The Role of the Precedence Effect in Sound Source Lateralization
by
Daniel E. Shub
BSE Bioengineering
University of Pennsylvania, 1997
SUBMITTED TO THE DEPARTMENT OF ELECTRICAL ENGINEERING AND
COMPUTER SCIENCE IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE
DEGREE OF
MASTER OF SCIENCE IN ELECTRICAL ENGINEERING AT THE
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
JUNE 2001
©2001 Daniel E. Shub. All Rights Reserved.
The author hereby grants to MIT permission to reproduce and to distribute publicly paper and
electronic copies of this thesis document in whole or in part.
Signature of Author: _
Department of Electrical Engineering and Computer Science
April 24, 2001
Certified by:
H. Steven Colburn
Professor of Biomedical Engineering
Boston University
The,%KSupervisor
Accepted by:
Arthur C. Smith
Department of Electrical Engineering and Computer Science
S Thaim
MASSACHUSETTS INSTITUTE
OF TECHNOLOGY
JUL 112001
BARKER
LIBRARIES
an, Committee for Graduate Students
The Role of the Precedence Effect in Sound Source Lateralization
by
Daniel E. Shub
Submitted to the Department of Electrical Engineering and Computer Science on April 24, 2001
in Partial Fulfillment of the requirements for the Degree of Masters of Science in Electrical
Engineering
Abstract
Sound source lateralization can be accomplished in many real world environments with a simple
cross-correlation model. The precedence effect predicts that in certain situations, such as sounds
with a single loud reflection, sound source lateralization performance of normal hearing listeners
could be better than performance predicted by a simple cross-correlation model. This thesis
examines sound source lateralization of ongoing broadband noise targets, alone and in the
presence of a single ongoing broadband noise jammer. Different jammer conditions were tested
when the jammer was either a simple reflection of the target or a sound uncorrelated with the
target. Two measurements were made for each subject: The identification threshold of ±300 psec
ITD targets was determined through a 1-interval 2-alternative forced-choice identification
experiment; the lateralization threshold was determined through a 1-interval lateralization
experiment. In both cases the minimum target-to-jammer level for criterion performance was
estimated as the threshold. The identification threshold was 3.2 dB lower (P value of 0.027) for
simple reflection jammers compared to jammers that were uncorrelated with the target. The
lateralization threshold was 2.85 dB lower (P value of 0.040) for the reflection jammers relative
to the uncorrelated jammers. A comparison between the lateralization thresholds of normalhearing listeners and two cross-correlation based models was also made. Both models obtained
lateralization thresholds as low as -13 dB, up to 10 dB better than normal-hearing performance.
There was a slight trend, in agreement with current understanding of the precedence effect, for
both the identification thresholds and the lateralization thresholds of the simple reflection
jammers to be dependent on the jammer ITD. Simple reflection jammers with an ITD of 0 tsec
had thresholds that were 1.9 dB lower (P value of 0.104) than the thresholds of simple reflection
jammers with an ITD of 643 psec.
Thesis Supervisor: H. Steven Colburn
Title: Professor of Biomedical Engineering, Boston University
Table of Contents
I.
INTRO DU CTION .............................................................................................................................................
5
II.
M ETHO D S ........................................................................................................................................................
9
...............................................................
SUBJECTS AND APPARATUS
....................................................................
IMPULSE RESPONSES
A.
B.
i.
ii.
C.
D.
iii.
iv.
9
10
Experim ent 1: Lateralization-in-quiet..................................................................................................
Exp eriment 2: Identification....................................................................................................................
Exp eriment 3: L ateralization...................................................................................................................
Proced u re ................................................................................................................................................
1
13
14
14
15
16
17
E.
M O DE L ..........................................................................................................................................................
F.
D A TA A N A LY SIS ...........................................................................................................................................
17
RESU LTS....................................................................................................................................................
20
A.
B.
C.
EXPERIMENT 1: LATERALIZATION-IN-QUIET ............................................................................................
EXPERIM ENT 2: IDENTIFICATION...................................................................................................................
EXPERIM ENT 3: LATERALIZATION.................................................................................................................
20
21
22
D.
M O D E L ..........................................................................................................................................................
23
DISCU SSIO N ..............................................................................................................................................
24
CONCLUSIONS ............................................................................................................................................
27
III.
IV .
V.
Target ........................................................................................................................................................
J am m er ....................................................................................................................................................
STIMULI
.............................................................................
EXPERIM ENTAL PROCEDURE .........................................................................................................................
i.
ii.
9
9
ACKNOWLEDGEMENTS .....................................................................................................................................
28
FIGU RE S ..................................................................................................................................................................
29
A PPENDIX ................................................................................................................................................................
42
REFEREN CES .........................................................................................................................................................
79
Figure list
Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Common magnitude spectrum of the target and jammer stimuli. (Spectrum
from Gardner and Martin 1994)
The first 10 msec of the left and right ear impulse responses (IRs)
corresponding to the different jammer conditions.
Example cross-correlation functions of the sound stimuli IRs for the different
stimulus conditions over a range of target-to-jammer ratios. (TJRs)
Confusion matrices for all subjects in the target-in-quiet condition.
Statistics summarizing the performance of subject S3 during the target-inquiet condition as a function of 1 00-trial block number.
Identification and lateralization thresholds and smart and dumb model
predictions for the different jammer conditions.
Confusion matrices of subject S4, jammer condition B'.
Normalized R 2 for subject S2 and all jammer conditions. The continuous
curves are cumulative Gaussian fits.
Cumulative Gaussian fits to the normalized R2 data for all subjects in
condition B.
29
30
31
32
33
34
35
36
37
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Confusion matrices of Model 1, the dumb cross-correlation model, for jammer
condition B'.
Cumulative Gaussian fits to the normalized R 2 data of Model 1 for all the
jammer conditions.
Confusion matrices of Model 2, the smart cross-correlation model, for jammer
condition B'.
Cumulative Gaussian fits to the normalized R2 data of Model 2 for all the
jammer conditions.
38
39
40
41
Table List
Table 1
Table 2
Table 3
Table 4
Properties of the jammer IRs for the 6 different jammer conditions.
Average values and the standard errors of the different statistics for the targetin-quiet condition.
Identification thresholds for each subject and condition.
Lateralization thresholds for each subject and condition.
11
21
22
23
I.
Introduction
Many factors affect sound source lateralization. These factors include reverberation and
competing sound sources. The precedence effect predicts that the inter-relationship of the target
(defined in this thesis as the sound source the listener is instructed to lateralize) and the
jammer
(defined in this thesis as a competing sound source) can affect sound source lateralization. Better
lateralization performance is predicted under some circumstances when the target and
jammer
are correlated then when they are uncorrelated. This thesis is primarily interested in the role that
the precedence effect plays in sound source lateralization. In this section, the background
inspiring this thesis is presented.
Mills (1958) showed that in anechoic environments without competing jammers normalhearing listeners can perform sound source localization tasks quite well: just noticeable
differences of less than two degrees are not uncommon in anechoic conditions. Good and Gilkey
(1996) and Lorenzi et al. (1999) studied the effect of noise on sound source localization. Their
results showed that at signal-to-noise ratios (SNRs) less than -10 dB, sound source localization
performance is seriously degraded. In studies of sound localization in reverberation, Hartmann
(1983), Giguere and Abel (1993) and Rakerd and Hartmann (1985) obtained results similar to
those in studies of sound localization in noise, namely degraded performance. Although much
previous work uses the standard notation of SNR, this thesis is primarily concerned with targetjammer interactions and will therefore refer to the more descriptive target-to-jammer ratio (TJR).
The two major cues used for lateralization are interaural time differences (ITDs) and
interaural level differences (ILDs). Wightman and Kistler (1992) studied the effect of conflicting
ILD and ITD cues in terms of sound source localization performance in headphone studies. The
stimuli were processed with head related transfer functions (HRTFs) to create virtual images and
5
the ILDs and the ITDs were then manipulated. For sounds containing low frequencies, horizontal
plane localization was dominated by the ITD cue. In fact horizontal plane localization, for wideband sound stimuli with only an ITD cue was quite good, almost the same as anechoic
performance. It seems that wide-band stimuli can be accurately lateralized with only an ITD cue.
Kuhn (1977) measured ITD values, at the ears of a mannequin, for a given a source angle
and presented expressions for calculating ITDs. The relationship between ITD and angle is a
function of many variables. The major contributing variables are head size and the frequency of
the source. Lower frequency sound waves have larger ITDs compared to sound waves of higher
frequencies. The ITD of a high frequency (above approximately 3 kHz) source can be calculated
with Eq. 1 for a given source angle, 0, and head size.
ITD =
Head Radius
Speed of Sound
*
(sin (o)+ 9)
(1)
It should be noted that Eq. 1 is a nonlinear function. For a 1 -degree change in angle, from
0 degrees, there is a change in ITD of 8.7 psec, whereas for the 1 -degree change in angle from
90 degrees, there is a change in ITD of only 4.4 psec. Since ITD is the major cue introduced to
the stimuli used in this thesis, the sound sources that were presented during the psychophysical
experiments have equal ITD spacing, as opposed to the more typical equal angle spacing used by
Hartmann (1983) and others.
Vedula (2000) and Martin (1993) explored computational methods for locating sound
sources in anechoic conditions without jammers. Although numerous methods of ITD parameter
extraction were examined, the cross-correlation method adequately calculates the sound source
location in the horizontal plane. As the level of noise and/or reverberation is increased, the crosscorrelation method is expected to begin to fail. This thesis explores how well normal hearing
6
listeners perform sound source lateralization tasks for conditions in which these simple crosscorrelation methods are expected to fail.
The precedence effect is of particular interest in this study because it could enhance
performance of sound source lateralization beyond a simple cross-correlation method. The
precedence effect is a well known perceptual phenomena (Litovsky et al. 1999) involving stimuli
that contain lead and lag sound components. The precedence effect is most clearly observed
when the lag sound is simply a time-delayed version of the lead sound, but where the lead and
lag sounds come from different locations. For clicks and brief noise bursts, if the lead-lag delay
is on the order of 5 to 10 msec, one sound source is heard, and the perceived direction is close to
that of the lead (i.e., the lead component has a larger influence on the direction.) If the lead-lag
separation is long, say 30 msec, two sound sources are heard coming from directions
corresponding to the lead and lag directions. If the lead-lag separation is very short, say 1 msec,
only one sound source is heard, coming from a combination of the lead and the lag directions. It
is generally hypothesized that the precedence effect could lead to increased performance of a
subject's ability to lateralize sound sources containing only ITD cues under circumstances when
a simple cross-correlation method fails to detect the correct source location.
This thesis helps understand the role of the precedence effect in sound source
lateralization. For long duration stimuli made up of target and jammer components, the
relationship between lateralization judgments and the ITD of the target component is explored
for various jammer conditions. In some conditions the target and jammer have a lead-lag
relationship while in other conditions the target and jammer are uncorrelated. This thesis
compares lateralization performance of jammer conditions with common cross-correlation
functions and different auto-correlation functions.
7
One model (Zurek, 1987) of the precedence effect postulates periods of attenuated
lateralization influence following stimulus onsets. For ongoing stimuli, this period of attenuated
is achieved by multiplying the stimulus with an attenuating "precedence" window whenever a
"peak" in the stimulus occurs. This windowing of the stimulus decreases the importance of
future "peaks" that occur within the window's duration. For stimuli containing correlated target
and jammer components, as reflected by peaks in the auto-correlation finction, the application of
a "precedence" window theoretically allows for improvements in lateralization performance.
