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This is to certify that the
dissertation entitled

THE USE OF INTERAURAL PARAMETERS DURING
INCOHERENCE DETECTION IN REPRODUCIBLE NOISE

presented by

MATTHEW JOSEPH GOUPELL

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THE USE OF INTERAURAL PARAMETERS DURING INCOHERENCE
DETECTION IN REPRODUCIBLE NOISE

By

Matthew Joseph Goupell

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the requirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Physics and Astronomy

2005

ABSTRACT

THE USE OF INTERAURAL PARAMETERS DURING INCOHEREN CE
DETECTION IN REPRODUCIBLE NOISE

By

Matthew Joseph Goupell

Interaural incoherence is a measure of the dissimilarity of the signals in the left
and right ears. It is important in a number of acoustical phenomenon such as a
listener’s sensation envelopment and apparent source width in room acoustics, speech
intelligibility, and binaural release from energetic masking. Humans are incredibly
sensitive to the difference between perfectly coherent and slightly incoherent signals,
however the nature of this sensitivity is not well understood. The purpose of this
dissertation is to understand what parameters are important to incoherence detection.
Incoherence is perceived to have time-varying characteristics. It is conjectured that
incoherence detection is performed by a process that takes this time dependency into
account.

Left-ear—right-ear noise-pairs were generated, all with a fixed value of interaural
coherence, 0.9922. The noises had a center frequency of 500 Hz, a bandwidth of
14 Hz, and a duration of 500 ms. Listeners were required to discriminate between
these slightly incoherent noises and diotic noises, with a coherence of 1.0. It was
found that the value of interaural incoherence itself was an inadequate predictor
of discrimination. Instead, incoherence was much more readily detected for those
noise-pairs with the largest fluctuations in interaural phase and level differences (as
measured by the standard deviation). N oise—pairs with the same value of coherence,
and geometric mean frequency of 500 Hz were also generated for bandwidths of 108 Hz
and 2394 Hz. It was found that for increasing bandwidth, fluctuations in interaural
differences varied less between different noise—pairs and that detection performance

varied less as well. The results suggest that incoherence detection is based on the size

and the speed of interaural fluctuations and that the value of coherence itself predicts
performance only in the wide-band limit where different particular noises with the
same incoherence have similar fluctuations.

Noise-pairs with short durations of 100, 50, and 25 ms, and bandwidth of 14 Hz,
and a coherence of 0.9922 were used to test if a short-term incoherence function is
used in incoherence detection. It was found that listeners could significantly use fluc-
tuations of phase and level to detect incoherence for all three of these short durations.
Therefore, a short-term coherence function is not used to detect incoherence. For the
smallest duration of 25 ms, listeners’ detection cue sometimes changed from a “width”
cue to a lateralization cue.

Modeling of the data was performed. Ten different binaural models were tested
against detection data for 14—Hz and 108-Hz bandwidths. These models included dif-
ferent types of binaural processing: independent interaural phase and level differences,
lateral position, and short-term cross-correlation. Several preprocessing features were
incorporated in the models: compression, temporal averaging, and envelope weight-
ing. For the 14-Hz bandwidth data, the most successful model assumed independent
centers for interaural phase and interaural level processing, and this model correlated
with detectability at r = 0.87. That model also described the data best when it
was assumed that interaural phase fluctuations and interaural level fluctuations con-
tribute approximately equally to incoherence detection. For the 108-Hz bandwidth
data, detection performance varied much less among different waveforms, and the

data were less able to distinguish between models.

This work is dedicated to my amazing wife Sarah and loving family.

iv

ACKNOWLEDGEMENTS

Along my long road of schooling, I have had many mentors. I might have become
a biologist, chemist, or mathematician if it had not been for my high school physics
teacher. Jim Gormley opened my eyes to the world of physics and I am truly grateful
to him for that.

Most memorable of my mentors were my professors at Hope College, who allowed
my mind to open to the love of learning. They helped me stay on track with my
studies, like Dr. Paul DeYoung. They gave me encouragement when I was down, like
Dr. Graham Peaslee. They gave me higher goals to strive for, like Dr. Cathy Mader.
They were good friends, like Dr. Tim Pennings.

At Michigan State University, I have received as much support as I could hope for
during graduate school. My advisor, Dr. William Hartmann, has been very influential
in my personal work ethic, my scholarly preparation, and my newly-acquired love for
the field of psychoacoustics. If nothing else, I think he and I were the perfect match
for advisor and student.

I would also like to acknowledge Dr. Steve Colburn, Dr. Nat Durlach, and Dr.
Brad Rakerd for providing invaluable insights that I used to complete this work. Dr.
Hayder Radha and Dr. Karim Oweiss also deserve mention for our discussions on
stochastic systems and signal detection theory, topics that I have found very useful

in my dissertation.

TABLE OF CONTENTS

LIST OF TABLES ....................................................................................... viii
LIST OF FIGURES ..................................................................................... x
KEY TO SYMBOLS .................................................................................... xiii
KEY TO ABBREVIATIONS ....................................................................... xvi
INTRODUCTION ........................................................................................ 1

1. INCOHERENCE AND FLUCTUATIONS OF INTERAURAL
PARAMETERS

1.1 Experiment 1: Narrow Bandwidth .................................................... 13
1.2 Experiment 2: Critical Bandwidth .................................................... 35
1.3 Experiment 3: Wide Bandwidth ....................................................... 44
1.4 Experiment 4: The Role of Bandwidth ............................................. 53
1.5 Experiment 5: The Effect of Monaural Cues .................................... 63
1.6 Discussion and Conclusion ................................................................ 68

2. FLUCTUATIONS WITH VARIED COHERENCE

2.1 Experiment 6: Narrow Bandwidth .................................................... 76
2.2 Experiment 7A: Critical Bandwidth ................................................. 81
2.3 Experiment 7B: Critical Bandwidth - Temporal Averaging ............. 88
2.4 Experiment 7C: Critical Bandwidth — TI Trading ............................ 92
2.5 Experiment 8: Wide Bandwidth ....................................................... 95
2.6 Experiment 9: The Role of Bandwidth ............................................. 98
2.7 Experiment 10: The Effect of Monaural Cues .................................. 106
2.8 Experiment 11: Contextual Effects ................................................... 109
2.9 Conclusion ......................................................................................... 115

3. EFFECTS OF DURATION ON INCOHERENCE DETECTION
3.1 Experiment 12: Narrow Bandwidth......, ........................................... 116

vi

4. BINAURAL MODELING: FIXED COHERENCE

4.1 Experiment 13: Narrow Bandwidth .................................................. 134
4.2 Models for Incoherence Detection ..................................................... 136
4.3 Experiment 14: Critical Bandwidth .................................................. 158
4.4 Multiple Parameter Model ................................................................ 172
4.5 Discussion and Conclusion ................................................................ 173

5. BINAURAL MODELING: VARIED COHERENCE

5.1 Experiment 15: Narrow Bandwidth .................................................. 177
5.2 Models for Incoherence Detection ..................................................... 179
5.3 Experiment 16: Critical Bandwidth .................................................. 190
5.4 Conclusion ......................................................................................... 208

6. PROBING MODELS WITH SELECTED NOISE—PAIRS

6.1 Experiment 17: Minimum Fluctuation Sets ...................................... 209
6.2 Experiment 18: Addition and Cancellation Sets ............................... 220
7. CONCLUSIONS ..................................................................................... 225
APPENDICES ............................................................................................ 229
BIBLIOGRAPHY ....................................................................................... 257

vii

LIST OF TABLES

Chapter 1

Table 1: Signal structure percentages ............................................................ 19
Table 2: 14—Hz p-values ................................................................................. 26
Table 3: 14-Hz listener correlations, phase set .............................................. 31
Table 4: 14-Hz listener correlations, level set ................................................ 32
Table 5: 108-Hz p-values ............................................................................... 42
Table 6: 108-Hz listener correlations, phase set ............................................ 42
Table 7: 108-Hz listener correlations, level set .............................................. 43
Table 8: 2394-Hz p—values ............................................................................. 50
Table 9: 2394—Hz listener correlations, phase set .......................................... 50
Table 10: 2394-Hz listener correlations, level set .......................................... 51
Table 11: Matched p-values .......................................................................... 55
Table 12: Matched listener correlations, phase set ....................................... 60
Table 13: Matched listener correlations, level set ......................................... 61
Chapter 2

Table 14: l4-Hz p-values .............................................................................. 80
Table 15: 14-Hz fixed vs. varied coherence .................................................. 80
Table 16: 136-Hz p-values ............................................................................ 86
Table 17: 136-Hz fixed vs. varied coherence ................................................ 87
Table 18: 136-Hz p-values — temporal averaging ......................................... 91
Table 19: 136-Hz p-values — TI trading ....................................................... 94
Table 20: 2394-Hz p—values .......................................................................... 97
Table 21: 2394-Hz fixed vs. varied coherence .............................................. 97
Table 22: Matched p-values ......................................................................... 100
Table 23: Matched fixed vs. varied coherence ............................................. 105
Chapter 3

Table 24: Moments and correlation for short-duration noise-pairs .............. 121
Table 25: Short-duration p-values ................................................................ 128

viii

Chapter
Table 26:
Table 27:
Table 28:
Table 29:

Chapter
Table 30:
Table 31:
Table 32:
Table 33:
Table 34:
Table 35:
Table 36:
Table 37:

Chapter
Table 38:
Table 39:
Table 40:

4

14—Hz free parameter values PC ..................................................... 152
14-Hz free parameter values CAS ................................................. 153
108-Hz free parameter values PC ................................................... 165
108-Hz free parameter values CAS ................................................ 166
5

14-Hz free parameter values Pc ..................................................... 185
14-Hz free parameter values CAS ................................................. 186
136-Hz free parameter values PC — independent center ................. 199
136-Hz free parameter values GAS — independent center ............. 200
136-Hz free parameter values PC — lateral position ....................... 203
136—Hz free parameter values CAS' - lateral position ................... 204
136-Hz free parameter values PC — STCC ..................................... 205
136-Hz free parameter values CA3 — STCC ................................. 206
6

Minimum level fluctuation set ....................................................... 213
Minimum phase fluctuation set ..................................................... 214
Effectiveness of preprocessing ....................................................... 218

ix

LIST OF FIGURES

Introduction

Figure 1: Jeffress coincidence matrix .............................................................
Figure 2: Incoherence perception ...................................................................

