPL (a) and 60 dB SPL (b), from measured data and fitted third-order polynomials.
2.5
2.5
Measurements
2
Measurements
2
Fitted curve
Fitted curve
1
ITD [ms]
ITD [ms]
1
0
-1
0
-1
-2
-2
-2.5
-2.5
-10
-5
0
5
10
-10
interaural level difference [dB]
-5
0
5
10
interaural level difference [dB]
(a) L p = 45 dB SPL
(b) L p = 60 dB SPL
Figure 2.5: Results of the time-intensity trade experiment for test subject EG at presentation levels of 45
dB SPL (a) and 60 dB SPL (b), from measured data and fitted third-order polynomials.
2.5
2.5
Measurements
2
Fitted curve
1
ITD [ms]
1
ITD [ms]
Measurements
2
Fitted curve
0
-1
0
-1
-2
-2
-2.5
-2.5
-10
-5
0
5
interaural level difference [dB]
(a) L p = 45 dB SPL
10
-10
-5
0
5
10
interaural level difference [dB]
(b) L p = 60 dB SPL
Figure 2.6: Results of the time-intensity trade experiment for test subject TL at presentation levels of 45
dB SPL (a) and 60 dB SPL (b), from measured data and fitted third-order polynomials.
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April 2008
Test subject
Chapter 2. Results
45 dB SPL
Trading ratio [µs/dB] Bias [µs]
DP
EG
TL
5.68
4.33
5.22
60 dB SPL
Trading ratio [µs/dB] Bias [µs]
-1.49
-4.10
-3.30
5.60
4.57
5.04
-1.73
-1.27
-2.68
Table 2.1: Values of the “trading ratio” and the bias, given by the first and zero order terms of the
polynomials calculated fitting the data from the time-intensity trade experiment.
2.3
Binaural Masking Level Difference
An experiment concerning the BMLD took place for three test subjects. In this experiment the masked threshold is measured with noise and signal presented in the same way
at both ears. More precisely for this experiment the signals were 480 ms sinusoids with an
◦
◦
interaural phase difference of 0 and 180 . Signal frequencies of 250, 500, 1000 and 2000
Hz were used. The masker was a bandpass 500 ms noise (2 octaves wide, 65 dB SPL)
geometrically centered around the signal frequency. The presentation of the masker starts
10 ms before and ends 10 ms after the presentation of the signal. The masked thresholds
in both the N0 S 0 and N0 S π conditions were measured using an adaptive three-interval,
three-alternative, forced-choice procedure with an one-up, two-down tracking rule. In figures 2.7, 2.8 and 2.9 the results obtained from the experiment for three test subjects (EG,
DP, TL) are presented.
A matlab script called “ECmodel” was composed in order to implement equation 1.6 (see
A) . In figures 2.7, 2.8 and 2.9 apart from the empirical results, the theoretical BMLD
curve by Durlach, that was calculated using equation (1.6), is also present (σδ = 105µs
and σ = 0.25). Finally, a curve showing the best fitting according to the results and the
model is also shown.
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Chapter 2. Results
Technical University of Denmark
Measured data
ECmodel σδ = 105µs and σ = 0.25
15
BMLD [dB]
ECmodel σδ = 40.4µs and σ = 0.55
10
5
0
125
250
500
1000
2000
4000
Frequency [Hz]
Figure 2.7: Data obtained from the BMLD experiment for test subject DP. Measured data only at 250,
500, 1000 and 2000 Hz.
BMLD [dB]
15
10
5
Measured data
ECmodel σδ = 105µs and σ = 0.25
ECmodel σδ = 61.5µs and σ = 0.32
0
125
250
500
1000
2000
4000
Frequency [Hz]
Figure 2.8: Data obtained from the BMLD experiment for test subject TL. Measured data only at 250,
500, 1000 and 2000 Hz.
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Intensity Discrimination and Binaural Interaction
April 2008
Chapter 2. Results
Measured data
ECmodel σδ = 105µs and σ = 0.25
15
BMLD [dB]
ECmodel σδ = 59.3µs and σ = 0.79
10
5
0
125
250
500
1000
2000
4000
Frequency [Hz]
Figure 2.9: Data obtained from the BMLD experiment for test subject EG. Measured data only at 250,
500, 1000 and 2000 Hz.