When the target and jammer components are not correlated there is no theoretical improvement
in lateralization when a "precedence" window is applied to the sound signal.
The target-jammer time delay can play an important role in the precedence effect. When
the target and jammer are uncorrelated the precedent effect does not predict improvements in
lateralization performance regardless of the jammer ITD. When the target and jammer are
correlated, the Zurek (1987) model of the precedence effect can predict varying levels of
improvements as a function of jammer ITD. This is due to the temporal pattern of the precedence
window. Longer target-jammer delays result in smaller attenuation of the importance of the
future "peaks." Since target-jammer delay is a function of jammer ITD, differences in
lateralization performance are predicted for precedent-like stimuli as a function ofjammer ITD.
Both psychoacoustic listening experiments and modeling were conducted to assess the
role of the precedence effect in lateralization. In Sec. II, the methods and procedures used for the
listening experiments and modeling are presented. Section III contains the results, and in Sec. IV
there is a discussion of the results. Finally, conclusions about the results are presented along with
some suggestions for future work.
8
II.
Methods
A. Subjects and Apparatus
Four male subjects, S1, S2, S3, and S5 and one female subject, S4, participate in the
experiments. Subjects S1, S3, S4 and S5 were paid to participate; subject S2 was the author.
Listeners ranged from 20 to 26 years in age. All subjects reported no hearing impairments and
audiometric testing showed normal hearing. (Pure tone thresholds were no poorer that 15 dB HL
between 250 Hz and 8 kHz.) Subjects had varying levels of experience with auditory listening
experiments and lateralization tasks. Testing was conducted in a sound proof chamber in the
Hearing Research Center of Boston University. Stimuli were presented through high quality
headphones (AKG MODEL K240) to the listeners. During experiments subjects sat in front of a
computer monitor and a mouse pointer method was used to record lateralization responses.
B. Impulse Responses
In an attempt to understand the role of the precedence effect in sound source
lateralization, stimuli with two major components (target and jammer) were explored. Listeners
were instructed to lateralize the target component. The properties of the jammer component were
controlled so that in some conditions the target-jammer relationship was of a precedence nature
while in other conditions the target-jammer relationship was uncorrelated. A description of the
properties of the target-alone and
jammer-alone
impulse responses (IRs) follows this section.
The properties of the combined stimulus containing both the target and jammer components are
presented in Sec. II.C.
i.
Target
The target IRs were created from an anechoic HRTF. Specifically, the HRTF was from a
measurement on the left ear of the Knowles Electronics Mannequin for Acoustics Research
9
(KEMAR) for a source located directly in front of the head, 0 degrees [obtained from Gardner
and Martin (1994)]. The target IRs varied only in ITD corresponding to changes in target
direction. As the target angle was varied, the left and right target IRs were simply delayed
versions of each other. The same target IRs were used throughout all conditions and experiments.
Figure 1 shows the frequency magnitude spectrum of the target IRs.
1H.
Jammer
There were five different jammer conditions, identified as A, A', B, B' and C. In
condition A, the jammer IRs were simply a 5-msec delayed version of the IRs for the 0 psec ITD
target. (This 0 psec ITD corresponds with a 0-degree azimuth jammer source; a source directly
in front of the listener.) Similarly in condition A', the jammer IRs were a 5-msec delayed version
of the target IRs with an ITD of 643 psec. (This 643 psec ITD corresponds with a 90-degree
azimuth source; a source located at the left ear of the listener.) In conditions B, B' and C, the
jammer IRs were 1-second tokens of noise, with the onset of the noise delayed by 5 msec from
the start of the jammer IRs. In condition B, the jammer had an ITD of 0 psec, whereas in
condition B' the jammner had an ITD of 643 psec. In condition C, the jammer was statistically
independent between the left and right IRs (independently chosen phase spectra.) For all the
jammer conditions, the jammer IRs had the same magnitude frequency spectrum as the target IR
(shown in Fig. 1) but the phase spectra was different for each condition. Table 1 presents the
general properties of the jammer IRs.
10
Table 1 Properties of the jammer IRs for the 6 different jammer conditions.
Condition
A
A'
B
B'
C
ITD
0 psec
643 psec
0 psec
643 [tsec
N/A
Duration
3 msec
3 msec
1 sec
1 sec
1 sec
Near Ear Latency
5 msec
5 msec
N/A
N/A
N/A
General Jammer Properties
Reflection from 0 degrees
Reflection from 90 degrees
Independent noise from 0 degrees
Independent noise from 90 degrees
Interaurally uncorrelated noise
Note. Figure 2 shows the actual IRs. No ITD is imposed on the jammer for stimulus conditions
C. The latencies stated correspond to the latency of the near ear only: There is an additional
latency of 643 pLsec for the far ear in conditions A'.
C. Stimuli
In general the sound stimulus was a 500-msec noise burst with a linear rise/decay time of
25 msec. Specifically, the convolution of a 5-second token of white noise with the target IRs for
an ITD generated the target waveform for that ITD. Similarly, the convolution of the same 5second token of white noise with the jammer IRs for the specific condition generated the jammer
waveform, which was then scaled to obtain the desired TJR. On every trial a 500-msec window,
with a rise/decay time of 25 msec, was multiplied with the target and jammer waveforms to
create the target and jammer stimuli. The location of this window was randomly chosen from
trial to trial, and was chosen to avoid both onset and offset effects by avoiding window locations
that included the first or last second of the target and jammer waveforms. The target and jammer
signals were then summed to create the sound stimuli. A personal computer generated the sound
stimuli, which were presented through Tucker Davis Technologies digital-to-analog converters
with a sampling rate of 44.1 kHz. The target signal was presented at a sound pressure level of 65
dB SPL for all conditions and the jammer signal level varied according to the TJR.
For a given sound stimulus (fixed target ITD, TJR and jammer condition), one can
construct transfer functions and overall stimulus IRs, using the fact that the convolution,
11
windowing, scaling and summation operations are all linear. Figure 2 shows sample IRs of this
type for a -100 psec ITD target and a TJR of 0 dB for conditions A and A' and -10 dB for
conditions B, B' and C. In each IR of conditions A and A', two prominent transients appear
separated by about 5 msec. The first of these transients corresponds with the target and the
second to the jammer. Jammer conditions B, B' and C show only one major transient followed
by noise. Only the first 10 msec of the IRs are shown, although the noise in the IRs of jammer
conditions B, B' and C has a duration of 1 second. Figure 3 shows the cross-correlation functions
of IRs similar to those shown in Fig. 2 for various TJRs. In all cases the target has an ITD of 100 tsec. Each column of Fig. 3 presents the cross-correlation functions of all the different
jammer conditions for a fixed TJR.
Examining the cross-correlations of condition A, in the top row of Fig. 3, there are three
clusters of activity. Two of the clusters are side lobes, with delays near ±5 msec. Since these
clusters are outside the physiologically relevant range of +1
msec, they are ignored in the
modeling presented in this thesis. For a TJR of 0 dB, there are two major peaks in the central
cluster within the range of ±1 msec. The peak in the central cluster at -100
tsec corresponds to a
lag in which the left and right targets are highly correlated. Similarly, the peak in the central
cluster at 0 ptsec corresponds to a lag in which the left and rightjammers are highly correlated.
The magnitude of the peak associated with the target is not a function of TJR, whereas the
magnitude of the peak associated with the jammer is a function of TJR. The reason the peak
associated with the target is not seen in the -10 dB TJR is due to the scale of the figure. There is
no "noise" outside the three clusters of activity. Results of the cross-correlation for condition A'
are shown in the second row of Fig. 3. The cross-correlation functions for condition A' are
similar to those of conditions A. The major difference is a shift in the peak locations associated
12
with the jammer, due to the change in the jammer ITD from 0 psec to 643 jisec. Again there is
no noise outside the three major clusters of activity.
Conditions B and B', which correspond to jammer IRs that are spread out in time, are
similar to each other but are substantially different from A and A' in that the side clusters are
missing, additionally there is "noise" outside the central cluster. For a TJR of 0 dB, conditions B
and B' have the same two large peaks corresponding to the target and jammer ITDs. Again the
magnitude of the peak associated with the target is not a function of TJR, whereas the magnitude
of the peak associated with the jammer is a function of TJR. The level of the "noise" outside the
central cluster of activity is inversely proportional to the TJR.
For Condition C, there is only a single cluster of activity, which in turn contains only one
peak. This peak is a result of the correlation between the left and right target IRs. The magnitude
of this peak is not a function of TJR (The peak is not noticeable for the -10 dB TJR due to the
scale.) Similar to conditions B and B', there is "noise" in the cross-correlation function outside
the central cluster of activity, again the level of this "noise" is a function of TJR.
D. Experimental Procedure
Subjects were first trained with a lateralization procedure for the target-in-quiet
condition, to familiarize them with the stimulus and response method. After the subjects became
adequately familiar with the target-in-quiet conditions they began running the different jammer
conditions. For each jammer condition the subjects would first undergo a 1-interval 2-alternative
identification procedure. After completing the identification procedure the subjects would begin
lateralization procedures for the different TJRs and jammer conditions. The specifics of how the
subjects were run and the procedures for the different experiments follows below.
13
Experiment 1: Lateralization-in-quiet
Experiment 1 used the target-only stimuli exclusively. On each trial, the 500-msec target
stimulus ITD was randomly chosen from 13 equally spaced ITDs between -600 and +600 ptsec,
corresponding to locations spanning the frontal hemifield. The subjects were asked to listen to
target stimuli and locate the target stimulus by clicking a mouse at the appropriate left-right
position along the image of a bar (hash marks were used to divide the bar into quarters.) Before
the responses were recorded subjects were instructed to familiarize themselves with the stimulus
set, especially the perceptual extremes, in terms of left/right, of the target. After familiarization,
subjects underwent 100-trial block test procedures. Feedback was not given during experiment 1.
ii.
Experiment 2: Identification
Experiment 2 was a 1-interval 2-alternative forced choice identification experiment. On
each trial, the target stimulus ITD was randomly chosen to be either ±300 psec. (approximately
±35 degrees) The experiment was carried out for stimulus conditions A, A', B, B' and C. The
jammer stimuli were consistent with the stimulus condition being tested and the TJR was
adaptively chosen based upon a 2-down- 1-up adaptive paradigm.
Subjects were asked to listen to target stimuli and to identify the target stimulus as either
left or right through a dialog box and a mouse "click". Before measurements were taken, subjects
listened to targets, from the set of target ITDs being tested, and jammers, for the conditions being
tested and with randomly chosen levels; they were instructed to familiarize themselves with the
left/right position of the two target stimuli as well as the jammer stimuli. After familiarization
responses were recorded for a total of 10 reversals. The step size for TJR was 2 dB initially (for
the first 4 reversals), and then the step size was reduced to 1 dB for the remainder of the
14
procedure. The mean of the last six reversals was taken as the subject's identification threshold
for the conditions being tested.
For each trial a random 500-msec sample of the jammer stimuli was played. The jammer
was followed by a 250-msec interval of quiet, which in turn was followed by the jammer stimuli,
again, summed with the corresponding target stimuli with a randomly chosen ±300 psec ITD.
The subjects were told in the instructions for the experiment that the target stimulus was played
during the second burst of noise. Implicit feedback was not given during experiment 2.
iii.