Chapter
Figure 3:

Figure 4:

Figure 5:

Figure 6:

Figure 7:

Figure 8:

Figure 9:

Figure 10:
Figure 11:
Figure 12:
Figure 13:
Figure 14:
Figure 15:
Figure 16:
Figure 17:
Figure 18:
Figure 19:
Figure 20:
Figure 21:
Figure 22:
Figure 23:
Figure 24:
Figure 25:
Figure 26:
Figure 27 :
Figure 28:

1
Frequency shaping .........................................................................
Temporal shaping ..........................................................................
14-Hz interaural parameters vs. time ............................................
14-Hz st[A<I>] vs. st[AL] ................................................................
Three-interval sequence .................................................................
Response box .................................................................................
14 Hz, PC, Phase set ....................................................................
14 Hz, CAS, Phase set ................................................................
14 Hz, PC, Level set .....................................................................
14 Hz, CAS, Level set .................................................................
Signals .........................................................................................
108-Hz interaural parameters vs. time ........................................
108-Hz st[A<I>] vs. st[AL] ............................................................
108 Hz, PC, Phase set ..................................................................
108 Hz, GAS, Phase set ..............................................................
108 Hz, PC, Level set ...................................................................
108 Hz, CAS, Level set ...............................................................
2394-Hz interaural parameters vs. time ......................................
2394-Hz st[A<I>] vs. st[AL] ..........................................................
2394 Hz, PC, Phase set ................................................................
2394 Hz, CAS, Phase set ............................................................
2394 Hz, PC, Level set .................................................................
2394 Hz, CA5, Level set .............................................................
Matched st[A<I>] vs. MAL] .........................................................
PC, Matched phase set ................................................................
CA5, Matched phase set ............................................................

6
7

15
17
19
21
23
24
27
28
29
30
34
36
37
38
39
40
41
44
45
46
47
48
49
53
56
57

Figure 29
Figure 30

Figure 31
Figure 32

Chapter

Figure 33:
Figure 34:
Figure 35:
Figure 36:
Figure 37:
Figure 38:
Figure 39:
Figure 40:
Figure 41:
Figure 42:
Figure 43:
Figure 44:
Figure 45:
Figure 46:
Figure 47:
Figure 48:
Figure 49:
Figure 50:
Figure 51:

Chapter

Figure 52:
Figure 53:
Figure 54:
Figure 55:
Figure 56:
Figure 57:
Figure 58:

: PC, Matched level set ..................................................................
: CAS, Matched level set ..............................................................

: Pc vs. P, for phase set ................................................................
: PC vs. P, for level set ..................................................................

2
14-Hz coherence histogram .........................................................
14-Hz st[A<I>] vs. s¢[AL] .............................................................
136 Hz coherence histogram .......................................................
136-Hz interaural parameters vs. time .......................................
136-Hz st[A<I>] vs. st[AL] ...........................................................
136-Hz st[A<I>] vs. st[AL] - collection 1 ......................................
136-Hz st[A<I>] vs. MAL] — collection 2 ......................................
136-Hz interaural parameters vs. time — temporal averaging .....
136-Hz interaural parameters vs. time — TI trading ...................
636-Hz st[A<I>] vs. st[AL] ............................................................
Matched st[A<I>] vs. st[AL] .........................................................
PC, Matched phase set ................................................................
CAS, Matched phase set ............................................................
PC, Matched level set ..................................................................
CAS, Matched level set ..............................................................
PC, Contextual effects phase set ..................................................
CAS, Contextual effects phase set ..............................................

CAS, Contextual effects level set ................................................

3
Spectral splatter, Phase set ........................................................
Spectral splatter, Level set .........................................................
PC, Phase Set ..............................................................................
CAS, Phase Set ..........................................................................
PC, Level Set ...............................................................................
CAS, Level Set ...........................................................................

25-ms interaural parameters vs. time .........................................

xi

PC, Contextual effects level set ....................................................

58
59
64
65

78
79
82
82
84
85
85
90
93
96
99

101
102
103
104
111
112
113
114

118
119
124
125
126
127
130

Chapter 4

Figure 59:
Figure 60:
Figure 61:
Figure 62:
Figure 63:
Figure 64:
Figure 65:
Figure 66:
Figure 67:
Figure 68:
Figure 69:
Figure 70:
Figure 71:

Chapter 5

Figure 72:
Figure 73:
Figure 74:
Figure 75:
Figure 76:
Figure 77:
Figure 78:
Figure 79:
Figure 80:
Figure 81:
Figure 82:
Figure 83:
Figure 84:
Figure 85:

Chapter 6

Figure 86:
Figure 87:
Figure 88:
Figure 89:
Figure 90:
Figure 91:

14 Hz, CAS and Nc scores ............................................................ 135
14 Hz, Model results, PC ............................................................... 147
14 Hz, Model results, CAS ............................................................ 148
14 Hz, Model comparison, PC ....................................................... 149
14 Hz, Model comparison, CA3 .................................................... 150
14 Hz, Model 1 free parameters .................................................... 155
108 Hz, CAS and NC scores .......................................................... 159
108 Hz, Model results, PC .............................................................. 160
108 Hz, Model results, CAS .......................................................... 161
108 Hz, Model comparison, PC ...................................................... 162
108 Hz, Model comparison, CAS .................................................. 163
108 Hz, Model 1 free parameters .................................................. 168
108 Hz, Model 4 free parameters .................................................. 169
14 Hz, CAS and Nc scores ............................................................ 178
14 Hz, Model results, PC“... .......................................................... 180
14 Hz, Model results, CAS ............................................................ 181
14 Hz, Model comparison, PC ....................................................... 182
14 Hz, Model comparison, CA5 .................................................... 183
14 Hz, Model 1 free parameters .................................................... 188
136-Hz st[A<I>] vs. st[AL], 60 noise-pairs ...................................... 192
136 Hz, CAS and NC scores .......................................................... 193
136 Hz, Model results, PC .............................................................. 195
136 Hz, Model results, CAS .......................................................... 196
136 Hz, Model comparison, PC ...................................................... 197
136 Hz, Model comparison, CAS .................................................. 198
136 Hz, Model 1 free parameters .................................................. 201
136 Hz, Model 4 free parameters .................................................. 202
S¢[‘I’A¢] VS. 3t[‘I’AL] ...................................................................... 212
Detection data for Listener DA ................................................... 215
Detection data for Listener E ...................................................... 216
Detection data for Listener M ..................................................... 217
Example of Addition and Cancellation Noises ............................ 221
Addition and Cancellation Set Data ........................................... 222

xii

KEY TO SYMBOLS

Introduction

7 : Interaural cross-correlation function
5 : Lag of the cross-correlation function
:rL : Signal to left ear

xR : Signal to right ear

T : Duration of signal or period

Chapter 1
Experiment 1

:1: A : Randomly generated noise A

$3 : Randomly generated noise B

N : Number of components

Cn : Amplitude of Fourier component

can : Angular frequency of Fourier component
(1),, : Phase of Fourier component

fn : Frequency of Fourier component

x3 : The new noise B after orthogonalization to noise A
M : Number of samples in a channel

Arms : Root-mean-square value of noise A
Buns : Root-mean-square value of noise B
p.413 : Correlation between noise A and B

a : Mixing factor

p : Coherence evaluated at time zero

s(t) : Temporal window

:2: Analytic signal

3? : Real part of analytic signal

3 : Imaginary part of analytic signal

xiii

¢(t) : Phase of analytic signal

E(t) : Envelope of analytic signal

A<I>(t) : Interaural phase difference

AL(t) : Interaural level difference

st[A<I>] : Standard deviation over time of the interaural phase difference

st[AL] : Standard deviation over time of the interaural level difference
0 E : Mean interaural phase difference, averaged over time

o E : Mean interaural level difference, averaged over time
Experiment 5

o s,[E] : Standard deviation over time of envelope

0 E : Mean of envelope, averaged over time

Chapter 2
Experiment 7

o é[ f (t)] : Exponential averaging function

0 1' : Exponential averaging time constant

0 TD : Duration of exponential averaging window

0 z(t) : Auditory image position variable

0 c : Time/ intensity trading ratio

0 pMR : Correlation of detection data between matched and random noise-pairs

Chapter 4
Experiment 13

o ‘IPM, : Compressed interaural phase difference

0 ‘II°AL : Compressed interaural level difference

wg(t) : Envelope weighting function

g : Envelope weighting threshold

\IIM.: Transformed interaural phase difference

\IIAL: Transformed interaural level difference

xiv

a : Weighting parameter for independent centers models
0 dn : Model number

0 W[h, \II(t)] : Threshold function

0 b : Weighting parameter for lateral position models

o ‘11, : Transformed lateral position variable

0 cyst(t) : Short-term cross-correlation

o ‘IICC : Transformed short-term cross-correlation

o st[\Il’] : Standard deviation over time of the derivative of the transformed inter-
aural difference

. st[E’] : Standard deviation over time of the derivative of the envelope
Appendix A

o Ncorr : Number of correct responses

0 conf : Number of confident responses

XV

KEY TO ABBREVIATIONS

2AFC : Two-alternative forced-choice
ASW : Apparent source width

AVCN : Anteroventral cochlear nucleus
CAS’ : Confidence adjusted score

EC : Equalization-cancellation

EE : Excitatory-excitatory

EI : Excitatory-inhibitory

DCN : Dorsal cochlear nucleus

IACC : Interaural cross-correlation

IC : Inferior colliculus

ILD : Interaural level difference

IPD : Interaural phase difference

ITD : Interaural time difference

jnd : Just-noticeable difference

LEV : Listener envelopment

LL : Lateral lemniscus

LP : Lateral position units

LSO : Lateral superior olive

No : Noise in-phase

NoS1r : Noise in-phase, signal out-of-phase
N7r : Noise out-of-phase

MLD : Masking level difference

MGB : Medial geniculate body

MSO : Medial superior olive

MTB : Medial nucleus of the trapezoidal body

NLL : Nucleus of the lateral lemniscus

xvi

P, : Percent correct

P, : Percent selected

pdf : Probability density function
PVCN : Posteroventral cochlear nucleus
RMS : Root-mean-square

STCC : Short-term cross-correlation

YN : Yes-no

xvii

INTRODUCTION

0.1 Road map to this work

This dissertation plans to study the ability of human listeners to detect interaural
incoherence, or the difference in the signals presented to the left and right ears. Lis-
teners are remarkably good at distinguishing slightly incoherent noise from coherent
noise, when the signals in the two ears are identical. The cue used to detect in-
teraural incoherence is thought to be much like the cue used to detect masking-level
differences, where an out-of-phase tone between the two ears is more easily detectable
than an in-phase tone in otherwise coherent noise. The reason for this is that the
out-of-phase tone adds a small amount of incoherence to the coherent noise. There
has been a vast amount of research done on masking—level differences in the last 60
years.