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Chapter 2. Results
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Technical University of Denmark
Intensity Discrimination and Binaural Interaction
April 2008
Chapter
Chapter 3. Discussion
3
Discussion
3.1
Interaural level discrimination
Weber´s law states that the intensity JND should be the same for any levels as seen in
equation (1.4). In figure 2.1 the results for monaural intensity JND as a function of two
levels can be seen. It can be noted that equation (1.4) only holds for test subject TL.
For the other two test subjects the JND became lower for 75 dB SPL. This can perhaps
be explained by the presence of fluctuating background noise and the reduced set of data
(average values calculated from 2 measurements).
In figure 3.1 the results from monaural and binaural intensity discrimination are compared. It can be seen that the binaural intensity JND is less than twice as high as the
monaural intensity JND for each test subject. This proves that all three test subjects
benefit from binaural hearing and have some kind of binaural processor. During the binaural intensity discrimination experiment the test subjects described the noise as one fused
object. They also mentioned that the method by itself was not good. It is surprisingly
difficult to press the right button (to indicate that the change was in the last interval)
when the sound was moving to the left. A perhaps better way to perform the experiment
is to have an instructor that will note in which interval the noise moves to the left, so the
test subject only has to say interval one, two or three to indicate the interval and thereby
preventing any confusions between left and right.
3.2
Time-intensity trading
The results of the trading experiment are presented in figures 2.4, 2.5 and 2.6 in section 2.2. The variability of the data and the range of ITD values (between -2 ms and 2
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Chapter 3. Discussion
Technical University of Denmark
4.5
dp
eg
tl
4
JND [dB]
3.5
3
2.5
2
1.5
Monaural intensity JND (x2)
Binaural intensity JND
Figure 3.1: Comparison of the JND obtained from monaural (multiplied by 2) and binaural intensity
discrimination experiments at a presentation level of 65 dB SPL.
ms) seem to be in agreement with the results from [David et al., 1959], shown in figure 1.4.
The curves are not symmetrical with respect to the origin, because the zero-order term
of the polynomial used to fit the data has a value different from 0. This term indicates
the ITD that is applied to perceive the source image at the median plane when the signals presented at both ears have the same level. The bias is negative at the different
presentation levels, meaning that the perception of a sound image as centered does not
correspond to sound events coming from the median plane, and this behavior is observed
on the three test subjects. According to [David et al., 1959, p.177], the bias should be
consistent among presentation levels (as it has been measured in this report) and the
average of the bias among test subjects should be ideally 0. This last statement is not
fulfilled in these measurements, likely due to the few test subjects used for the measurements (only 3). [David et al., 1959] suggested that the reason for the bias could be errors
in the listener’s centering judgment, imbalance in interaural sensitivity, or unspecific physiological sidedness imbalance. In addition, the authors thought about the correlation with
the different development of the brain at both sides (as happens with the ability to write
with one of the hands), but it was refused as there was no correlation between the sign
of the bias and the hand that the test subjects use for writing (TL is the only left-handed).
The first-order coefficient of the fitted polynomial gives the trading ratio. The values
of this term for every test subject at all presentation levels are presented in table 2.1. For
test subjects DP and TL, there is a slight decrease of the trading value when increasing
the presentation level from 45 dB SPL to 60 dB SPL (-0.08 µs/dB for DP and -0.18 µs/dB
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Intensity Discrimination and Binaural Interaction
April 2008
Chapter 3. Discussion
for TL). In contrast, the trading value increases for EG (0.25 µs/dB) under the same conditions, differing from the predictions by [David et al., 1959], who found that the trading
ratio decreased with increasing level. However, the obtained results should not lead to the
conclusion that ITD and ILD are coded and interpreted by the brain in the same way,
because the stimuli were not perceived as a single sound event coming from the center
of the head. The test subjects described the effects as perception of two different sound
events at both ears or “sound image broadening” instead of sound image displacement
between the two presentations, i.e. having a clear lateralization.
3.3
Binaural masking level difference
In figures 2.7, 2.8 and 2.9 the BMLD results for the three test subjects are plotted as a
function of the stimulus frequency. In addition, the theoretical BMLD predicted by [David
et al., 1959] with values σδ = 105µs and σ = 0.25 is plotted. The curves with the parameters σδ and σ that offered the best fitting for the actual measurements are also plotted
in each figure.