Experiment 3: Lateralization
Experiment 3 was also performed for stimulus conditions A, A', B, B' and C. On each
trial, the target stimulus ITD was randomly chosen from 13 equally spaced ITDs between -600
and +600 psec, corresponding to locations spanning the frontal hemifield. The jammer stimuli
were consistent with the stimulus condition being tested. The jammer level was determined from
the TJR being tested. The subjects were asked to listen to target stimuli and locate the target
stimulus by clicking a mouse at the appropriate left-right position along the image of a bar (hash
marks were used to divide the bar into quarters.) Before responses were recorded, subjects were
instructed to familiarize themselves with the stimulus set, especially the perceptual extremes, in
terms of left/right, of the target, by playing token samples of the target alone stimulus.
Additionally they were asked to familiarize themselves with jammer stimuli in the same manner.
After familiarization, subjects underwent 100-trial block test procedures. For each trial a random
500-msec sample of the jammer stimuli was played. The jammer was followed by a 250-msec
interval of quiet, which in turn was followed by the jammer stimuli, again, summed with the
corresponding target stimuli with a randomly chosen ITD. The subjects were told in the
15
instructions for the experiment that the target stimulus was played during the second burst of
noise. Feedback was not given during experiment 3.
iv.
Procedure
A jammer condition sequence was created for each subject, randomly determining the
order that the jammer conditions A, A', B, B' and C would be run in. Eight TJRs were examined,
(+12 dB, +8 dB, +4 dB, +0 dB, -4 dB, -8 dB, -12 dB and -16 dB.) For each subject and jammer
condition a TJR sequence was created containing the eight TJR in a pseudo random order. The
first TJR of all the TJR sequences was always +12 dB. This was done to allow the subject
additional time to familiarize themselves with the experiment.
Each subject first underwent a series of lateralization-in-quiet runs. These measurements
were concluded when the subjects had completed a minimum of six 100-trial blocks and the
difference in the standard deviations of the marked location (averaged over the actual ITDs) was
less than 100 ptsec between the last two successive 100-trial blocks.
The subject then began testing of the different stimulus conditions. First the subjects
completed an identification run for the jammer condition (determined by the subject's stimulus
condition sequence). The subject then completed seven, 100-trial block, lateralization runs. The
jammer condition was held constant throughout the seven, 100-trial blocks. The TJR was varied
between 100-trial blocks according to the TJR sequence for the subject and stimulus condition.
Before the third 100-trial block, of the series of seven lateralization runs, the subject underwent
another 100-trial block lateralization-in-quiet run. After completing all the stimulus conditions, if
a subject's schedule permitted, additional 100-trial blocks were run of various jammer conditions
and TJRs.
16
E. Model
Two relatively simple cross-correlation models were designed. Model 1 was a dumb
model that did not make use of the known location of the jammer, and model 2 was a smart
model that did make use of the known location. Both models are wide-band, long-time crosscorrelation models. The left and right ear sound stimulus was cross-correlated for lags between
±1 msec for each stimulus. Model 1 used the ITD of the peak in the cross-correlation function as
the predicted ITD. Model 2 used information about the jammer condition being tested; it
calculated a cross-correlation for a single jammer-only stimulus and used this as a template
throughout a testing block. (Possibly similar to what subjects do during the familiarization stage
of the psychoacoustic experiments.) For each stimulus the smart model subtracts this jammer
only cross-correlation template from the target plus jammer cross-correlation function. The ITD
of the peak in this resulting function was taken as the predicted ITD.
Both models were run for a 500-trial block for jammer conditions A, A', B, B' and C
with TJRs between +10 dB and -20 dB, in 2 dB steps, for each jammer conditions. On each trial
the target stimulus ITD was randomly chosen from 13 equally spaced ITDs between -600 and
+600 psec. The jammer stimulus was consistent with the jammer conditions and TJR being
tested.
F. Data Analysis
One of the first steps in analyzing the data involves transforming the subject's response
on the bar, with the mouse pointer method, to an ITD. This is accomplished by arbitrarily calling
the left extreme of the bar -1,
the right extreme of the bar +1. The detected angle for a given
lateralization response can then simply be calculated with the arcsin function. From this detected
17
angle combined with Eq. 1 the detected ITD for a given lateralization response can be
determined.
There are three major divisions of the analysis of the data. One is based on the leastmean-squared best-fitting straight line (LMS-line) relating the actual ITD of the target and the
lateralization responses, i.e. the detected ITD, of the subject. This first division includes the
intercept of the LMS-line, the root mean squared (RMS) difference between the detected ITDs
and the LMS-line, the slope of the LMS-line, and the square of the correlation coefficient (R2 ) of
the detected ITD and actual ITD results. As discussed below, the R2 statistic has the best
properties for exploring the differences for both inter-subject and inter-condition differences. The
second division of the analysis of the data is based upon the TJR dependence of a summary
statistic. This second division of the analysis is used to determine both lateralization and
identification thresholds for each subject and condition. The final division of the data analysis
involves determining the statistical significance of these thresholds.
The intercept of the LMS-line is an indicator of the perceived location of a 0 psec ITD
target stimulus. The intercept value relies heavily upon the "guessing" strategy employed by the
subjects when they can no longer correctly determine the target ITD; therefore it is not a good
summary statistic. The RMS difference between the detected ITDs and the LMS-line also relies
heavily upon the "guessing" strategy and is not a good summary statistic. However in
experiment 1, the RMS difference does help to show that the subjects are able to correctly and
repeatable lateralize the target stimuli with the mouse pointing response method. The slope of the
LMS-line is an indicator of how much of the response bar was used by the subject. Although
subjects were instructed to use as much of the response bar as possible, different subjects used
different amounts of the bar, therefore the slope is not a good summary statistic. The square of
18
the correlation coefficient is a measure of the differences in the linearity of the response mapping
from actual ITD to detected ITD. R2 seems to be a good summary statistic. An even better
summary statistic in terms of highlighting the differences between the different jammer
conditions seems to be a normalized version of R2 .
The normalized R 2 for a the detected ITD responses and the actual ITDs for a given
subject, jammer condition and TJR is defined simply as the R2 for that subject, jammer condition
and TJR divided by the R2 for that subject in quiet. Equation 2 defines the normalized R2 .
Normalized
02
Rcondition
m in1
R2
condition
R 2(2)
The second division of the data analysis is based upon the results of the cumulative
Gaussian function that best fits the normalized R2 versus TJR data for each subject and
condition. The cumulative Gaussian function is taken as the psychometric function of the subject
ability to lateralize the target in the jammer conditions. The normalized R2 is limited to a
maximum value of 1 since a cumulative Gaussian function is also limited to a maximum value of
1. The lateralization threshold TJR is defined as the TJR for which the psychometric function has
a normalized R2 value of 0.5.
The final division of the data analysis was a single factor ANOVA to determine the
significance of the differences between the results for the different conditions. Numerous
pairings were made. The differences between conditions A and A' were examined, as well as the
differences between A and A' and B and B' to name just a few of the comparisons examined.
19
III.
Results
A. Experiment 1: Lateralization-in-quiet
The purpose of Experiment 1 was to determine whether the subjects were able to
correctly lateralize the target stimuli in the quiet condition. Figure 4 presents the confusion
matrices (detected ITDs versus actual ITDs) of each subject, for the target-in-quiet condition.
The bin size for the confusion matrices is 100 psec, and the area of the symbol is proportional to
the number of points in each bin. In general the subjects place targets with different ITDs at
different locations along the bar. Additionally for each 100-trial block, the slope, intercept, RMS
difference and R2 statistics were calculated. Figure 5 shows, for subject S3, the values of these
statistics as a function of 100-trial block number. The statistics appear to be time-invariant after
the first few blocks; no steadily increasing or decreasing trends can be seen as a function of
block number. This implies that the subjects were given adequate time, a minimum of 6, 100trial blocks to become familiar with both the target stimulus and response method used during
the experiment.
Table 2 presents the mean and the standard error, over 100-trial blocks, of the statistics
for each subject. It should be noted that although all the statistics for the subjects are time
invariant (Fig. 5) there are differences between subjects. For example, subject Si has a much
higher RMS difference than S5, and subject S5 has a much shallower slope than S2. As
mentioned in Sec. II.F, the differences in these statistics arise from the mouse pointing method.
For instance the intercept, for each subject, is a function of the perceived center of the bar. The
slope is a measure of how much of the bar the subjects used in their responses. In summary, all
the subjects were able to correctly locate the target for the target-in-quiet condition. The values
of R 2 presented in Table 2 are used in the calculations of the normalized R 2 in Experiment 3.
20
Table 2 Average values and the standard errors of the different statistics calculated over all the
100-trial blocks of Experiment 1 for each subject.
Slope
Intercept ( sec)
R
RMS Difference ([tsec)
S1
0.72±0.02
15.0±8.1
0.65±0.03
196.7±9.8
S2
0.78±0.02
6.7±7.6
0.88±0.02
106.9±7.1
S3
0.73±0.03
4.9±4.2
0.89±0.01
91.1±2.6
S4
0.57±0.02
17.6±6.8
0.89±0.01
76.9±4.6
S5
0.48±0.03
2.9±5.7
0.80±0.02
85.5±2.9
B. Experiment 2: Identification
Experiment 2 determined the identification threshold for the different jammer conditions
summarized in Table 1. The identification threshold is defined as the lowest target-to-jammer
ratio (TJR) for which the subjects were able to correctly identify, at least 70% of the time, which
target ITD (either ±300 psec) was presented in the presence of the jammer. Table 3 presents the
identification thresholds of the individual subjects, the threshold averaged across subjects and the
standard deviation across subjects, for the five different jammer conditions. Figure 6 shows the
data in Table 3 graphically along with model predictions that are discussed later in Sec. III.D.
The standard deviation of the thresholds for a given condition between subjects is
relatively modest, on the same order of magnitude as the variance in a subject's threshold from
day to day (data not shown). There is, however, a significant 3.2 dB difference (P value of 0.027)
between the mean identification thresholds for the precedent-like jammer conditions, jammer
conditions A and A', and the corresponding non-precedent-like jammer conditions, jammer
conditions B and B'. Due to the nature of the jammer conditions this difference in identification
threshold is interpreted as a result of the precedence effect.
21
Table 3. Identification thresholds for each subject and condition as well as the across subject
average threshold and standard deviation.
Condition
A
A'
B
B'
C
S1
Threshold
(dB)
-10.0
-10.7
N/A
-3.7
-5.0
S2
Threshold
(dB)
-9.3
-9.7
-6.0
-8.0
-3.0
S3
Threshold
(dB)
-12.1
-7.2
-9.0
-4.8
-6.3
S4
Threshold
(dB)
-14.8
-7.8
-6.7
-11.3
-3.3
S5
Threshold
(dB)
-7.5
-6.8
-6.3
-1.3
-4.0
Average
Threshold
(dB)
-10.75
-8.4
-7.0
-5.8
-4.3
Standard
Deviation
(dB)
2.80
1.68
1.36
3.90
1.35
C. Experiment 3: Lateralization
Experiment 3 determined the lateralization threshold for the different jammer conditions.
Example confusion matrices of subject S4, for jammer condition B', for the different TJRs, are
presented in Fig. 7. For high TJRs the subject has performance similar to the performance in
quiet (cf, Fig. 4). As the TJR decreases, performance is less dependent on the target ITD. This
change with TJR is not seen in all statistics. (See the appendix for complete data) For example,
the RMS difference of the subject is not a function of TJR. Some subjects however exhibit a
change in the RMS difference statistic as a function of TJR. For jammer condition B', the
intercept of S4 (in Fig. 7) is a function of TJR. Again, this result is consistent neither across
subjects nor across conditions. Changes in the intercept and RMS difference statistics depends on
how the subject responds when they cannot detect the correct ITD of the target. Some subjects
have biases towards the ITD of the jammer, others to the center of the bar. Both the slope and the
R2 statistics vary consistently with the TJR, and across conditions. The R 2 statistic seems to be
the most consistent measure for interpreting the results across conditions. The normalization of
the R2 statistic leads to the best statistic for making comparisons across both subjects and
conditions.