Incoherence detection is thought to be described wholly by the coherence function,
which is an overlap integral over the left and right signals over the duration of the
stimulus. If this is the case, dynamic features in the incoherent noise will be lost.
However, the perception of incoherent noise has dynamic characteristics. Therefore,
it seems appropriate to ask the following two questions: 1) Is cross-correlation or
coherence function an adequate parameter for incoherence detection? 2) If not cross-
correlation or coherence function, then what parameter is important to incoherence
detection? These questions will be addressed by selecting noise—pairs that will explore
the effect of bandwidth on incoherence detection. Chapter 1 will use noise-pairs with
a fixed value of coherence. The results of this chapter will find that the noise-pairs
with the largest standard deviation over time (fluctuations) of the interaural phase
difference and interaural level difference will have incoherence that is much more
readily detectable than noise-pairs with the smallest fluctuations. Since the coherence

function predicts that incoherence detection should be the same in all these noises,

it will be concluded that the coherence function is not used in incoherence detection.
As the bandwidth increases, the rate of fluctuations also increases and the difference
between noise-pairs with the largest fluctuations and smallest fluctuations in the
interaural parameters is less perceptible to listeners. In the case of wide bands, it
would be possible to use the coherence function to describe the detection data, but
only because of the ergodicity of the fluctuations for wide bands.

Chapter 2 will use noise-pairs with varied values of coherence, but similar distri-
butions of fluctuations in phase and level differences. The values of coherence ranged
from 0.969—998. For the average listener, incoherence would be very easy to detect in
a noise-pair with a value of coherence of 0.969. For the average listener, incoherence
would be almost impossible to detect in a noise-pair with a value of coherence of
0.998. There are no new results in Chapter 2, and its value is that the results of
Chapter 1 are reproduced by using only the fluctuations in phase and level.

The binaural integration time is tens to hundreds of milliseconds. Therefore there
may be a fundamental flaw to the results of Chapters 1 and 2, which had 500—ms
noises. It may be the case that incoherence detection is done in small analysis windows
much shorter than 500 ms. Chapter 3 will address this criticism by using the same
method of selecting noise-pairs with large and small fluctuations as was done in
Chapters 1 and 2. However, the noises will now be five to twenty times shorter
in duration and only the narrow bandwidth will be used. The results of this chapter
will find that listeners will be able to use interaural fluctuations of phase and level
for stimuli as short as 50 ms. The results will be comparable to those in Chapters
1 and 2. For 25-ms noise-pairs, listeners will use a lateralization cue instead of a
width cue to perform the task. Coherent noise is normally described as a compact
sound image in the center of the head. Incoherent noise is normally described as a
wide or diffuse sound image in the center of the head. A lateralization cue, for this

experiment, would be a compact sound that has moved from the center of the head,

usually associated with a static interaural phase difference or static interaural level
difference. It was necessary for listeners to use lateralization because it was found
that the interaural differences did not change much over the 25—ms duration of the
noises.

After these preliminary experiments, the results from Chapters 1-3 will motivate
the direction of the modeling of the incoherence detection data. Chapter 4 will
concentrate on deve10ping and refining models that describe incoherence detection
from a reference correlation of unity. The models will use different combinations of
phase and level statistics and several aspects of the models will be similar to those
used in describing masking-level difference data, since so much work has been done
in this area. As was done in Chapter 1, Chapter 4 will use noise-pairs with a fixed
value of coherence. Three types of models will be explored. The first type of model
will add fluctuations of phase and fluctuations of level independently. The second
type of model will combine phase and level differences and then calculate a statistic
for fluctuations. In this model type, it would be possible for a phase difference to
the right ear to be cancelled by a level difference to the left ear. This cancellation
has been shown to occur in time-intensity trading experiments with static interaural
differences. The last type of model reduces the coherence function to a short-term
coherence function, that evaluates the coherence over very small time intervals. It
will be shown that the incoherence detection data can be best described by a model
that independently adds the standard deviation of phase to the standard deviation in
level with equal weight for phase and level. Compression of the interaural difference
scale, temporal averaging, and envelope weighting will also be applied to improve the
model.

As was done in Chapter 2, Chapter 5 will use noise-pairs with varied values of
coherence. Again, there are no new results in Chapter 5, and its value is that the

results of Chapter 4 are reproduced.

Lastly, Chapter 6 will apply the modeling results of Chapters 4 and 5 to directly
answer these two questions: 1) Can listeners use just phase fluctuations or just level
fluctuations to detect incoherence? and 2) Do listeners use independent IPDs and
ILDs as a function of time and not a single auditory image made of the combination
of the two interaural parameters? It will be found that the answer to both of these
questions is “yes”. However, not all of the variation of the data will be explained,
motivating more studies.

From the experiments in these six chapters of research, it will be concluded that
incoherence detection is done by detection fluctuations in the interaural phase and
level differences, contrary to other recent results. Before this dissertation, van de
Par and Kohlrausch (1999) found no use for interaural parameters in incoherence
detection. The reason for the discrepancy is that van de Par and Kohlrausch did
not find a bandwidth dependence for interaural parameters, whereas there was one
found in this dissertation. Another reason that the coherence function has been used
to describe incoherence detection is possibly due to the stimuli that have been used
in previous experiments. Critical bandwidth noises of about 100 Hz (for a center
frequency of 500 Hz) and wide bandwidth noises of thousands of Hz have been used
for experiments where individual features in the interaural parameters are shown to
be too fast to consistently recognize.

Two types of models that are often used to describe masking-level difference data
are the equalization-cancellation model and correlation model. However, from the
results that will appear in the following chapters, both of these models should only
be applied to stimuli that have wide bandwidths and similar fluctuations. This is
because these models are energy—based models that have no mechanism to analyze
interaural parameters differences over short intervals.

The results of this dissertation have the potential to motivate several new studies

in the area of incoherence detection. For example:

o More research will need to be done to understand why listeners confuse monau-
ral and interaural fluctuations. The monaural confusion results can then be
applied to false-alarm rates as measured in single-interval masking-level differ-
ence experiments in reproducible noises (Gilkey et al., 1985, 1986; Isabelle and

Colburn, 1991; Evilsizer et al., 2002).

o It will be important to study the eflect of varying the center frequency of the in-
coherent noises and apply the results to high frequency masking-level difference

data (Bernstein and Trahiotis, 1992).

o It will be important to vary the value of the interaural coherence to change the
distribution of fluctuations of phase and level. The detection of incoherence
might be different enough that results in this dissertation does not apply to

other values of coherence.

o It will be important to make a more sophisticated model to describe incoherence
detection data. This can be done by modeling brainstem nuclei firing patterns

in the superior olivary complex.

0.2 Coherence

Interaural coherence is a measure of the similarity of signals between a listener’s two
ears. It is derived from the interaural cross-correlation function, 7(6), which is a

function of the interaural time shift 6,

 

7(5) ___ foT 1'L(t)1'R(t + 5)dt
x/it‘xandtig‘aamt’

where x}; is the signal in the right ear, and 2:1, is the signal in the left. The cross-

(1)

correlation is bounded by —1 g 'y _<_ 1.

With respect to perception, interest normally centers on the peak of 7(6). The

 

§
59
:9

   

-3 0 +3
Si nal from LAG 8(ms) Signal from
le car right ear

Figure 1: The Jeffress coincidence matrix. The characteristic frequency of bands
(horizontal lines) increase logrithmically. The vertical arrows represent fibers at-
tached to neurons (black dots) that fire when signals from both the left and right
ears temporally coincide for different values of the interaural lag 6. (From Hartmann,
1999)

value of 6 for which the peak occurs is the perceptually relevant interaural time
difference (ITD) cue for the location of the sound image. This value of 5 was given a
place representation in the famous binaural model by J effress (1948). Figure 1 shows
how the Jeffress coincidence model is composed of different bands with a certain
characteristic frequency. Different cells fire depending on the ITD and frequency of
the signals presented to the ears.

The height of the peak is thought to determine the compactness of the image. If

the sounds in the two ears are identical except for an interaural delay or interaural

< Wfi?

Figure 2: An artist’s rendition of incoherence perception. The left figure shows a
compact, coherent stimulus between the listener’s ears. The right figure shows how
the image is broader and more diffuse for an incoherent stimulus.

 

level difference, then 7 has its maximum value of 1, and the image is expected to be
maximally compact. If the height of the peak is less than 1, the image is broader or
more diffuse (Barron, 1983; Blauert and Lindemann, 1986). Figure 2 shows a cartoon
of the perception of incoherence.

The height of the cross-correlation peak is defined as the coherence. It is pos-
tulated that to be physiologically relevant, the peak must occur at a value of the
interaural lag that lies in a range of perceptible ITDs (:t 763 us for the average
human head, which is determined by dividing the width of the head by the speed
of sound), and this requirement may place restrictions on the peaks for which the
concept of coherence is valid.

As applied in architectural acoustics, the coherence is called the IACC (interaural
cross-correlation), and it refers to the height of 7(6) for 6 in the range —1 S 6 S 1 ms
(Beranek, 2004). In recent years this objective architectural measure has been divided
into two separate measures. One is the apparent source width (ASW), based on co-
herence within 80 ms of the onset of a sound (Barron and Marshall, 1981). The other
is listener envelopment (LEV), determined by the coherence of later arriving sound,
as measured after 80 ms (Bradley and Soulodre, 1995; Barron, 2004). Together, the
ASW and LEV greatly influence the spatial impression of a sound in a room. Nor-
mally, the architectural measurements are made with microphone techniques and not
with artificial heads.