In figure 1.7 on page 8 the data obtained for 18 different test subjects deviate a lot
from each other, resulting in a cloud of data points. Therefore, the expected variability among test subjects is high, and the equation (1.6) (also plotted in the same figure)
just provides an approximation to the population average. The measurements for this
report were obtained with just one run for each frequency of the three test subjects in a
noisy environment. With these sets of data, it is not possible to get statistical values that
give precise information about the average BMLD at a certain frequency and its deviation.
However, test subject EG seems to have less benefit from BMLD as compared to the
test subjects DP and TL. In figure 2.8 the test subject TL seems to have a dip at 1 kHz.
Prior to this report test subject TL has measured his audiogram which presents a dip in
hearing threshold at 1 kHz which is different for each ear. This could explain the lack of
benefit from binaural hearing at this frequency and thereby the dip in BMLD. Nevertheless, more measurements are necessary in order to reduce the uncertainty and prove the
latest hypothesis.
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Chapter 3. Discussion
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Technical University of Denmark
Intensity Discrimination and Binaural Interaction
April 2008
Chapter
Chapter 4. Conclusion
4
Conclusion
In this report, the intensity discrimination and binaural interaction of the human auditory system have been discussed theoretically and from measurements. Intensity JND was
measured both monaurally and binaurally. Time-intensity trading was investigated and
additionally the effects of BMLD were examined.
The reduction in the measured binaural JND with respect to the equivalent monaural
JND show that humans have a kind of binaural processor, which takes advantage from
binaural hearing detection cues.
It is possible to change the perception of the position of the source image by modifying the values of ITD and ILD. ITD is not processed in the same way as ILD, as the
stimuli in the experiment are not perceived as single sound events at a certain location,
but as separated events.
Results show that there is an improvement in the ability of detecting a signal in background noise when the noise signals presented at both ears are correlated and the signal
to detect is presented to just one ear or to both in antiphase. This improvement, known
as BMLD, presents values up to 15 dB in these measurements.
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Chapter 4. Conclusion
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Intensity Discrimination and Binaural Interaction
April 2008
Bibliography
Bibliography
[Dau, 2008] Dau, T. (2008). Intensity coding and binaural processing in the auditory system. Slide show.
[Dau et al., 2008] Dau, T., Christiansen, T. U., and Santurette, S. (2008). Intensity Discrimination and Binaural Interaction. 1.1.2 edition.
[David et al., 1959] David, E.E., J., Guttman, N., and van Bergeijk, W. (1959). Binaural interaction of high-frequency complex stimuli. Journal of the Acoustical Society of
America, 31(6):774–782.
[Durlach, 1963] Durlach, N. (1963). Equalization and cancellation theory of binaural
masking-level differences. Acoustical Society of America – Journal, 35(8):1206–1218.
[Moore, 2004] Moore, B. C. J. (2004). An introduction to the psychology of hearing.
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Bibliography
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Technical University of Denmark
Intensity Discrimination and Binaural Interaction
Project group 5
Appendix
April 2008
A
Matlab code
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function vBMLD = ECmodel ( vFreq , sigmaD , sigmaE )
% ECmodel c a l c u l a t e s t h e BMLD ( N0S0 − N0Spi ) a c c o r d i n g t o t h e EC model
%
% s y n t a x : vBMLD = ECmodel ( vFreq , sigmaD , sigmaE )
%
% C a l c u l a t e s t h e BMLD o f a N0S0 and and N0Spi c o n f i g u r a t i o n a c c o r d i n g
% t o t h e EC model ( s e e Eqn . 5 . 1 o f t h e e x e r c i s e g u i d e ) .
%
% input :
vFreq
center frequency of the auditory f i l t e r with the
%
t a r g e t s i g n a l ; can be g i v e n as a v e c t o r ( i n Hz ! )
%
sigmaD s t a n d a r d d e v i a t i o n o f t h e random j i t t e r i n time ( i n s )
%
sigmaE s t a n d a r d d e v i a t i o n o f t h e random j i t t e r i n a m p l i t u d e
%
% o u t p u t : vBMLD
t h e b i n a u r a l masking l e v e l d i f f e r e n c e i n dB ; i f vFreq
%
i s a vector , t h i s i s also a vector
vBMLD =10* log10 (1+2*exp( -((2* pi * vFreq ) .^2) * sigmaD ^2) ./(1+ sigmaE ^2 -exp( -((2* pi * vFreq )
.^2) * sigmaD ^2) ) ) ;
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