22
Figure 8 shows the normalized R2 , for subject S2, plotted as a function of TJR for all the
jammer conditions. Also shown in Fig. 8 is the best fitting cumulative Gaussian function for each
jammer condition. The transition region of the psychometric function seems to be captured well
by the shape of the cumulative Gaussian function. Figure 9 shows the best fitting cumulative
Gaussian functions for all the subjects and jammer condition B.
The lateralization threshold is defined as the TJR at which the normalized R2 statistic is
equal to 0.5. Table 4 contains a tabulation of the lateralization thresholds, which are presented
graphically in Fig. 6. Similar to Experiment 2, there is a 2.85 dB difference (Significant with a P
value of 0.040) in the thresholds between the precedent-like jammer conditions, conditions A
and A' and the corresponding non-precedent-like jammer conditions, conditions B and B'. As
explained in Section I, due to the nature of the stimuli the differences are interpreted as a result
of the precedence effect.
Table 4 Lateralization thresholds for each subject and jammer condition as well as the across
subject average and standard deviation.
Condition
A
A'
B
B'
C
S1
S2
Threshold Threshold
(dB)
(dB)
-9.5
-9.5
-9.6
-9.7
-6.6
-7.6
-2.6
-11.3
-4.2
-2.4
S3
Threshold
(dB)
-4.4
-5.7
-5.7
-5.3
-5.2
S4
Threshold
(dB)
-13.6
-6.4
-5.5
-8.1
-2.6
S5
Threshold
(dB)
-8.8
-7.3
-0.4
-2.9
-4.1
Average
Threshold
(dB)
-9.2
-7.8
-5.2
-6.0
-3.7
Standard
Deviation
(dB)
3.3
1.8
2.8
3.7
1.2
D. Model
Figure 10 shows the confusion matrices for Model 1, the dumb model, for condition B'
and a variety of TJRs. From these confusion matrices it is apparent that when the model fails to
predict the target ITD it predicts the jammer ITD. Figure 11 presents the normalized R2 statistic
as a function of TJR for the different jammer conditions along with the best fitting cumulative
23
Gaussian functions for Model 1. The lateralization thresholds of Model 1 are approximately 0 dB
for conditions A, A', B and B' and -13 dB for jammer condition C.
Figure 12 shows the confusion matrices for Model 2, the smart model, for condition B'
and a variety of TJRs. Model 2 either predicts the target ITD or a random ITD. Figure 13
presents the normalized R2 statistic as a function of TJR for the different jammer conditions and
the best fitting cumulative Gaussian function for Model 2. The lateralization thresholds of Model
2 are approximately -13 dB for all jammer conditions.
Figure 6 graphically shows the lateralization threshold predicted by both models as well
as the lateralization thresholds determined in experiment 2. This allows for a direct comparison
between the human subject and model performances. It is interesting to note that the smart model
outperforms the human subjects for all conditions.
IV.
Discussion
This thesis shows three major points. The first is the differences between conditions A
and A' and B and B'. This difference, as explained earlier, is predicted to be a direct result of the
precedence effect. The second major point is found in the differences between conditions A and
A' and the similarities between conditions B, B' and C. The similarities in conditions B, B' and
C help to show that the differences between conditions A and A' are a results of how the
precedence effect is implemented by the auditory system. Finally an overall comparison between
the psychophysically measured thresholds of normal-hearing individuals can be compared to the
performance of simple cross-correlation models.
In an attempt to illustrate the three major points of this thesis some similarities between
the identification and lateralization thresholds need to be explained. Some of these similarities
seem to be incidental, while others are a direct result of the stimulus properties. For example the
24
average identification threshold (4.3 dB) and the average lateralization thresholds (3.7 dB) for
jammer condition C are similar only because of the choice of ITD values in experiment 2. For
any given conditions the identification threshold should be dependent upon the size of the
difference between the left and right target ITDs. (In the case of this work the difference was 600
psec.) Therefore the similarities of the identification threshold levels, for any jammer condition,
with the lateralization threshold levels of either corresponding or non-corresponding jammer
conditions simply reflect the choice of the difference in ITD of the left and right targets. Other
similarities between the identification thresholds and the lateralization thresholds may be more
fundamental. For example, the differences between the mean identification thresholds of
conditions A and B (-3.8 dB) can be attributed to the precedence effect.
The lead-lag relationship between the target and jammer in condition A is thought to
allow for improved lateralization performance from the precedence effect. The relationship
between the target and the jammer in condition B is such that lateralization performance is not
improved by the precedence effect. The similarities between the interaural cross-correlations of
conditions A and B lead cross-correlation based models to achieve similar lateralization
performance in both conditions. A similar explanation can be for the differences in lateralization
performance between conditions A' and B'.
Further evidence for the precedence effect playing a role in lateralization performance
comes from examining the differences between conditions A and A' and the differences between
conditions B and B'. It is argued here that the difference in thresholds between conditions B and
B' will be smaller than the difference in the thresholds between conditions A and A'. The stimuli
do not rule out the possibility of differences in lateralization or identification performance based
upon the jammer ITD. The precedence effect, as described in Sec. I, predicts a difference in the
25
threshold level as a function of jammer ITD. In conditions A' the far ear stimulus has an
additional 643 msec of lag. The decrease in importance of "peaks" in the stimuli associated with
the precedence window is time dependent; the decrease in importance decreases with time. With
this in mind, the differences in threshold between conditions A and A' should be slightly larger
than the differences in threshold between conditions B and B'. The results however do not show
this finer point of the precedence effect as clearly as expected.
The difference in thresholds between conditions A and A' was 1.9 dB. The results of the
ANOVA analysis however yielded a P value of 0.104; meaning the results are not significant.
This does not however tell the entire story. In the view of the author, the results are significant
due to the limited number of subjects and the relatively small effect. The author believes that
there is in fact a difference in the thresholds for conditions A and A'. This belief is based upon
the fact that in both the lateralization and the identification experiments the average thresholds
for condition A was higher than the average thresholds for condition A'. (1.6 dB difference for
the lateralization experiment and 2.4 dB difference for the identification experiment.) However,
the difference between conditions B and B' were not consistent between the lateralization
experiment and the identification experiment. It seems the consistencies between conditions A
and A' and the inconsistencies between conditions B and B' yield further evidence that there is
in fact a slight effect ofjammer location for the precedent like stimuli of conditions A and A'.
In terms of the goal of this thesis and the determination of the role the precedence effect
in sound source lateralization, the differences between conditions A and A' and B and B' for
both the lateralization and identification thresholds suggests approximately a 3 dB role for the
precedence effect. Since this work only examined a single 5 msec lead-lag separation, the
26
importance of the precedence effect for different lead-lag separations is not known, however, it
seems that the precedence effects role is significant in the cases examined in this work.
Although it seems the precedence effect has been found to be significant an interesting
result is found when a comparison between the performance of normal-hearing listeners and the
smart model is made. The smart model outperformed normal hearing listeners by up to 10 dB in
some situations. It seems that normal-hearing subjects are not efficient at performing peak
extraction from cross-correlation functions. The results of this thesis suggest a more detailed
comparison between
the performance
of simple cross-correlation
models and human
performance needs to be done. Neither model explored in this thesis takes into account the
precedence effect. It would be interesting to examine the performance of a cross-correlation
based precedence model in terms of the performance of non-precedence cross-correlation models
and normal-hearing listeners. In addition to further modeling efforts, an examination of the role
of the precedence effect for other stimuli (clicks, narrow-band noises, ongoing noise burst and
multiple jammers) should be carried out.
V.
Conclusions
The role of the precedence effect in both sound source identification and sound source
lateralization, for wide-band ongoing targets in the presence of a perfectly correlated, 5 msec
delayed, wide-band ongoing jammer of a known location is approximately 3 dB. For all the
jammer conditions tested a smart cross-correlation model was able to outperform the human
subjects by a minimum of 5 dB and up to nearly 10 dB. More jammer conditions (the number of
jammer sources, target-jammer delays and spatial separations) need to be investigated to begin to
fully understand the role of the precedence effect in sound source lateralization.
27
Acknowledgements
Work supported by NIH. (Grant Numbers ROI DCOO 100 and T32 DC00038)
28
Figures
Target Spectrum
/
-5
\
I\
-10
K
-151
-20
~-25
-30
-35 -
-40
I-
-45
2
I
I
4
6
I
8
I
10
12
Frequency (kHz)
I
14
16
18
20
Fig. 1 Common magnitude spectrum of the target and jammer stimuli taken from a 0-degree
HRTF measurement made on KEMAR obtained from Gardner and Martin (1994). The amplitude
is in dB re the maximum.
29
Right ear IR
Left ear IR
<
0.5
0.5
0
0
-0.5
0
2
4
6
8
10
0.5 r
0
0
0
2
4
6
8
10
0
0
2
4
6
8
10
0. 5 r
4
6
8
10
2
4
6
8
10
r
k
~.
.
-0.5'
0
0 ~
0
2
2
4
6
8
10
2
4
6
8
10
8
10
0.5
0
2
4
6
8
10
-0.5
A
0.5
0.5 r
0
0
-0.5
0
0
-0.5-
-0.5
-0.5'L
0.5
0.5 r
o
C
0. 5 r
-0.5
Cal
-0.5
r
0
2
4
6
Time (msec)
8
10
-0.5'
0
2
4
6
Time (msec)
Fig. 2 The first 10 msec of the left and right ear impulse responses (IRs) for example sound
stimuli of types corresponding to the different jammer conditions. In all cases the target has an
ITD of -100 psec. The target-to-jammer ratio (TJR) is 0 dB for conditions A, A' and -10 dB for
conditions B, B' and C. The amplitude scale is consistent across conditions and ears.
30
TJR= 0 (dB)
TJR =-10 (dB)
.
15
TJR = 10 (dB)
1.5
1.5
1-
10-
<(
5-
0.5
04
-5.
0
-0.5
-10.
-5
0
5
15
-1
0.5.
0
-0.5
-5
1.5
105-
0
5
-1
_
-5
0
5
-5
0
5
0
5
0
5
0
5
1.5
.
1
1
0.5-0.5-
-10
5
-0
-1
0.5- -5
0
0-~-A
15
-1
1.5
1
1.5
0.5-
0.5-
5-
-10
5
-0.5
10-
-5
0
0---0.5
-0.5-
-
-5
15
0
5
.
-1
'
-5
1.5
-
0
' 1
5
-1
1.5
10-
1
5-5-10
-5
''
-5
0
0.5-
0.5-
0
0
-0.5-
-0.5-
5
-5
1.5
0
5
-1
-
-5
-
1.5
..
1 -
0
-5
-10
0.5 -
0.5-
-0.5 -
-0.5-
--------------
-
.
-5
0
Lags (msec)
5
-1
.'.
-5
0
Lags (msec)
5
-1
-5
Lags (msec)
Fig. 3 Example cross-correlation functions of the sound stimuli IRs, similar to those presented in
Fig. 2, for the different stimulus conditions over a range of target-to-jammer ratios (TJRs). The
target has an ITD of -100 psec in all cases. Note the change in the scale of the ordinate for the
different TJRs. The amplitude scale values are consistent across conditions and TJRs.
31
S1I
600
S2
600
..
.
-
*
,,
400
400.
200
200
.,e.
*.
C.)