Perceptual aspects of cross-correlation function and interaural coherence have been

7

studied by psychoacousticians, usually using bands of noise as stimuli. Noise provides
an abstraction of real-world sounds that is devoid of meaningful information, and it
affords many opportunities for parametric variations. Using broadband noise, Pol-
lack and 'I’rittipoe (1959a,b) found thresholds for changes in cross-correlation for two
values of the reference correlation, namely 1.0 (i.e. No) and —1.0 (i.e. N1r). They
explored the effects of duration, sound level, frequency range, and interaural level
difference.

Listeners are particularly sensitive to deviations from a reference correlation of
1.0. Using narrowband noise, Gabriel and Colburn (1981) found that listeners could
easily distinguish between noise with a coherence of 1.0 and noise with a coherence of
0.99. They also reported the somewhat counterintuitive result that as the bandwidth
of the noise increases, the just-noticeable difference (jnd) also increases. One might
have expected the jnd to decrease instead given that a wider bandwidth generally
offers the listener more information.

For a reference coherence less than unity, a listener’s ability to discriminate a
difference in incoherence degrades appreciably.’ This decrease is approximately an
order of magnitude for a reference coherence of 0.0 (Gabriel and Colburn, 1981). It
is possible for the signals to the two ears to become anti-correlated (when the signal
in the left ear is equal to the signal in the right ear except for a difference in the
sign). An anti-correlated signal places an image at both of the listener’s ears, rather
than at the center of the head. Boehnke et al. (2002) found that discrimination
from a reference coherence of —1.0 was significantly worse than a reference of +1.0.
It was also found that discrimination from a reference coherence of 0.0 was worse for
partially anticorrelated noise when compared to partially correlated noise.

A reference coherence of 1.0 is also of interest in connection with the masking-
level difference (MLD). The MLD phenomenon is the difference that occurs in the

threshold to detect a tone in noise depending on the binaural masker and signal phase

configuration. Numerous studies have concluded that the threshold signal-to-noise
ratio in the NoS1r (noise in-phase, signal out-of-phase by 180°) condition is essentially
determined by the ability to detect the incoherence introduced by the out-of-phase
signal (Wilbanks and Whitmore, 1967; Koehnke et al., 1986; Durlach et al., 1986;
Bernstein and Trahiotis, 1992; van de Par and Kohlrausch, 1995).

The concept of coherence may be important to speech recognition, as discussed by
Culling et al. (2001). The line of reasoning is as follows: Jain et al. (1991) showed that
the reduction in the interaural cross-correlation function of the signal is monotonically
related to the strength of the signal for signal intensities less than that of the masker.
A crucial factor in identifying several speech sounds is an accurate estimation of
the frequency of the first formant. It is thought that the accuracy of the estimation
process is determined by relative intensities of peripherally-resolved harmonics in that
frequency region. If this is the case, then the ability to discriminate different degrees of
decorrelation might explain the binaural intelligibility level difference (Licklider, 1948;
Carhart et al., 1969a,b; Levitt and Rabiner, 1967a,b; Bronkhorst and Plomp, 1988).
The binaural intelligibility level difference is the difference between using monaural

and binaural information when trying to understand speech in a noise background.

0.3 Fluctuations of interaural parameters

Despite the prevalent use of the cross-correlation function to describe incoherence
detection, time-dependent fluctuations seem to play a part in the perception of inco-
herent stimuli. This perception, which occurs when incoherent stimuli are presented
with headphones, is usually described as including an auditory width or lateral dis-
placement that varies in time. Given that the form of Eq. 1 is a “time-averaging”
function that integrates over the entire duration of the stimulus, as opposed to a
time-varying function, there appears to be a disconnection between the perception of

incoherence and the measure of it via Eq. 1.

From the extensive work on modeling incoherence detection and the present knowl-
edge of auditory physiology, it seems possible that the interaural parameters are more
physically relevant than incoherence per se to the incoherence detection task. Fluc-
tuations in interaural phase differences (IPD) and interaural level differences (ILD)
have been studied for a few conditions. For example, probability distributions of IPDs
and ILDs have been calculated by Zurek (1991) and Breebaart et al. (1999); they

have been measured in rooms by Nix and Hohmann (2001).

0.4 Physiology

The pathway by which physical signals are transformed into neural signals starts
with the acoustic wave impinging on the tympanic membrane (ear drum). The wave
is then transferred via the ossicles (incus, malleus, and stapes) to the cochlea. The
ossicles act as an impedance matching device; if the sound met the oval window
directly, only 10% (or less) of the acoustic wave energy would be transferred to the
inner ear or cochlea for a 1 kHz tone. Instead 65% of the acoustic wave energy is
transferred (Moller, 1965). The cochlea is filled with fluid; the acoustic wave, via
the middle-ear ossicles, causes pressure waves in the fluid, which, in turn, cause the
basilar membrane to move. Attached to the basilar membrane are hair cells, which
depolarize under mechanical stress and stimulate the generation of action potentials
by the auditory nerve. Measurements of vibration patterns of the basilar membrane
show that it is tonotopz'cally organized or organized by increasing frequency. All of
the auditory system is tonotopically organized.

From the cochlea, information travels on the auditory nerve. The cochlear nucleus
is subdivided into the sections: the anteroventral nucleus (AVCN), the posteroventral
nucleus (PVCN), and the dorsal nucleus (DCN). The AVCN projects to both the
ipsilateral and contralateral superior olivary complexes and therefore is important

to providing binaural information such as ITDs and ILDs, which are used in sound

10

localization. The DCN projects only contralaterally and therefore is important to
monaural acoustic information such as level discrimination. The DCN processes the
signals with non-monotonic firing rate-intensity functions and inhibitory sibebands.
The PVCN is thought to perform both monaural and binaural processing because it
has characteristics of both the AVCN and DCN. Unlike the DCN, the AVCN does
little processing of the signals and projects to the superior olivary complex with
myelinated fibers that keep the timing information intact.

It is well known that the superior olivary complex processes time and level differ-
ence between the ears in mammals. Specifically, Goldberg and Brown (1968, 1969)
found that the medial superior olivary nucleus (MSO) in dogs analyzes time differ-
ences. This is done with excitatory-excitatory (EE) cells that fire when impulses are
received at the same time. Tsuchitani and Boudreau (1966) and Tsuchitani (1977)
found that the lateral superior olivary nucleus (LSO) in cats analyzes level differences.
The LSO contains mostly excitatory-inhibitory (EI) cells.

Yin and Chan (1990) and Smith, Joris, and Yin (1993) showed that it is plausible
for the M80 to act as the J effress coincidence matrix seen in Figure 1. They discovered
delay lines from the cochlear nucleus to the EB cells in the M30 of cats. However,
new work on the necessity of including EI cells in the M30 to accurately measure time
diflerences has recently presented some problems to the Jeffress model (Brand et al.,
2001). Measurements by Goldberg and Brown (1968) showed that the MSO contains
approximately 75% EE cells and 25% El cells. However, the results of Brand et al.
(2001) imply that a majority of M80 cells need inhibitory inputs. In either case, an
additional inhibitory component to the Jeffress model appears both physiologically
possible and pertinent.

Beyond the superior olivary complex, neurons project to the nucleus of the lateral
lemniscus (NLL), then the inferior colliculus (IC) where auditory maps of space are

made (Knudsen and Konishi, 1979), then the medial geniculate body (MGB), and

11

finally the auditory cortex. The processing of stimuli becomes increasingly complex
and is still being researched in these areas. Given that interaural parameters are
processed in the midbrain and that detection of incoherence is perceived as time-
varying fluctuations, investigating the tie between incoherent stimuli and interaural

differences is both psychologically and physiologically motivated.

0.5 Purpose of this work

This dissertation is concerned with incoherence detection starting with perfectly co—
herent noise as a reference. Its working hypothesis is based on the suspicion that
the extreme sensitivity shown by listeners to small amounts of incoherence is not
properly described by the cross-correlation function. The reason is that when a small
amount of incoherence is added to an otherwise perfectly coherent noise, the image of
the noise acquires lateral fluctuations that are not present when the coherence is 1.0.
The hypothesis continues with the observation that, whereas coherence is a measure
that is averaged over time, the fluctuations that are imagined to be the basis of co-
herence discrimination are dynamic. Thus, although the coherence measure may be
a mathematically useful characterization of the similarity or dissimilarity of signals
in the two ears, this measure may not be the most perceptually relevant characteriza-
tion. Instead, it is possible that some measure that specifically considers fluctuations
is better. A similar point of view with respect to the MLD has been taken by a
number of authors, e.g. Jeffress et al. (1956). The rest of this dissertation describes

experiments that test this hypothesis.

12

1 INCOHERENCE AND FLUCTUATIONS OF
INTERAURAL PARAMETERS

1.1 EXPERIMENT 1: NARROW BANDWIDTH

The purpose of Experiment 1 was to determine whether the height of the peak of the
cross-correlation function (the coherence) adequately describes incoherence detection
given a reference coherence of 1.0. The experiments employed reproducible noises (to
be called left-right noise-pairs, or noise-pairs), as have been used in MLD experiments
by Gilkey et al. (1985, 1986), Isabelle and Colburn (1991), and Evilsizer et al. (2002).
An advantage of using reproducible noises instead of randomly generated noises for
incoherence detection is that reproducible-noise data should provide a more stringent
and confining test of the binaural models. This is because the individual properties
of the noise-pairs will be accessible to the experimenter after the experiment is per-
formed. An advantage of using incoherence detection data instead of MLD data is
that incoherence detection employs a simpler stimulus, which is spectrally homoge—
neous unlike a tone-in-noise situation. Certain problems may arise for MLD tasks
that would not during incoherence detection; Wightman (1971) noted inconsistencies
in narrowband MLD results that may have been due to off-frequency listening.

In Experiment 1 and all the other experiments in this chapter, the different re-
producible left-right noise-pairs had the same value of interaural coherence. If the
coherence is an adequate measure of perception, then all the reproducible noise-pairs

will be equally distinguishable from perfectly coherent noise.

1.1.1 Stimuli

A collection of 100 two-channel noises with reproducible amplitudes and phases was

created for Experiment 1. The process began with two waveforms, A and B, written

13

as a sum of cosines in the form

N
xA(t) = 2 C: cos(w,,t —l— (25$)
n=1

and
N

xB(t) = 2 Cf cos(w,,t + 9255)
n=l
where the Cn’s and (pn’s are the amplitudes and phases of the spectral components.
The narrowband noises were generated with components having random phases over
a frequency range of 490—510 Hz and with a frequency spacing of 2 Hz. Components
between 495—505 Hz had equal amplitudes of unity. Frequencies below 495 Hz had a

raised-cosine window applied to the amplitude spectrum of the form

7r(fin — 490)

cAchz~2

] for 490 g f, g 495 (2)

to minimize any spectral edge effects in the noises. The amplitudes of components
from 505—510 Hz were similarly windowed. This frequency shaping can be seen in
Figure 3. The 3-dB bandwidth of the noise was therefore 14 Hz.

For each noise in a collection of 100 reproducible noise—pairs, the B noise (x3)
was orthogonalized to the A noise (xA) by the Gram-Schmidt orthogonalization pro-
cedure, which was used in Culling et al. (2001), and which is described below. The
orthogonalized B noise is here denoted as x’B. This was done to ensure that the signals
were uncorrelated and that the final value of the cross-correlation after mixing would
be precise. For large bandwidths, the large number of random variables (the ain’s
are uniformly distributed) yields statistically independent noise-pairs. In the case of
large noise bands, orthogonalization is probably not necessary. However, there are a
small number of random variables (random phases) for the 14-Hz bandwidth noises of

this experiment. Experimental observations showed the projection between randomly

14

1.50 I‘IY'IVVV'VVVV'VYV—VIVVVVIVVVV

 

1.25

VV‘IYf71

 

0‘: 0.75

V V V ' V V V V

0.50 f
l

0.25 '-

 

 

 

 

 

 

 

 

 

 

 

435 490 495 500 505 510 sis

f (Hz)

Figure 3: The frequency shaping in Eq. 2 that is applied to all stimuli in Experiment
1. This raised-cosine window was applied to remove any spectral edge effects.

generated noise-pairs can be as large as 10% for this bandwidth. Therefore, it was im-
perative to use the orthogonalization procedure for the 14—Hz bandwidth noise-pairs
in order to be able to generate noise—pairs with the desired interaural coherence.

To orthogonalize x B to x A, the root-mean-square (RMS) is found for each channel:

Arms _ _\/Zt=M1[$A(t) ]2=\/Zt: lizn: 10A C03(07th + ¢R)l2 l % "2::1(C;;‘)2,
__¢Zfiw1lxaltfl_\/Z. 1523.: 03.0.6... + 4310] =i.l >30.

where M is the number of samples in each sound. Then the overlap between the two

 

 

 

 

and

 

 

 

 

channels is calculated:

2,11 xA(t)xB(t) _ Ex, 22;] Cfo cos(w,,t + 43:?) cos(w,,t + 45,?)
”AB _ MAm,B,m, ‘ MAmBm,

1 N CACf,3 cos(¢A— (:33)

5 "a A rm,B,,,,

 

 

 

15

Next, the correlated component of x A is subtracted from a scaled x3 ensuring the

two channels have equal power,

 

, (t) _ Arms pAB

_ t _ _—
Brrnsv 1 - pinB( ) V 1 - p.248

The two perfectly uncorrelated noises were then mixed, with mixing factor a, to

xA(t) for 1 S t g M.

create the final left and right (L and R) noise-pairs to be sent to the listeners,

$1,223};

x3: (1—a2)xA+ax'B.

The coherence, as defined by Eq. 1, is then computed to yield,

P=7(0)=V1—02~ (4)

For values of p near 1, the value of interaural lag that maximizes p is zero. Because the
mixing factor used in all of the experiments was a = 0.125, the interaural coherence
of all the noise-pairs was p = 0.9922.

After mixing, each noise was given a time interval shape with a total duration of
500 ms. A temporal window, s(t), was applied such that there were cosine-squared
edges with rise/fall times of 30 ms and a full-on duration of 440 ms, which can be
seen in Figure 4. The application of the temporal window could change the coherence
of the noise; therefore, the value of the coherence was measured after the window was
applied so that p = 0.9922 i 0.0001. Noise-pairs that did not meet this criterion were
rejected. For the 100 noise-pairs accepted in this experiment, 875 were rejected. Also,
note that after orthogonalization and applying the temporal window, the noise-pairs
do not necessarily have equal amplitudes.

To determine the time-dependent interaural phase difference (IPD) and interaural

16

 

 

 

 

l.50 " r I 'l' VI I I I '1 I 'r' r
1.25:- 1
C I
l _- : """"""""""""""""""""""""""" . ‘
. 5 i l
A : l I
3 075 -: EI-
0’ :5 :1
0.50 _-: 5-
:5 E:
0.25 1 :-
I. 0‘
h: I‘
- i
l t
0 AAAAAAAA 1AlAA‘AAAAIJJAAIMAAIAAAAIAA-Al ........
o 50 100 150 200 250 300 350 400 450 500
1 (ms)

Figure 4: The temporal window, s(t), that is applied to all stimuli in this chapter.
All the stimuli had 30 ms rise / fall times and a full-on duration of 440 ms.

level difference (ILD), the analytic signals were found. By eliminating the negative

frequencies, the analytic signal for either x L or x]; is

N
W) = 8(t) 2 Cu eXP[i(wnt + 4%)].

n=1

where s(t) is the temporal window, the Cn’s are the left or right amplitudes, and ¢n’s
are the left or right phases as required.

By Euler’s relation, the analytic signal becomes

:t(t) = s(t) Z Cn[cos(wnt + 6,.) + isin(w,,t + 4%)] = éR(t) + 28(t). (5)

n=1

The phase and enve10pe of the analytic signal as a function of time are
$0) = arglglt), 5%)] (6)

and

 

=\/3i2(t) )+ 32(t (7)

17

where the arg function is the arctangent with possible quadrant correction. The

time-dependent IPD (radians) and ILD (dB) of the analytic signal are then defined

as
MW) = $30) - ¢L(t)- (8)

and
AL(t) = 2010g10 [53%f3] . (9)

Equation 8 yields a positive value of A<I>(t) for signals that lead in the right ear.
Similarly, Eq. 9 gives a positive value of AL(t) for a signal that has a larger level in
the right ear. The interaural phase A<I>(t) was required to remain in the physically
relevant region of in radians at every point in time, and was corrected by adding
or subtracting 27r when necessary. The ITD is proportional to the IPD for narrow
bandwidths. The ITD can be calculated by dividing the IPD by the angular center

frequency of 27r x 500.

1.1.2 Signal Structure Analysis

Figure 5 shows a plot of the IPD and ILD as a function of time for an arbitrarily
chosen noise-pair from the collection of noise-pairs with p = 0.9922 and a bandwidth
of 14 Hz. The figure shows that the IPD and ILD fluctuate as a function of time.
Peaks in the IPD and ILD sometimes coincide in time and can be directed towards
the same ear or opposite ears.

An analysis was done to find how often the interaural differences were in the same
and different lateral directions. This was done by comparing the direction of the
interaural differences for each of the 4000 samples in all the 100 noise-pairs from this
experiment. The percentage of time that the interaural differences were in the same
direction was calculated for the average noise—pair (averaged over 100). In addition,

the individual noise-pairs with the minimum and maximum percentage of samples

18

s,(AL)=1.87 dB

 

 

st(A¢)=l 1.76 degrees

 

 

 

 

 

 

 

 

 

 

 

60 r ' ' ' ' T 1 'fi , 15 I I I ffi T I
40 E l to :-
5’7
L .
U, I
:3 ° W
3 a
i -10 E
1 1 l 1 4 ’ _15 ’ 1 I l 1 1 1 l l l ’
250 500 0 250 500
t (ms) t (ms)

Figure 5: The IPD and ILD plotted as a function of time for an arbitrary 14-Hz
bandwidth noise-pair. Above the plot are the fluctuation values of the IPD and ILD.
Positive values of the IPD are defined as leading in the right ear; positive values of
ILD are defined as being louder in the right ear.

that had interaural differences in the same direction were found; so were the noise-
pairs that had interaural differences in opposite directions. Lastly, it was found how
often the IPD was large when the ILD was large, irrespective of lateral direction.
Each parameter was defined to be large when it was greater than the respective RMS
value of the interaural differences over time.

Table 1: Average (over 100 noise-pairs), minimum (over 100 noise-pairs), and max-
imum (over 100 noise-pairs) percentage of samples where IPD and ILD are directed

towards the same ear or different ears. It also shows when the IPD and ILD are large
with respect to the RMS interaural difference.

 

Average Minimum Maximum
Same direction 46.3% 19.4% 72.9%

Opposite direction 48.8% 20.1% 74.8%
Large in both 43.0% 20.8% 82.0%

 

 

 

 

 

Table 1 shows that for the 100 noise-pairs in this experiment the IPD and ILD
can be either in the same direction (both towards the right or both towards the
left) or in the opposite direction (one to the right, one to the left). The IPD and

ILD are in the same direction and opposite directions about 50% of the time for the

19

average noise-pair. The total of 46.3% and 48.8% do not add up to 100% because
either the IPD or ILD is zero 4.9% percent of the duration for a typical noise—pair.
However, there are improbable noise-pairs where the interaural differences go in the
same direction as little as 19.4% of the duration and as much as 72.9%. This is similar
to the percentages for the interaural differences going in different direction.

Possibly the most interesting part of this analysis is whether a large peak in one
interaural difference implies a large peak in the other interaural difference at the same
sample number. Figure 5 shows a large peak (greater than the RMS value) in IPD
going to the left ear at 225 ms and large peak in ILD going to the right at the same
time. On average, only 43.0% of the large peaks in IPD or ILD correspond to large
peaks in both IPD and ILD. The most extreme stimuli have peaks that coincide as
little as 20.8% of the time and as much as 82.0% of the time. Therefore, there is a
great amount of variability in individual noise-pairs with respect to fluctuations of

IPD and ILD depending on the phase relationship.