..
a)
0-
0
Actua
*TD (
* 0-200
se)
-400
-400
-600
-600
S3
'
-500
.
.
600 r
600 r
400
400
200
U
0)
200
H
.
*
-o
*
-
*
0
*
0)
a)
0
0 -200
-
*
200
0,~0.
*
0*5
.. 9'S.
-200
*
4
~,S .
*
0
* .7.
U
.
S,-SS.
W
0)
./-
.
0 -200
-400
-400
-600
-500
0
Actual
ITD (psec)
500
0*
*
0*
*
*E
4
9r'.
*
0*
0
4
/
..
iIi.
**0
..
*
*
*
S/%'@*
0*5*9
4
-
*
4..
*
0
.
S5
o
400
.
500
0
Actual ITD (psec)
S4
600
0
/A
00
0
-50
-200
0
4
.....
a)
0*
0O
S..
-400
**
-600 L '
-500
0
Actual
lTD (psec)
500
*
-600 L
-500
0
500
Actual ITD (psec)
Fig. 4 Confusion matrices for all the subjects in the target-in-quiet condition
32
S3
1
100-
±
80-
0.9
*
60-
*
0.8
+
±+
±
0.7
40-
*
0.6 - *
*
4-
*
*
(D
0.4-
C
-20
-
0.2
-
-60
-
0.1 -
-80
'
15
10
1 00-Trial Block #
20
'-100'
0.9 -
-
0.8
S*
+ *
,*
*
1-
*
*
*
*
5
10
15
100-Trial Block #
20
-
180-
+
* -I
*
*
*
*
0
200
**
+
*
*
-40
5
**
*
-
1
+
160-
*
0.7
140-
0.6 I('
+
+
0
0.3
00
*
*
20*
-120
±
100-
0.5
-
0.3
-
60
0.2
-
40-
0
*
[
+
-A-,
*
*
**
*
*
*
*
20
0.1 -
0'
*
80 -
0.4
r
+
*
S**
5
15
10
100-Trial Block #
20
O'
0
5
10
15
100-Trial Block #
20
Fig. 5 Statistics summarizing the performance of subject S3 during the target-in-quiet condition
as a function of 1 00-trial block number. The top left panel shows the slope of the LMS-line and
the top right panel shows the intercept of the LMS-line. The bottom left panel shows R2 between
the detected ITD and the actual ITD. The bottom right panel shows the RMS difference between
the detected ITD and the LMS-line.
33
Threshold Values
2
0-
-2
-
-4-
V-
-6
0 Identification
* Lateralization
* Dumb Model
*Smart Model
-
-8
r
-10 --
-12
-14-
A
A'
B
B'
C
Jammer Condition
Fig. 6 Threshold values for the different jammer conditions. Across subject average values for
the identification and lateralization thresholds, error bars represent the standard error. The smart
and dumb model thresholds are the results of 500-trial lateralization runs.
34
S4 Condition: B'
SNR:8 (dB)
SNR:12 (dB)
SNR:4 (dB)
600
600
600
G400
- 400
400
200
20
200
I-
.
200
. .
0
0 ...
*.
0 .
-200
-200
Z-200
o -400
o -400
(D-400
-600
-500
0
Actual
-600-500
500
ITD (jpsec)
0
Actual
lTD (psec)
-600
500
-500
600
600
400
400
200
200
00
'
.
-200
-200
0 -400
00-400
-600-500
0
Actual
500
-600
ITD (jsec)
.
-500
. .. .
0
Actual
.
500
ITD (isec)
SNR:-16 (dB)
SNR:-12 (dB)
600
600
200
200
0
0
-200
-200
0
'-400
-600
0
500
Actual ITD (psec)
SNR:-8 (dB)
SNR:-4 (dB)
Z
....
-500
0
Actual
ITD (psec)
500
-400
-600
-500
0
Actual
500
ITD (psec)
Fig. 7 Confusion matrices of subject S4 for jammer condition B'.
35
S2
1
C4
Jammer Condition: A'
Jammer Condition: A
/ *
0.9-
0.9-
0.9
0.8-
0.8 -
0.8
0.7-
0.7 -
0.7
C4
0.6N
Jammer Condition: B
NI
0 .6-
0.6
-o 0.5
0.5-
0)
.5 -
0.4-
N
.4 -
0.4-
0.3-
0.3 -
0.3-
0.2 -
0.2 -
0.2-
0.1 -
0.1
0.1 -
0)
0,
-20
0
0
-"
0-20
20
0--
-20
0
20
SNR (dB)
Jammer Condition: C
Jammer Condition: B'
1-
I
0 .9-
0.9-
0.8-
0.8-
0 .7 -
0.7-
.6 -
0
0.6-
.5 -
N
0.5-
0
0 .4 -
0.4 -
0.3 -
0.3-
0 .2 -
0.2-
0.1
0.10
SNR (dB)
20
SNR (dB)
SNR (dB)
0
-20
0
20
0
-20
0
SNR (dB)
20
Fig. 8 Normalized R 2 of subject S2 for the different TJRs and jammer conditions. The
continuous curves are cumulative Gaussian functions fit to the measured R2 values shown.
36
Condition B
1
.-
0
0.9
-lk
0.8
0.7
I
I
0.6
-
I
I
S0.5
90
*S3
0.4
0.3
-S
0.2
I.
0.1
|-
(3
0
TJR (dB)
Fig. 9 Cumulative Gaussian functions, for each subject, that best fit normalized R2 data for
condition B.
37
Dumb Model Condition: B'
SNR:-20 (dB)
SNR:-12 (dB)
SNR:-16 (dB)
600
600-
600
' 400-
400
200-
400
200-
200
-
0
0
-200
-200
-200
0-400
-400
-400
-600
Actual
-600
500
0
-500
-500
ITD (psec)
SNR:-8 (dB)
600
*
600
400
0
-
-600
'
0
500
Actual ITD (psec)
..
600
0.
400
-0400
200
200
200
o
0
H
Z -200
o -200
I -200
0-400
-400
c -400
-600
-500
0
-600
0
500
Actual ITD (psec)
.
-500
SNR:4 (dB)
-600
-500
0
500
Actual ITD (psec)
400
200
=L200
0
-
0
6 -200
"U -200
0-400
-400
-600
0
500
Actual ITD (psec)
0
SNR:8 (dB)
400
-
-
0
600
*
600
0
500
Actual ITD (psec)
SNR:0 (dB)
SNR:-4 (dB)
a)
0
-500
-500
0
Actual
ITD (psec)
500
-600
-500
0
Actual
500
ITD (psec)
Fig. 10 Confusion matrices of Model 1, the dumb cross-correlation model, for jammer condition
B' and different TJRs.
38
Dumb Model Results
Jammer Condition: B
Jammer Condition: A'
Jammer Condition: A
1
1
0.9
0.9
0.9
0.8
0.8
0.8
0.7
0.7
0.7
1
CIA'
0.6
N
0.5
C-
0.6
0.5
0.6
0
zd
0.5
O0.4
0.4
z 0.4
0.3
0.3
0.3
0.2
0.2
0.1
0.1
0.2
-
0.1
0
-20
0
20
01
-20
SNR (dB)
Jammer Condition: B'
1
1
0.9
0.9
0.8
0.8
0.7
0.7
0.6
0.6
0.5
0.5
0 0.4
00.4
N
0.3
0.3
0.2
0.2
0.1
0.1
0-
-20
0
SNR (dB)
20
0
SNR (dB)
20
0
-20
0
20
SNR (dB)
Jammer Condition: C
+i
-20
0
SNR (dB)
20
Fig. 11 Cumulative Gaussian functions that best fit the normalized R 2 data of Model 1 for all the
jammer conditions.
39
Smart Model Condition: B'
SNR:-20 (dB)
600 .,,,,,,,,,,,
SNR:-16 (dB)
600 r.. .....
400
400 I
200 I
0
0
-200
H
-200
**
600
*
Z 400
.9
.0*900*
-200
SNR:-12 (dB)
, 0
200
0
0-
@0
*
..-
200
~
-400
-400
400.
-600.
-500
Actual
-600
-600
500
0
-500
ITID (psec)
0
500
Actual ITD (psec)
600
600
400
3. 400
-a400
200
200
0
H
0
H
0
6'r
-400
-600
0
Actual
0
500
200
H
Z-200
o-200
-600
-500
,0
0
0-400
0
500
Actual ITID (psec)
SNR:0 (dB)
SNR:-4 (dB)
SNR:-8 (dB)
600
d -200
-500
'-400
-500
ITD (psec)
0
500
Actual ITD (psec)
SNR4 (dB)
-600-500
0
500
Actual ITD (psec)
SNR:8 (dB)
600
600
400
C.)
4)
-9200
0 0-
0
H
-o
4)
-200
C.)
400
200
0
-200
4)
0-400
0
-600-500
0
Actual
ITD
500
(psec)
-400
-600
-500
0
500
Actual ITD (psec)
Fig. 12 Confusion matrices of Model 2, the smart cross-correlation model, for jammer condition
B' and different TJRs
40
Smart Model Results
Jammer Condition: A
C4)
N
Jammer Condition: A'
1
1
0.9
0.9
Jammer Condition: B
I
0.8
0.8-
0.7
0.7
0.9
/
0.8
0.7
0.6
0.6
X
0.6
N
C1
0.5
~0
41
0.5
-O
N
0.4
0.4
z 0.4
0.3
0.3
0.3
0.2
0.2
0.2
0.1
0.1
0.1
0.5
za
0
-20
0
SNR (dB)
0
20
0.8
0
SNR (dB)
20
0
-20
0
SNR (dB)
20
Jammer Condition: C
Jammer Condition: B'
I
1
1
0.9
-20
.1
0.9
0.8
0.7
0.7
0.6
0.6
N
0.5
~0
0)
"0.5
z.0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1-
0
0
SNR (dB)
-20
0
SNR (dB)
20
Fig. 13 the cumulative Gaussian functions that best fit the normalized R 2 data of Model 2 for all
the jammer conditions.
41
Appendix
The appendix consists of a series of figures representing all of the data collected and used
in this thesis. The figures are identical in format to figures presented in the body of the thesis,
varying only in the data of the subject and jammer condition being presented. Figures A-i
through A-4 are identical in format to Fig. 5, showing summary statistics for performance in
quiet, but for subjects Si through S5 respectively. Figures A-5 through A-32 are identical in
format to Fig. 7, confusion matrices for a given subject and jammer conditions, but for subjects
SI through S5 respectively. Subject S3 performed certain jammer conditions twice. The results
obtained from the first and second runs of these conditions are denoted S3 and S3' respectively.
Figures A-33 through A-36 are identical in format to Fig. 8, normalized R2 for the different
jammer conditions, but for subjects SI through S5 respectively.