1.1.3 Signals

Next, a quantitative measure of interaural fluctuations is defined. The IPD fluctuation

over time is defined as

 

stlA‘Pl = (l i 2WD“) - 371312 (10)

where M is the number of samples in the 500 ms noise (M = 4000 samples), 375 is
the mean IPD computed over time, and the t subscript indicates that this standard

deviation value is computed over time. The ILD fluctuation over time is defined as

 

8‘[AL]:\J'1il4-i[AL(t)— AT]? (11)

Figure 5 shows the IPD and ILD changing as a function of time, with values of st[A<I>]

20

 

 

 

 

 

ID

v . r ' f1 ' ' ' l ' r I I ..
s :- ® -:
to F. .5
3m ' 1
g :
.336 1.
.—.o 5
ON «I
3 :
079 SW = 14 Hz .-
o mama) = 10.50 '
- u(s,[AL]) = 1.45 1
_ o(s,[A¢]) = 6.66 .
‘0 o(s,[AL]) = 0.68 1
corr‘ = 0.70 1

o . I l l l l l l l l E I Ml L4 L4 J_L L J j_A L
0 1 2 3 4 5

Sf[AL] dB

Figure 6: Fluctuations of IPD versus fluctuations of ILD for the collection of 100
reproducible noise-pairs having a 14-Hz bandwidth, as used in Experiment 1. Each
noise-pair is labeled by a serial number indicating only the order of creation. The
means, standard deviations, and IPD-ILD correlation of the distributions are re-
ported.

and st[AL] above each panel. For the entire collection of 100 14-Hz bandwidth noise-
pairs, Figure 6 shows st[A<I>] plotted against 3, [AL]. The mean, standard deviation,
and correlation of st[A<I>] and st[AL] are reported on the figure. This figure shows that
st[A<I>] and st[AL] are strongly correlated. However, there are still some improbable
noise-pairs, which were predicted to occur from the signal structure analysis of the
previous section. For example, noise-pair #11 has the largest IPD fluctuations but
only average ILD fluctuations. (It is interesting to see that the correlation between
phase fluctuations and level fluctuations across different noise-pairs is fairly strong,
0.70. However, as shown in Appendix B, a value of 0.70 is somewhat low relative to
a value computed for 5000 noise-pairs and for this bandwidth.)

Numerical studies were done to compare the equal-amplitude noise-pairs used in

this experiment to Rayleigh distributed noise-pairs. It was found that there was no

21

difference in the probability density functions of the IPD and ILD over time. It was
also found that using Rayleigh distributed noise-pairs did not affect the distributions
of st[A<I>] and st[AL].

To perform Experiment 1, the five noise-pairs with the greatest fluctuations of
IPD and the five noise-pairs with the smallest fluctuations of IPD were selected to
form a phase set of ten reproducible noise-pairs. Similarly, the ten noise-pairs with
the greatest and smallest fluctuations of ILD were selected to form a level set. The
convention in this dissertation is to plot detection data of phase sets with circles and
level sets with boxes.

The two channels of noise were computed and downloaded by a Tucker-Davis
AP2 array processor (System II) and converted from a digital signal by 16-bit DACs
(DDl). The buffer size was 4000 samples per channel and the sample rate was 8
ksps. The noise was lowpass filtered with a corner frequency of 4 kHz and a —115
dB / octave roll off. The noises were presented at 70 dB :l: 3 dB with levels determined
by programmable attenuators (PA4) operating in parallel on the two channels. The
levels of the two channels were equal and were randomized over a range of i3 dB
for each of the three intervals within a trial in order to discourage the listener from

trying to use overall level cues to perform the task.

1.1.4 Procedure

Listeners were tested individually, seated in a double—walled sound attenuating room,
and using Sennheiser HD414 headphones. Six runs were devoted to listening to a set
of ten reproducible-noise pairs. A noise-pair could be presented either incoherently -
the dichotic presentation of x], and 3:3 - or it could be presented coherently - the diotic
presentation of xL. A run consisted of 60 trials, where each of the ten reproducible
noise-pairs in a set was presented incoherently a total of six times. Thus, listeners

heard an individual noise-pair incoherently a total of 36 times (six runs times six

22

 

 

 

Figure 7: A pictorial representation of the three-interval sequence used in this exper-
iment. The first interval was always coherent, represented by the straight line on the
far left. The second interval can be either incoherent or coherent. In this figure the
second interval is incoherent, represented by a fuzzyness or increased width between
the ears. The last interval needs to be opposite from the second interval. Therefore,
for this example, it is a coherent, compact image.

presentations per run).

On each trial the listener heard a three-interval sequence, as illustrated in Figure
7. The first interval was the standard interval, which was always a coherent noise.
The second interval was randomly chosen to be either incoherent or coherent. The
third interval was the opposite of the second (e.g. if the second interval was coherent,
the third interval was incoherent). The two coherent presentations were randomly
selected from the remaining nine reproducible noises in the set except that they were
required to be different from the incoherent “odd” interval and to be different from
one another. The inter-interval duration was 150 ms.

Listeners were instructed to “choose the interval that was different from the other
two.” Initial training with noise-pairs with a small values of coherence (i.e. p =
0.95) were used so that the difference between incoherent and coherent stimuli would
be obvious. Feedback was given to the listeners so that the task could be properly
learned. The value of coherence for the noise-pairs was increased to a final value of
0.9922 as listeners became better at identifying incoherent noise-pairs. The training

was finished when listeners could identify the incoherent noise-pair approximately

75% of the time for noise-pairs with a bandwidth of 136 Hz.

23

 

®@@®

 

 

 

Figure 8: The response box used in the experiments.

1 . 1 .5 Data collection

Listeners used a four-button response-box to make decisions as seen in Figure 8. Four
buttons were used so that the listeners could respond to the correct interval with a
confidence estimate. The buttons from left to right were 2!, 2, 3, and 3!, representing
confident second interval, second interval, third interval, and confident third interval
respectively. Listeners were instructed to use a confident response only if there was
no uncertainty as to which interval was incoherent. If a run included more than, one
incorrect confident response, the run was terminated immediately and the listener was
obliged to replace this run. There was no time limit for a response. After a decision
was made by the listener, the next trial began following an inter-trial duration of 900
ms.

There were several reasons to introduce the confidence measure in this experiment.
The first was that for a given coherence, it proved to be noticeably easier to detect
incoherence in some stimuli. Thus, extra weighting was wanted for identifying obvi-
ously incoherent sounds. The second reason was that it was necessary to use the same
waveforms, with a coherence of p = 0.9922, for all the listeners, and it was further de—
sired to use the same coherence for waveforms with different bandwidths. However,
some listeners were better at the task than others, as shown by the percentage of
correct (PC) responses, and some bandwidths led to better performance than others.

Consequently there was a need to increase the “dynamic range” of the experiment to

24

prevent ceiling effects for the most successful listeners and easiest bandwidths.

The data collection procedure kept track of both the percentage of correct re-
sponses, which ignored the confidence estimate (e.g. responses of 2 and 2! were not
treated differently), and a confidence adjusted score (CAS). The CAS is defined as
the number of times the listener responded correctly plus the number of times that
the listener was confident about the correct response. Since an individual noise-pair
was heard 36 times, it was possible for a listener to get a score of 72 if the listener
was able to respond correctly and confidently for all 36 presentations. In comparison
with PC, the use of CAS improved inter-listener correlation, moved p—values of t-tests
to greater significance, and improved the agreement that was achievable by models of

binaural processing. Phrther justification of this technique is given in Appendix A.

1.1 .6 Listeners

The experiments in this chapter employed four male listeners, D, M, P, and W.
Listeners D, M, and P were between the ages of 20—30 and had normal bearing
according to standard audiometric tests and histories. Listener W was 64 and had a
mild bilateral hearing loss, but only at frequencies four octaves above those used in

this experiment. Listener M is the author.

1.1.7 Results

Figure 9 shows the selected P, values and Figure 10 shows the selected CAS values
for the phase set in Experiment 1. The five smallest st[A‘I>] noise-pairs are to the left
of the dashed line. The five largest st[A<I>] noise—pairs are to the right of the dashed
line. The dashed line thus represents a gap of 90 unused noise-pairs. All four listeners
show, in general, a greater P, and CAS for the largest s¢[A<I>] noise-pairs compared
to the smallest.

The statistical test that will be used to test the hypothesis that the five noise-pairs

25

with the largest fluctuations in phase have detection scores that are indistinguishable
from the five noise-pairs with the smallest fluctuations in phase is the two-sample
t-test. If there is a difference between the largest and the smallest fluctuation noise-
pairs, it will be considered significant when there is at least a 95% level of confidence
(the p-value is 0.05 or less). It will be considered more significant if there is at least
a 98% level of confidence (the p-value is 0.02 or less). Significant differences would
mean that the value of the coherence function does not describe the detection data
from the phase and level sets. The t-test will be used on both the phase and the level
sets that are selected in the first three chapters of this dissertation.

In a two-sample t-test, three of four differences were significant at the 0.05 level
for the P, data. All four differences were significant at the 0.02 level for the CA5
data. The individual p—values are shown in Table 2. Figures 9 and 10 also show
that listeners tend to agree upon the difficultly of detecting incoherence in individual
noise-pairs. Table 3 shows the correlations between listeners; all of them are equal to
or greater than 0.391 for the P, data and are equal to or greater than 0.769 for the
CA5 data.

Table 2: The p-values from a one-tailed t-test for 14-Hz bandwidth data. The test
compared the five noise-pairs with the largest fluctuations to the five noise-pairs with
the smallest fluctuations. The p-values with at least a 95% level of confidence are in

bold.

 

P, Phase Level CA5 Phase Level
Listener Set Set Listener Set Set
0.095 0.006 <0.001 <0.001
0.021 0.047 0.002 0.002
0.025 0.007 0.011 <0.001
0.015 0.014 0.001 <0.001

 

 

 

gnaw
Evan

 

 

 

 

 

 

 

Figure 11 shows the P, values and Figure 12 shows the CA5 values for the level set

for Experiment 1. The figures show results similar to Figure 9 and 10 for the phase

26

s,[A<l>] degrees

 

 

2.67 3.18 23.51 40.72
I I l I

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so I l I l I l l l l

 

 

 

L
20 84 4o 99 86 1 44 57 34 ll
Noise-Pair Number

Figure 9: The percent (P,) for five listeners for the phase set of Experiment 1, the 14-
Hz noise-pairs. The noise-pairs were chosen to have the smallest and largest s,[A<I>] in
the collection of 100 noise-pairs. The noise-pairs are rank ordered by increasing s,[A<I>]
along the horizontal axis. The vertical dashed line represents 90 unused reproducible-
noise pairs. The P, values are higher for noise-pairs with the largest s¢[A<I>] than for
noise-pairs with the smallest s,[A<I>] for all listeners. The plots of P, scores vs. noise-
pair serial number show a large measure of agreement among listeners.

27

s+[A<l>] degrees

 

 

2.67 3.18 23.51 40.72
I l T I I 17 I I --_
3.21 : 43‘“: ‘
60 b : "Tare ~04” -
55 - i I, I” “OI "
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' O Listener W
15 - :
10 '- l l I I l ' l l l l l

 

 

 

20 64 4o 99 66144 57 3411
Noise-Pair Number

Figure 10: The confidence adjusted scores (CA5) for five listeners for the phase set of
Experiment 1, the 14-Hz noise-pairs. The CA5 values are higher for noise-pairs with
the largest s,[A<I>] than for noise-pairs with the smallest s,[A<I>] for all listeners. The
plots of CA5 scores vs. noise-pair serial number show a large measure of agreement
among listeners.

28

s,[AL] dB

 

 

 

 

 

0.19 0.53 2.73 2.96
I I I I
100 _- ,fi.’ p , ’-;, 41k 1': 5| 1
r I, l‘k ‘ " 'I- II ‘ ’ i I l
90 I: d, I \ \\fi’ 3” l [I d
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60 . 1 I, 1 f . I LIstener D .
I- l ‘ III
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60 1' \ i : C] Listener W 1
p ‘ I
b \ I ' q
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50 '- \ I ' d
I I 1 I I I I I I I I I

 

4o 95 1‘ 97 ,’ 56 66 60 32 44 69 57
‘, [Noise-Pair Number

‘I
‘I

Figure 11: The percent correct (P,) for five listeners for the level set of Experiment 1,
the 14-Hz noise-pairs. The noise-pairs were chosen to have the smallest and largest
s,[AL] in the collection of 100 noise-pairs.

29

Sf[AL] dB

0.19 0.53 2. 73 2.96
70- I I I I I l ¢—--‘D--::9_--.fi-‘ I
55" I ’ ‘.‘~~-.__-:g
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D Listener M

 

65 I-
60 -
55 -
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35 - U \
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25
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' n

=:""""'-
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l l l l I l l l l l

40 95 97 56 66 80 32 44 69 57
Noise-Pair Number

 

Figure 12: The confidence adjusted scores (CAS) for five listeners for the level set of
Experiment 1, the 14—Hz noise—pairs. The noise-pairs were chosen to have the smallest
and largest s¢[AL] in the collection of 100 noise-pairs.

30

Table 3: The inter-listener correlations for 14-Hz bandwidth IPD data. It can be seen
that correlations between listeners are near 1.0 for the CAS data. It can also be seen
that using the CAS data increases the average correlation compared to the PC data.

 

 

 

 

PC D M P W

D 1 0.732 0.614 0.391

M — 1 0.421 0.796

P — — 1 0.429

W — — — 1
Average 0.564

 

 

 

 

CAS D M P W

 

D 1 0.902 0.846 0.666
M — 1 0.769 0.970
P — — 1 0.787
w - — — 1

 

 

 

 

Average 0.857

 

set. As shown by Table 2, all the p-values are significant at the 0.05 level for the PC
data and at the 0.02 level for the CAS data. Table 4 shows correlations between the
individual listeners are all greater than or equal to 0.291 for the Pc data and increase

to greater than or equal to 0.855 for the CAS data.

1 .1 .8 Discussion

Experiment 1 shows that the peak of the cross-correlation function is not an ade-
quate predictor of the detectability of incoherence for narrowband noise. Instead, the
fluctuations in interaural phase and interaural level clearly play a role in incoherence
detection. This can explicitly be seen in the p—values of the t-tests for the phase and
level sets chosen in this experiment.

The large inter-listener correlations of this experiment indicates that listeners
agree in detail about the kinds of fluctuations that are easy or hard to detect. This

correlation can be seen graphically in Figures 9—12 or numerically in Tables 3 and 4.

31

Table 4: The inter-listener correlations for 14-Hz bandwidth ILD data. Correlations
are comparable to those for the IPD data. Once again, inter-listener correlations are
higher for the CAS data compared to the PC data.

 

 

 

 

PC D M P W

D 1 0.291 0.707 0.447

M — 1 0.662 0.967

P — — 1 0.774

W — —— — 1
Average 0.641

 

 

 

 

CAS D M P W

 

D 1 0.855 0.931 0.925
M — 1 0.885 0.974
P — — 1 0.933
W — — — 1

 

 

 

 

Average 0.917

 

It general, p—values moved to greater significance and inter-listener correlations
increased when using the CAS values over the PC values in this experiment. Although
it was probably not necessary to introduce the CAS to show conclusive results that
the cross-correlation function is not an adequate predictor of the detectability of
incoherence for narrowband noise, it was predicted that the CAS would be necessary
for larger bandwidths.

Lastly, it should be reported that some noise-pairs led to values of percent cor-
rect that were well below chance. Through informal listening experiments, it was
found that these noise-pairs had very little roughness or action in the envelope of
their waveforms. It seems possible that when the fluctuations of IPD and ILD are
barely detectable, listeners may sometimes mistake roughness or action for incoher-
ence. They would then be reluctant to say that a particularly smooth sounding
noise-pair is incoherent, which could lead to a PC less than 50%. Figure 13 shows the

left and right channels for three sample noise-pairs. It appears that the enve10pe for

32

noise-pair B is smoother (more gradually sloped) or has less action than the other
two noise-pairs. Listeners detected the incoherence in noise-pair B with a PC of only
27%. This can be compared to noise-pair A with PC = 96% and noise-pair C with PC
= 71%. This idea of using monaural cues during incoherence detection will be more

thoroughly explored in Experiment 5.

33

 

 

   

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

 

 

   

 

 

 

 

 

 

a g 5 t 4
E. 5
57’ >5" A
h >.
:3 ‘5:
x x
.10 h I I I I I I I I I ‘ _ l I I L I I I I I I l
0 250 500 100 250 500
t (ms) t (ms)
10 r T ‘ l0 ’ T T—I I fifi
a 5 7 *
z .
S
if 0 B
>
‘c’: .
X _5 _
. i C
-10 ’ l l ‘ l — 0 ’ 1 I L
0 250 500 l 0 250 500
t (ms) t (ms)
10 ’ T I fi fi 10 I w I
l .
5 r .
. 0 l C
:- -s:~ a
E . E 1
_10 A I I I I I I I I _ 0 I I I I l l I I l
0 250 500 l 0 250 500
t (ms) t (ms)

Figure 13: The left and right channels for three sample noise-pairs A, B, and C with p
= 0.9922 and a bandwidth of 14 Hz. Each channel was normalized by the RMS value
of the channel. It appears that B is smoother or has less action in it compared to the
other noise-pairs, which led to the hypothesis that listeners may be using monaural
cues during incoherence detection for noise-pairs with small interaural fluctuations.

34

1.2 EXPERIMENT 2: CRITICAL BANDWIDTH

Experiment 2 was identical to Experiment 1 except that the bandwidth was increased
from 14 Hz to 108 Hz, near a critical bandwidth at 500 Hz. The value of the coherence

remained fixed at 0.9922.

1.2.1 Method

As for Experiment 1, the geometric mean frequency was 500 Hz and the spectral
spacing was 2 Hz. The bandwidth was increased to 108 Hz. As for Experiment 1, the
spectral edges were 5 Hz wide. Therefore, components between 444 and 449 Hz and
between 555 and 560 Hz were given a raised-cosine edge; components between 449 and
555 Hz had unity amplitude. The variation of the interaural parameters as a function
of time can be seen in Figure 14. Notice that the fluctuations are approximately eight
times faster when compared with Figure 5 because the bandwidth is approximately
eight times larger. Note that with a larger bandwidth of 108 Hz, the conversion of
IPD to ITD is not necessarily as straightforward as in the 14-Hz bandwidth case.
However, given an IPD, the value of the ITDs is uncertain by only approximately
10% for this bandwidth.

Another collection of 100 noise-pairs was used in this experiment. A phase set
and level set were chosen from the collection, as in Experiment 1. Figure 15 shows
st[A<I>] versus st[AL] for the first collection of 108-Hz bandwidth noise-pairs. The
black dots represent the noise-pairs with 14-Hz bandwidth from Experiment 1 for
comparison. The means of the distributions of fluctuations increased slightly when
compared to the the 14-Hz bandwidth waveforms, but the standard deviations over
the noise-pair ensemble of the phase fluctuations decreased from 6.66 degrees to 3.72
degrees. The standard deviation of the level fluctuations decreased from 0.68 dB to
0.40 dB. The correlation between st[A<I>] and st[AL], evaluated over the ensembles of

100 waveforms, was essentially the same, 0.73 compared to 0.70. Appendix B shows

35

s,(A¢)=l4.76 degrees s,(AL)=l.62 dB
50.f...... 15,rf......f,

 

 

 

MI (degrees)
N
O O
f
6::

 

 

 

 

 

 

 

 

 

 

 

 

 

0 250 500 0 250 500
1‘ (ms) t (ms)

Figure 14: The IPD and ILD plotted as a function of time for an arbitrarily chosen
108-Hz bandwidth noise-pair. Above the plot are the fluctuation values of the IPD
and ILD. Note that when compared with Figure 5, the fluctuations are about eight
times faster.

that a value of 0.73 is in line with expectation based on statistics for 5000 noise-pairs.

1.2.2 Results

Figures 16 and 17 show the PC and CAS values for the phase set for the 108-Hz
noise-pairs of Experiment 2. A comparison between the phase set of this experiment
and the phase set of Experiment 1 show that listeners are not nearly as good at
distinguishing incoherence from coherence at this larger bandwidth. Similar results
are seen for the level set in Figures 18 and 19.