42
SI
100-
1
80-
0.9
*
0.8
60-
*
*
0.7
40-
*
*
*
0.6
*
*
*
S
20
0-
8-0.5
0.4
-20
0.3
-40
0.2
-60-
0.1
-80-
0
0
5
15
10
1 00-Trial Block #
-1000
20
+
*
*
*
*
5
10
15
1 00-Trial Block #
*
180
0.9-
* *
*
*
160
0.8*
0.7-
+
0.60.5
*
*
**
*
.120
*
*
ci)
100
0.4-
80
0.3-
60
0.2-
40
0.1 -
20
5
15
10
100-Trial Block #
*
140
*
*
01
0
20
200
1 -
C"
+
20
0
0
5
15
10
1 00-Trial Block #
20
Fig. A- 1
43
S2
100-
1 -
0.9-
80-
*
*
0.8*
*
*
*-*
*
60-
**
*
0.7-
40-
*
*
0.6-
4)
20-
4)
0
0
4)
C
-20
(I)
0.4-
*
*
*
0.30.2-
-60-
0.1 -
-80-
0-
0
5
15
10
100-Trial Block #
-100
20
*
*
±
-40-
*
*
0
5
+
15
10
100-Trial Block #
20
200
1
*
0.9
-
0.8
**
*
180
**
*
*
*
160
*
140
0.7
"
*
-120
0.6
0.5
C,)
X
0.4
*
*
0.2
40
0.1
20
5
15
10
100-Trial Block #
20
*
*
80
60
0
*
100
0.3
0
*
-
0
0
*
5
*
*
15
10
100-Trial Block #
20
Fig. A- 2
44
S4
100-
1 -
0.9-
80-
0.8-
60-
*
*
40-
0.7**
0.6-
*
U
0
U)
*
*
20
S**
+
±
05
*
0-
0
U
0
0.4-
C
-20-
0.3-
-40-
0.2-
-60
0.1 -
-80-
00
5
10
15
100-Trial Block #
20
**
-100
-
0
5
10
15
100-Trial Block #
20
200
1
*
*
0.9
*
****
180
+*
*
0.8
160
0.7
140
0.6
-120
-
100
"0.5
*
0.4
0: 80
0.3
60
0.2 [
40
0.1
20
*
*
*
*
0
-
0
''
5
10
15
100-Trial Block #
20
*
*
**
0
5
*
15
10
100-Trial Block #
20
Fig. A- 3
45
S5
1 -
100-
0.9-
80-
0.8-
60-
0.7-
40-
*
+
0.6 -*
20-
CL
"0.5 -
*
*
*
0-
*
+*
*
*
-4*
0.4 -
4'
*
-20-
0.3-
-40-
0.2
-60
0.1 -
-80-
00
10
5
15
20
-100
*
*
-
0
5
1 00-Trial Block #
*
*
*
0.80.7-
"::
20
200-
1 -
0.9-
10
15
1 00-Trial Block #
*
180-
*
*
160140-
+
0.6-
120 -
0.5-
100
*
*
4-
& 80-
0.4-
*
*
**
*
*
0.3-
60-
0.2-
40-
0.1 -
20-
00
5
15
10
100-Trial Block #
20
0
0
5
15
10
100-Trial Block#
20
Fig. A- 4
46
S1
Condition: A
SNR:12 (dB)
SNR:8 (dB)
SNR:4 (dB)
600
600
600
G400
-X 400
400
200
200
200
0
0
0
!
t0 Z -200
-- 200
-600
o-400
-400
S-400
-500
0
Actual
500
-600
-500
ITD (psec)
SNR:0 (dB)
0
500
Actual ITD (psec)
-600
SNR:-4 (dB)
SNR:-8 (dB)
400
400
400
200
200
200
0
0
0
t-200
-200
t; -200
.
400
40
0
Actual
500
ITD (psec)
-600
500
ITD (psec)
600
600
0-400
0
Actual
600
-600--500
-500
-500
0
Actual ITD (psec)
500
-600
-500
0
Actual
500
ITD (psec)
SNR:-12 (dB)
600
400
200
0
-
S-200
-400
-600
-500
0
Actual
500
ITD (psec)
Fig. A- 5
47
S1
Condition: A'
SNR:8 (dB)
SNR:12 (dB)
600
''400
'>
SNR:4 (dB)
600
600
400
Z.>400
00 200
200
0.
0.
0
-200
200
-200
-400
-400
-600
-500
0
-400
-600
500
-500
ITD (psec)
Actual
-600
0
500
Actual ITD (psec)
-500
SNR:0 (dB)
600
600
o 400
400
200
SNR:-8 (dB)
200
0
0
-
0
500
Actual ITD (jisec)
4)
Z -200
-o400
-600
.
-500
.
'D-400
-6001
-500
0
500
Actual ITD (psec)
SNR:-12 (dB)
SNR:-16 (dB)
600
600
o400
400
4)200
200
0
0
- -200
-200.
o-
0-400
-600
-500
0
500
Actual ITD (psec)
0
500
Actual ITD (psec)
........
400
-600
-500
0
Actual
500
ITD (psec)
Fig. A- 6
48
S1
Condition: B
SNR:4 (dB)
SNR:8 (dB)
SNR:12 (dB)
600
600
U400
400
600
400
200
200
200
00
-
0
-400
-600
500
0
-500
Actual
ITD (psec)
0
.-
200
4
.o-400*
-600
500
0
-500
Actual ITD (isec)
400
0-200 .
-200
-600
-500
SNR:-8 (dB)
SNR:-4 (dB)
600
600
...
400
'
-
Z 400
200
200
0
z
.~
m 200
-400
-400
*
-500
500
0
Actual ITD (isec)
0
-500
Actual
500
ITD (psec)
600
400 -
400
20 0.
000
.
.
0
. .
0
. .
.
-
U-200
Z -200
0-
0-400
40 0
-600
-600
SNR:-16 (dB)
SNR:-12 (dB)
600
9
0
.
-200
-600
500
0
Actual ITD (psec)
0
-500
Actual
ITD (psec)
500
-600
-
--
0
-500
Actual
500
ITD (psec)
Fig. A- 7
49
S1 Condition: B'
SNR:8 (dB)
SNR:12 (dB)
SNR:4 (dB)
600
600
600
400
400
400
200
200
200
0
.
-200 -
o-
40 0
-600
..
.'0.
.
0-
.
.
-500
0
500
0
-
-200
-400
-400
-600
-500
Actual ITD (psec)
*0
-
~
400
400
.
S-400 -.
0
-500
Actual
0
200
0.*
-~
--
-200.-200
*-200
-600
600
200
500
ITD (psec)
SNR:-8 (dB)
600
0
0
0
Actual
200
200
t=
-500
SNR:-4 (dB)
.
400
0
-600
500
Actual ITD (psec)
SNR:0 (dB)
600
0
.500
ITD (psec)
400
-400
..
-600"-500
0
Actual
lTD (psec)
500
-600-500
0
Actual
500
ITD (psec)
SNR:-12 (dB)
600
'400
200
0
-200
c -400
-600
0
-500
Actual
500
ITD (psec)
Fig. A- 8
50
S1 Condition: C
SNR:4 (dB)
SNR:8 (dB)
SNR:12 (dB)
600
600
600
400
Z' 400
.400
200
200
200
0
0
0
-200
-400
-600
-400.
. ..
-500
-200
*
*-200
0
-600
500
....-
400
-500
Actual ITD (psec)
0
500
SNR:0 (dB)
SNR:-4 (dB)
600
400
400
200
00
200
-200-.
0
500
Actual ITD (jpsec)
SNR:-8 (dB)
600
400
*
*
.- 200
. . . . .
. t -200.
-400
0-4
200
-500
-500
Actual ITD (psec)
600
-600
-600
0
-600
500
-500
0
500
Actual ITD (psec)
Actual ITD (psec)
-600
-500
0
500
Actual ITD (Jsec)
SNR:-16 (dB)
600
400
0
.200
V
-200
0
-400
-600
0
-500
Actual
500
ITID (psec)
Fig. A- 9
51
S2 Condition: A
600
600
400
400
400
200
200
200
0
0
0
t 0
0-200
Z -200
C -400
8-400
-600'
-500
0
Actual
-600
500
0
'-200
/
-500
ITD (psec)
-400
500
0
Actual lTD (psec)
SNR:0 (dB)
4)
SNR:4 (dB)
SNR:8 (dB)
SNR:12 (dB)
600
-600
-500
500
0
Actual ITD (psec)
SNR:-4 (dB)
600
600
400
400
200
200
0
U)
0
I-
a)
C.)
-
0
V
-200
-200
4)
0-
0 -400
-600
.
-500
500
0
Actual ITD (psec)
40 0
-600
-500
SNR:-16 (dB)
SNR:-12 (dB)
600
600
**
400
400
200
200
0
0
-200
-200
is
0 -400
o- 4 00
C.)
4)
0
IV
4)
4)
-600
0
-500
Actual
500
0
Actual ITD (psec)
ITD (psec)
500
-600
-500
500
0
Actual ITD (jisec)
Fig. A- 10
52
S2 Condition: A'
600
400
400
7.1
4)
7.
7
-400
-600
0
-500
Actual
0
H
0
A'
-200
o
600
200
200
0
400
200
0.*
Z -200
V
4)
C.)
4)
-200
o -400
0
-400
-600
500
-500
ITD (pse c)
500
0
Actual ITD (isec)
-600
-500
0
500
Actual ITD (psec)
SNR:-8 (dB)
SNR:-4 (dB)
SNR:0 (dB)
600
600
600
'00
SNR:4 (dB)
SNR:8 (dB)
SNR:12 (dB)
600
400
400
200
200
A200
~200
00
-20020
4)4)4
-400.
v-400
-600
0
-500
Actual
-600
500
-500
0-400
0
500
Actual ITD (jisec)
ITD (psec)
-600
-500
500
0
Actual ITD (psec) -
SNR:-16 (dB)
600
400
0
200
H0'
z -200
S-400
-600
-500
500
0
Actual ITD (jpsec)
Fig. A- 11
53
S2 Condition: B
SNR:4 (dB)
SNR:8 (dB)
SNR:12 (dB)
600
600
600
400
400
400
200
200
0
0
1-200
Z-200
200
-600
~-400
0
-500
Actual
-600
500
-
..
0
-500
500
0
Actual ITD (psec)
-600
-500
'G
V
200
00
500
0
Actual ITD (jisec)
SNR:-8 (dB)
SNR:-4 (dB)
SNR:0 (dB)
400
x
Q
0,;-400
..
ITD (psec)
600
,7
-200
00
S-400
0
t
600
600
400
400
200
200
0
0
-200
3 -200
-200
-400
0 -400
-600
-400
'0
-600'
0
-500
500
Actual ITD (psec)
-500
500
0
Actual ITD (psec)
-600
-500
500
0
Actual ITD (psec)
SNR:-12 (dB)
600
400
~200.
..
20
..
-200..
0-400
-600
0
-500
Actual
500
ITD (psec)
Fig. A- 12
54
S2 Condition: B'
SNR:12 (dB)
'400
7.4
U
a)
200
S0
-200
-200
0-400
0-400
0
-500
Actual
ITD
0
I-
0
-
-600
600
Z'400
200
0
SNR:4 (dB)
SNR:8 (dB)
600
600
-600
500
400
200
x,.
0
G)
1:;a) -200
-is
0 -400
0
-500
Actual
(psec)
-600
500
-500
lTD (psec)
0
Actual
500
ITD (psec)
SNR:-8 (dB)
SNR:0 (dB)
600
600
400
400
200
200
0.
0
0-
-200
-200
0-400
c -400
-600-500
0
Actual
ITD
-600
500
600
400
400
200
200
0
200
F~
0.
500
0
0
-
-200
6-
0-400
-600
0
ITD (psec)
SNR:-16 (dB)
SNR:-12 (dB)
600
~-
-500
Actual
(ssec)
0
-500
Actual
ITD (psec)
500
40 0
-600
0
-500
Actual
500
lTD (psec)
Fig. A- 13
55
S2 Condition: C
SNR:8 (dB)
SNR:12 (dB)
600
7 -
'- 400
4)
74
Y.
200
0
0
4)
g
600
400
400
200
200
I*0
4)
-200
4)
4)
-600
-600
Actual
-200
-200
0 -400
500
0
ITD (psec)
0
.7
-400
-500
SNR:4 (dB)
600
-400,;
-500
0
Actual
500
-600
SNR:-4 (dB)
SNR:0 (dB)
600
t 400
5400
400
200
200
200
0
0.
0
S-200
-200
0-2:-200
0-400:
-400
-400
0
-600
500
-500
Actual ITD (psec)
0
Actual
500
ITD (psec)
SNR:-8 (dB)
600
-500
0
Actual
600
-600
-500
ITD (psec)
500
ITD (psec)
-600
-500
0
Actual
ITD
500
(psec)
SNR:-16 (dB)
600
400
200.
(D
.........
0
-200
16-400
-600
-500
0
Actual
500
ITD (psec)
Fig. A- 14
56
S3 Condition: A
SNR:8 (dB)
SNR:12 (dB)
600
0
SNR:4 (dB)
600
600
7,
.7.
400
77...
200
400
200
.7.
-200
-600'
CD
-400,
-
500
0
-500
Actual
-600
-j
500
-
-200
500
-600
-500
ITD (psec)
0
500
Actual ITD (psec)
SNR:-8 (dB)
600
60C
.
200
40(
400
20C0
200
U,
0
.20C
0
-200
-600
.
0-
SNR:-4 (dB)
. . ,
400
a -400
0
Actual
SNR:0 (dB)
.
7.
9,
-400
ITD (psec)
600
/
-
-200
-400,
200
0
0
0
*
400
1..
-200
-20C
c-400C
.
-500
0
Actual
500
ITD (psec)
-60C
0-400
-500
0
Actual
ITD (psec)
500
-600
-500
0
500
Actual ITD (psec)
SNR:-12 (dB)
600
400
200
0
z-200
-400
-600
-500
0
Actual
500
ITD (psec)
Fig. A- 15
57
S3 Condition: A'
SNR:12 (dB)
SNR:8 (dB)
SNR:4 (dB)
600
600
'a'400
400
200
200
0
0
-200
-200
t;-200
-400
-4 0 0
V-400
-600
(D
0
-500
500
-600
600
'400
200
-500
Actual ITD (psec)
0
Actual
ITD
-600
500
-500
SNR:0 (dB)
400
5'400
A 200
200
0
-
-200
-400
0-400
0
Actual
-600
500
ITD (psec)
SNR:-12 (dB)
600-
400
400
200..
200
0
0
Z -200
-200
0-400
-400
-500
0
Actual
ITD (psec)
-500
0
500
Actual ITD (psec)
SNR:-16 (dB)
600.
-600
500
ITD (psec)
0
-200
-500
.
SNR:-8 (dB)
600
-600
0
Actual
(psec)
600
~~ 0.
. .
.
~
500
-600
-500
0
500
Actual ITD (ssec)
Fig. A- 16
58
S3 Condition: B
400
.7
7
200
7
0
.7,..
H
'7
7
.7.
-200
600
600
400
400
200
00
200
0
Actual
500
7
7
-400
-600" *
-500
C)-400
-600 1
-500
<
C)-400
200
-
0
0
-200
S400
o -400
-500
0
500
Actual ITD (psec)
-600'
500
SNR:-8 (dB)
U -200
-200
0
ITD (Asec)
400
200
0
'''
*
600
. 400
400
-600'
-500
Actual
600r
0
-600
SNR:-4 (dB)
SNR:0 (dB)
0
500
0
Actual ITD (psec)
600
,
-200
7
7.
ITD (Psec)
200
,*
0
.7.
-200
.7.
7,...
0-400
SNR:4 (dB)
SNR:8 (dB)
SNR:12 (dB)
600
-
0
-500
Actual
ITD (jpsec)
500
-600
-500
0
Actual
500
ITD (jisec)
SNR:-12 (dB)
600
400
200
0
-200
0-400
-600
0
-500
Actual
500
ITD (psec)
Fig. A- 17
59
S3 Condition: B'
SNR:4 (dB)
SNR:8 (dB)
SNR:12 (dB)
600
600
600
400
'&400
400
200
200
00
00200
0.
..
..
0
-- 200
U-200
.
.2
-200
-400
o-400
.
0-400.
-600
0
.
-500
Actual
-600
500
0
-500
ITD (psec)
0
Actual lTD (psec)
-600
500
-500
SNR:-4 (dB)
600
SNR:-8 (dB)
400
.
200
200
~
-o
-o
-400
-600
(D)
0 -400
-500
0
500
Actual lTD (psec)
400.
.
.
600
.
400
200- .
0
Z -200
Z -200
0
3 -400
0
-500
0
Actual
ITD (psec)
-500
0
500
Actual ITD (isec)
200
.....
0
-600
-600
SNR:-16 (dB)
SNR:-12 (dB)
600
0
-200
0 -200
0
500
ITD (psec)
600
*
400
0
Actual
500
-400
-600
-500
0
Actual
lTD (psec)
500
Fig. A- 18
60
S3 Condition: C
SNR:8 (dB)
SNR:12 (dB)
600
600
400
t3 400
200
200
0
0
-200
-200
C-400
o-400
-600
Actual
ITD
-600
500
0
-500
-500
0
Actual
(psec)
ITD
500
(psec)
SNR:-4 (dB)
SNR:0 (dB)
SNR:-8 (dB)
600
600
400
400
200
200
200
0
0
0
-200
-200.
-200
-400
0-400.-.
600
400
-600
'
-500
0
Actual
-600
500
00-400
-500
ITD (psec)
0
Actual
SNR:-12 (dB)
500
ITD (jisec)
-600
-500
0
500
Actual ITD (psec)
SNR:-16 (dB)
600
600
' 400
400
200
200
0
0
-200
(D)
-400
0-400
-600
-200
-500
0
Actual
ITD (psec)
500
-600
-500
0
Actual
ITD
500
(psec)
Fig. A- 19
61
S3' Condition: A
SNR:12 (dB)
600
'' 400
200
0
Z-200
S-400
-600"
-500
0
500
Actual ITD (psec)
Fig. A- 20
62
S3' Condition: A'
600
'& 400
400
200
600
1'''400
200
200
I-
...
-~*0 0
-
0
-200
-200
0-400
400
-
-600
SNR:4 (dB)
SNR:8 (dB)
SNR:12 (dB)
600
Actual
7
-- 7.
ITID (psec)
0
Actual
SNR:O (dB)
ITD
- 0 .
SNR:-8 (dB)
-400
200
0
0-
-200
-200
0 -400
-400
0
Actual
ITID
-600
500
0
500
Actual ITD (jusec)
600
200
200
-500
*
-500
SNR:-4 (dB)
400
--
7
(jisec)
600
600
-600
-200
-600
500
'7.
0
o -400
.7
-600' - *
-500
500
0
500
-oo
.7.
-200
aD-
-500
0
Actual
(psec)
500
ITD (psec)
400
-600
-500
0
Actual
500
ITD (psec)
SNR:-16 (dB)
600
400
H
200 .
0
c. -200
-400
-600
-500
0
Actual
500
ITD (psec)
Fig. A- 21
63
S3' Condition: B'
600
400
400
200
200
-200
t
-500
0
-200
o
-400
-600-
0
500
Actual ITD (psec)
-
-500
-500
0
500
Actual ITD (psec)
400
C.)
U)
200
200
0
I-
0.
0
-o
a)
-200
C.)
U)
V
o-400
0
-500
0
0.
-200
-400
-600
500
-500
Actual ITD (psec)
0
500
Actual ITD (Jusec)
SNR:-16 (dB)
SNR:-12 (dB)
600
600
-
400-
.. 400
.
.
200-
2000
0.
-200
0 -400-600
-600
600
' 400
-600
500
0
Actual ITD (psec)
-400
SNR:-4 (dB)
SNR:0 (dB)
600
-
400
200
-200
CD
-400
-600
600
0.
0-
0
SNR:4 (dB)
SNR:8 (dB)
SNR:12 (dB)
600
-200
o -400
500
0
Actual
ITD (psec)
500
-600' -500
0
500
Actual ITD (psec)
Fig. A- 22
64
S3' Condition: C
SNR:8 (dB)
SNR:12 (dB)
600
-7
400
SNR:4 (dB)
600
600
'& 400
- 400
200
200-
200
0
7-
0
4,
7
-200
7
y'.
-400-600'-
-
0
-200
-400
-400
Actual
ITD
-6001
-500
500
0
Actual
(psec)
.7.
.7
0
6-200
0
-500
.7.
-7.
7
-6001
-500
500
ITID (psec)
SNR:-4 (dB)
SNR:0 (dB)
600
400
S.
200
0
S~
.
0
500
Actual ITID (psec)
SNR:-8 (dB)
600
600
400
400
200
200
0
-
-200
'5 -200
0
-200
-400
| -400
~ 400
; ;.......
-4
-600' -500
0
500
-6001
-500
'
0
Actual lTD (psec)
Actual ITD (psec)
'
500
-600
-
-500
0
Actual
500
ITD (psec)
SNR:-12 (dB)
600
400
200
0
* ..............
.
.
.
S-200
| -400
-600
500
0
Actual
500
ITD (psec)
Fig. A- 23
65
S4
Condition: A
SNR:12 (dB)
t
SNR:8 (dB)
SNR:4 (dB)
600
600
600
400
400
400
200
200
200
0
0
0-200
-200
o -400
0 -400
0
0
-200
-9-
*
0
-400
-600
-500
0
Actual
500
-600 L
-500
ITD ( isec)
0
Actual
500
-600
SNR:-8 (dB)
600
600
400
400
'G 400
200
200
0
200
0
-~
0.
t-200
-200
'D-400
6 -400
-600
-500
0
0
500
Actual ITD (pusec)
SNR:-4 (dB)
SNR:0 (dB)
600
~ 0.
-500
ITD (psec)
500
-600-500
0~~
-200
0-400
0
Actual ITD (psec)
Actual ITD (psec)
9-.--
0
500
-600
-500
0
500
Actual ITD (psec)
SNR:-12 (dB)
600
400
200
S-200
o -400
-600
-500
0
Actual
500
ITD (psec)
Fig. A- 24
66
S4 Condition: A'
SNR:12 (dB)
SNR:4 (dB)
SNR:8 (dB)
600
600
600
400
400
400
200
200..
200
.- '
0.''''
0.
0
-200
Z -200
0-200'
-400
-400
-400
-600
-600
-500
0
Actual
-600-500
500
ITD (psec)
500
0
Actual
SNR:0 (dB)
600
400
400
200
S200
0
.
-
0
-200
-200
o -400
0 -400
-600
-600'
0
-500
Actual
500
ITD (psec)
600
400200
*
.
0
0
Z -200
Z -200
o -400
-600
0 -400
-600
0
ITD (psec)
500
0
Actual ITD (psec)
500
*
*
*
* .
.
*0
200
0
Actual
-500
............
''400
-500
.*
SNR:-16 (dB)
SNR:-12 (dB)
600'
0
500
Actual ITD (psec)
SNR:-8 (dB)
600
S
-500
ITD (psec)
-500
500
0
Actual ITD (psec)
Fig. A- 25
67
S4 Condition: B
600
600
400
400
c(D 400
200
200
200
0
0
-200
-200
-200
-400.
o -400
o -400
0.
U
4)
4)
0
SNR:4 (dB)
SNR:8 (dB)
SNR:12 (dB)
600
-600
-7
-500
0
Actual
-600 L
-500
500
ITD (psec)
Actual
-600-500
500
ITD (psec)
600
400
~~0)
C.)
600
400f
C.)
4)
(h
200
200 .
*
0
~
V
4)
y-200
C.)
0)
0-400
0
-500
0
500
0
I-
0
V
4)
-200
C.)
4)
-400
0
-600 '
-500
0
Actual
Actual ITO (psec)
0
500
Actual ITD (psec)
SNR:-8 (dB)
SNR:-4 (dB)
SNR:0 (dB)
600
-600
0
ITD (psec)
500
400
200
0
-200
-400
-600'
-500
0
500
Actual ITO (psec)
SNR:-12 (dB)
600
400
200
0
*
..
.....
*..*
-200
0-400
-600
0
-500
Actual
500
ITD (psec)
Fig. A- 26
68
S4 Condition: C
SNR:8 (dB)
SNR:12 (dB)
t
600
600
400
400
200
0.
200
0
0
-200
(4
) -400
-200
o -400
600
0
-500
Actual
-600
500
-500
ITD (psec)
SNR:0 (dB)
500
0
Actual lTD (psec)
SNR:-4 (dB)
SNR:-8 (dB)
600
600
600
400
-. 400
400
200
200
200
0
0-
-200
-200
-200
l -400
0*-400
g
0-400
-600-500
0
Actual
ITD
-600 L
500
-5
500
600
400
400
200
- 200
F- -****** *0 **;-*.*.
** **
S
0-200
-400
o -400
0
Actual
ITD
500
(psec)
(psec)
-600
-500
0
500
Actual ITD (psec)
0
-200
-500
lTD
500
SNR:-16 (dB)
SNR:-12 (dB)
-600
0
Actual
(psec)
600
0
0
*------------------
-600
-5
**
*9
*.....O
0
500
Actual
500
lTD (pusec)
Fig. A- 27
69
S5 Condition: A
SNR:8 (dB)
SNR:12 (dB)
SNR:4 (dB)
600
600
600
400
400
400
200
200
200
0
-200 .
-200
0-200:
o -400
-600
0
4
S-400
-500
-600
500
0
-500
ITD (psec)
Actual
S-400
.
0
Actual lTD (psec)
500
-600
SNR:-4 (dB)
SNR:0 (dB)
600
600
400
400
3' 400
200
200
''
00
.
-200
.
.
.
.
.
-200 -400
-400
-400
-500
0
Actual
500
-600-500
ITD (gsec)
0
Actual
500
ITD (psec)
-600
-500
0
Actual
500
ITD (pisec)
SNR:-16 (dB)
SNR:-12 (dB)
600
600
400 a(D
200
400
200
0
0
-200
-200........
0 -400
0-400
-600
.
0
Q
-600
0
F-
z -200
.
0
500
Actual ITD (psec)
SNR:-8 (dB)
600
200
-500
-500
0
Actual
ITD (psec)
500
-600
-500
0
Actual
500
ITD (psec)
Fig. A- 28
70
S5 Condition: A'
SNR:4 (dB)
SNR:8 (dB)
SNR:12 (dB)
600
600
600
400
400
c3 400
200
200
200
0.
0.
0
o-200
Z -200
Z -200
-400-
-400
-400
(D
-600
600
-n
500
0
500
500
Actual ITD (psec)
0
Actual
ITD (psec)
-
400
200
0.
600
400
400
200
200
00
0
~
0
tS -200
-200
u-200
-400
oD-400
0-400
-600'
-500
Actual
-600
-600
500
0
500
0
SNR:-12 (dB)
0
Actual
500
ITD (psec)
SNR:-16 (dB)
400
,
200.
'
.
200
.
. . . . . .
.
.
0.
0
-200
o -200
16
o -400
0-400-
-600
-500
600
600400
500
Actual ITD (psec)
ITD (psec)
500
ITD (psec)
SNR:-8 (dB)
600
~~
0
Actual
SNR:-4 (dB)
SNR:0 (dB)
600
~
-600L
-500
500
-500
0
Actual
ITD
500
(isec)
-600
-j
500
0
500
Actual ITD (psec)
Fig. A- 29
71
S5 Condition: B
SNR:12 (dB)
4)
400
200
-~
~0
SNR:4 (dB)
SNR:8 (dB)
600
600
*
400
400
.
200
600
..
200
.7,
0
0
1 -200
* -200
o -400
-400
-600 I
0
-500
~
A
0-400
-500
Actual ITD (gsec)
500
0
Actual
SNR:0 (dB)
0
-200
'A
-Ann L
500
*
-600
SNR:-4 (dB)
600
600
400
a 400
400
=L 200
1 200
A 200
0--o--o
z-200 .....
-00
0
Z-200.
-200
0-400
-400
0-400
-600
-600
0
Actual
500
0
500
Actual ITID (jisec)
SNR:-8 (dB)
600
-500
-500
ITID (psec)
ITD (psec)
500
0
-500
Actual
ITD
(psec)
-600
-500
0
500
Actual ITD (psec)
SNR:-16 (dB)
SNR:-12 (dB)
600
600
-a
400
(D
200
40C
20C
S0
-200
t -20C
0-400
-600'
-40C
500
0
Actual
ITD (psec)
500
-600
0
-500
Actual
500
ITD (psec)
Fig. A- 30
72
S5 Condition: B'
SNR:12 (dB)
SNR:8 (dB)
SNR:4 (dB)
600
600
600
400
400
400
200
200
200
_
'
.
0
0
..-..
*
t-200
0-400
-600
-500
0
Actual
500
.
.
.
4)
.
-200
0-400
-400
-600
0
-500
ITD (gsec)
Actual
SNR:0 (dB)
.
-200
500
-600
-500
ITD (psec)
SNR:-4 (dB)
0
500
Actual [TD (psec)
SNR:-8 (dB)
60C
600
6400
-400
200
0--
-200
400
200
200
0
-20(
-
200
-40C
-400
-600
-040C
-500
0
500
-600
-500
Actual ITD (psec)
0
500
Actual ITD (psec)
SNR:-12 (dB)
-600
-500
0
Actual
500
ITD (psec)
SNR:-16 (dB)
600
600
400:
400
200
200
~
.-
0-400
00
0
-200
Z -200
-400
o-400
-600'
-500
0
Actual
ITD (psec)
500
-600 L
-500
0
Actual
500
ITD (jisec)
Fig. A- 31
73
S5 Condition: C
SNR:12 (dB)
SNR:8 (dB)
600
400
U
a)
200
~
0
0
H
*
0
-200
400
G' 400
-500
0
200
200
~I0
1-
0.
0
-200
-200
0 -400
o -400
a)
a)
-400
-600'
600
V
a)
SNR:4 (dB)
600
-600--500
500
0
500
-600
SNR:-4 (dB)
SNR:0 (dB)
400
400
5' 400
200
200
0 200
600
-=-0
-'~0
-200
V
0-400
-200,
z -200
-400
i-400
LAn0
0
Actual
500
0
-600L -500
500
Actual ITD (jsec)
ITD (psec)
-600
-500
0
Actual
ITD
500
(psec)
SNR:-16 (dB)
SNR:-12 (dB)
OWU
600
400
400
200
200
0
0
*
0
0
9
0
00*.
0
-200
0 -200
o-400
6 -400
-r0An
500
ITD (pusec)
SNR:-8 (dB)
600
0.
0
Actual
600
-500
-500
Actual lTD (jisec)
Actual ITD (psec)
'
'
-500
0
Actual
ITD (psec)
'
500
-600L
-500
*
.0.90
0
Actual
500
ITD (jisec)
Fig. A- 32
74
SI
Jammer Condition: A
Jammer Condition: B
Jammer Condition: A'
*
*
1I
-
0.9
0.9.
0.9-
0.8-
0.8
0.8-
0.7/
cr0.6
0.6 -
/
0.6
_0
(D
N
0.5
0.5-
z 0.5
N
0.4
z0.4-
0.4-
0.30.2-
/
0.1
0
-20
0
20
4
/
0.3
0.3
0.2 -
0.2 -
0.1 -
0.1
-20
'
0
20
-20
0
20
SNR (dB)
SNR (dB)
SNR (dB)
Jammer Condition: C
Jammer Condition: B'
-
1-
0.9-
0.9-
0.8-
0.8-
0.7-
0.7
c 0.6 -
+ *
0.6 -
0.5
10.5 -*
90.4-
-
z90.4 -
0.3-
0.3-
0.2-
0.2-
0.11
0.1
0
-20
/
0.7
0.7 -
0
SNR (dB)
2C
0
-20
0
SNR (dB)
20
Fig. A- 33
75
S3
Jammer Condition: A
1 -
Jammer Condition: B
Jammer Condition: A'
*
1
0.9-
0.9-
0.9-
0.8-
0.8-
0.8 -
0.7-
0.7-
0.7 -
a 0.6 -
W-0.6 -
0.6 -
0.5
0.4
ca=0.5
90.4 -
z 0.4
0.3 -
0.3-
0.3
0.2-
0.2-
0.2-
0.1 -
0.1 -
0.1 -
0
+
0
-20
2C
0
-20
Jammer Condition: B'
1-
0.9-
0.9-
0.8-
0.8-
0.7-
0.6 -
M 0.6-
0.5 -
N 0.5 -
/
0
-20
+
0
20
SNR (dB)
Jammer Condition: C
0.7
*
90.4
20
SNR (dB)
SNR (dB)
1
0
*
*
0.4 -
0.3-
0.3 -
0.2-
0.2 0.1 -
0.1 *
0
-20
0
SNR (dB)
20
0.
-20
0
SNR (dB)
20
Fig. A- 34
76
S4
Jammer Condition: A
4 A
A
Jammer Condition: A'
Jammer Condition: B
* * *
f
1-
1-
0.9
0.9-
0.9-
0.8
0.8-
0.8 -
0.7
0.7-
0.7
0.6 -
0.6
w0.6 -
1
N0.5
0.5 -
-0.5
g 0.4-
z
-
z 04
04
-
+
9 0.4
0.3 -
0.3-
0.3-
0.2 -
0.2-
0.2 -
0.1 -
0.1 -
0.1 -
0
-20
0
20
0-20
0
20
SNR (dB)
1
0.9-
0.9-
0.8 -
0.8-
1*
0.7
0.7
r0.6 -
0.6
0.5 -
0.5-
/
90.4z
O'-z
0.4-
/
0.3
0.30.2-
0.2-
01
0
-20
Jammer Condition: C
Jammer Condition: B'
1 -
-20
20
SNR (dB)
SNR (dB)
0.1 -
0
0.1 -
,
'A'
0
SNR (dB)
20
0
-20
0
SNR (dB)
20
Fig. A- 35
77
S5
Jammer Condition: A
1
*
Jammer Condition: A'
1
*
N
Jammer Condition: B
1 -
*4-4--+---
*
0.9
0.9-
0.9
0.8-
0.8-
0.8
0.7-
0.7-
0.7
0.6
0.6-
0.6
N
0.5
0.5
+
-
0.4-
z90.4
04
0.3
0.3-
0.3
0.2
0.2-
0.2
0-1
0.1 -
0.1
-*
20
0
-20
0-20
0
Jammer Condition: B'
1
20
SNR (dB)
SNR (dB)
1-
*
0.9 -1*
0.9-
0.8-
0.8-
0.7 -
0.7-
4
/
0.5
,
0.4
0
/ m
-
0
-2 0
K
0
20
SNR (dB)
Jammer Condition: C
C'4
0.6
or0.6 -
1
0.5-
0.5 -
ca
90.4-
z 0.4-
z -
0.3-
0.3-
0.2-
0.2-
0.1 -
0.1 -
0
-20
0
SNR (dB)
20
0
-20
+
0
20
SNR (dB)
Fig. A- 36
78
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79