The Figures 16 and 18 show Listeners D and M near the ceiling of Pc for many
of the ten noise-pairs and always above 75%. However, Listeners D and M do not
reach the ceiling for CAS as seen in Figure 17 and 19. Listeners P and W are not so
dramatically close to ceiling for Pc or CAS.

Table 5 shows that only one of the four t-tests from the phase sets PC values led
to differences that were significant at the 0.05 level between the results for the five
largest fluctuations and the results for the five smallest fluctuations. This increased

to three of four significant p—values when using the CAS values. One of the four

36

 

U'r'fvtirtf'IU'UUIVVffi

 

 

 

 

m

<- . ‘

i ,

0 L O _1
<1- .

= i

In -_ :

m . -

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88 r 1

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bun -_ .:

8‘“ : :

Ho L _:

0N . .

S 1 1

59 L SW = 108 Hz :

o i u(s,[A¢]) = 13.40 _

"' u(s,[AL]) = 1.73 1

~ 0(st[A¢]) = 3.72 3

‘0 r a(s,[AL]) = 0.40 -

:. corr = 0.73 t

o .4 I I I l I I I I I I I I I l I 141 I l I I I I E

0 1 2 3 4 5

Sf[AL] dB

Figure 15: The fluctuations of IPD versus fluctuations of ILD for the collection of
100 reproducible noise-pairs having a 108-Hz bandwidth, as used in Experiments 2.
Each noise-pair is labeled by a serial number indicating only the order of creation.
The means, standard deviations, and IPD-ILD correlation of the distributions are re-
ported. The black dots represent the 14-Hz bandwidth noise-pairs from the collection
in Experiment 1.

37

sflA<l>l degrees
3.21 8.50 21.51 24.25

 

 

 

 

I I I
100: 6‘ b—-|--‘~-,.5~“ l I ”.6 1
. \ ”\ lp‘y‘I‘O. ' l’ ‘--.H---. .
: \ ’ \\ ’ I j- :1
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60 T : O Listener M j
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' ‘1’ 4». l’ 1’ ‘ I ‘
70 l: l"\ I, ‘ “‘0' , : \‘ l” 1
b O \\ I, \ I : ‘ d
C ’ ‘ ,’ 1 O Listener P I
b \ .
50 f 1 [I : O Listener W 1
; ‘~ ' 1 ;
b \ ” : ‘
50 h I I l \u ’ l I I I l I -

 

49 9310 3' 64 73 9 4o 32 76
Noise-Pair Number

Figure 16: The Pc results for the phase set of Experiment 2 with a 108-Hz bandwidth.
The phase set was constructed by the same method as was used in Experiment 1.
When compared to the 14-Hz bandwidth phase set in Figure 9, there is a much less

drastic difference between noise-pairs with the largest and smallest fluctuations of
IPD.

38

s,[A<l>] degrees
8.21 8.50 21.51 24.25

T I l I I I I I I I

 

70
65
60
55
50
45
40 \ \‘7
35 ‘ ' - —O
30
25 -
20 -
15 1-
10 -

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65- :
60'- :
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50- : ~
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I
)
I

j
l

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-O”
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I I

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CAS
‘8 ‘b

1

O Listener D
O Listener M

Q
I
I
I
I
\4
\
I
0'
\
——-——-—-_--———\-\.-—--—
l

 

IL]

L

45 - , o‘ .0. -
40 . ’ x ,I’ x
35 , . ‘0 ,4‘ x _
i- In I ,‘.’ ‘\8
30b "0.3,:8?‘~ ’, ’4".-~- ,’ -
25 _ \"’ \\ U , | .‘
20 _ \ ,I 1 O Listener P
"’ : O Listener W
15 - ,
I

CAS

I

‘1-
O’

I

10-

 

 

l J l l J l A l I l

49 9310 54 84 73 9 40 32 75
Noise-Pair Number

 

Figure 17: The CAS results for the phase set of Experiment 2 with a 108-Hz band-
width. The phase set was constructed by the same method as was used in Experiment
1. When compared to the 14—Hz bandwidth phase set in Figure 10, there is a much
less drastic difference between noise-pairs with the largest and smallest fluctuations

of IPD.

39

SIIAL] dB

 

 

 

 

0.91 1.15 2.50 2.66
100L- 151‘ ' T ' ' 4,45.-- 1 ,-—fl1~‘~ ' ,45 -
; \\ ’8‘ ’0’. ” ‘ ‘D’ ‘
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70>- \\ I, I \‘U 1
I- \ ’ I \ cl
P \ I I i 1
50; i : ;
: l I Listener P 1
C : El Listener W 1
50' I 1 I 1 I . l I J I I 1

 

49 93 54 5715 53 38 9 33 73
Noise-Pair Number

Figure 18: The Pc results for the level set of Experiment 2 with a 108-Hz bandwidth.
The phase set was constructed by the same method as was used in Experiment 1.
When compared to the 14-Hz bandwidth phase set in Figure 11, there is a much less
drastic difference between noise-pairs with the largest and smallest fluctuations of

ILD.

40

 

7O
65 -
60 " \

55 '- x I

\ I
50 "' \ x I
‘ I ‘z‘ )1”
45 - \ I \B‘ M -I
a a ’ ‘\ Ill

40'.
35r- ”t! I .I
30-
25-
20-
15+
10*-

70I— -
65'-
50-
55-
50-
45'
40-

CAS

I
I
I
l I Listener D
: Cl Listener M
I

I

 

CAS
q‘......_.._.....
\
I
I
\
l J J l

\

35- 33*

30 - Dan—330’ In”
259 3‘,

20-

I5-
10-

\

-T‘.‘ \ I
‘i—«i-
“I
I Listener P
CI Listener W

I
\
3U’

l

l

_--_--_--\.

 

 

L l l l l l l l l l

49 93 54 5715 53 33 9 33 73
Noise-Pair Number

 

Figure 19: The CAS results for the level set of Experiment 2 with a 108-Hz bandwidth.
The phase set was constructed by the same method as was used in Experiment 1.
When compared to the 14—Hz bandwidth phase set in Figure 12, there is a much less
drastic difference between noise-pairs with the largest and smallest fluctuations of
IPD.

41

t-tests from the level sets for the PC values led to differences that were significant at

the 0.05 level. This increased to three of four significant p-values when using the CAS

values.

Table 5: The p-values from a one-tailed t-test for 108-Hz bandwidth data.

 

 

 

 

Pc Phase Level CAS Phase Level
Listener Set Set Listener Set Set
D 0.061 0.029 D 0.024 0.007
M 0.085 0.060 M 0.019 0.047
P 0.248 0.226 P 0.187 0.187
W 0.005 0.069 W 0.002 0.026

 

 

 

 

 

 

 

Table 6: Inter-listener correlations for 108-Hz bandwidth phase set.

 

 

 

 

 

 

 

 

 

 

Pc D M P W
D 1 0.071 -0.044 0.634
M — 1 0.148 0.202
P — —- 1 0.337
W — — — 1
Average 0.225
CA8 D M P W
D 1 0.422 0.053 0.668
M — 1 0.312 0.328
P — — 1 0.492
W - — — 1
Average 0.379

 

 

 

 

Further, as shown in Tables 6 and 7, the correlation between listeners was smaller
for the wider bandwidth for all listener pairs. The correlation between listeners was
0.225 on average for the phase set for the PC data. This increased to 0.379 for the
CAS' data. Likewise, there was an increase in inter-listener correlation for the level

set, from 0.117 to 0.278, when using CAS data over the Pc data.

42

Table 7: Inter-listener correlations for 108-Hz bandwidth level set.

 

 

 

 

 

 

 

 

 

 

Pc D M P W
D 1 0.000 0.007 0.093
M - 1 —0.031 —0.093
P — — 1 0.724
W — — — 1
Average 0.1 17
CAS D M P W
D 1 0.543 —0.039 0.583
M — 1 —0.026 0.298
P — — 1 0.309
W — — — 1
Average 0.278

 

 

 

 

1.2.3 Discussion

The standard deviation of the fluctuations of st[A<I>] and st[AL] computed across
the 100 different waveforms of the ensemble decreased by more than 40% when the
bandwidth was increased from 14 Hz to 108 Hz. Since these fluctuations were found
to correlate with incoherence detection from Experiment 1, it was not surprising to
find that there was less variation in the listeners’ ability to detect incoherence at the
wider bandwidth.

The bandwidth of 108 Hz may be of special interest because this bandwidth ap-
proximately corresponds to a critical bandwidth at 500 Hz, and critical band noise
has often been used in binaural experiments. For instance, Koehnke et al. (1986)
used a noise with a bandwidth of 114 Hz centered on 500 Hz, and Evilsizer et al.
(2002) used a bandwidth of 100 Hz. It was found that the tests comparing detection
performance (CAS) with the size of the phase and level fluctuations led to a signifi-
cant difference at the 0.05 level on six of eight of the t-tests. This can be compared to

all of the tests being significant at the 0.02 level in Experiment 1. The PC results had

43

s,(A¢)=13.46 degrees 51(AL)=1.78 dB
r v r I r 15 I . . . .

 

 

v

    

       

4o 10-
gee. A 5
L [D
8’ o 3 o
3 _I
o—zo <1 -5-
<

 

 

 

 

0 250 500 0 250 500
t (ms) t (ms)

Figure 20: The IPD and ILD plotted as a function of time for an arbitrary 2396-Hz
bandwidth noise-pair. Above the plot are the fluctuation values of the IPD and ILD.
only two significant p—values at the 0.05 level compared to seven significant p—values
in Experiment 1. It was expected that if the bandwidth were further increased the
variation in fluctuations would continue to decrease and the incoherence detection
performance would be approximately the same for all the waveforms in the ensem-
ble. In that case, the ability to detect incoherence would be only a function of the

incoherence measure itself. That expectation led to Experiment 3.

1.3 EXPERIMENT 3: WIDE BANDWIDTH
1.3.1 Method

Experiment 3 was identical to Experiments 1 and 2 except that the bandwidth was
increased to 2394 Hz. The geometric mean frequency of 500 Hz and the coherence of
0.9922 remained the same. Spectral components between 105 and 2495 Hz had unity
amplitude and components in the ranges 100—105 and 2495—2500 Hz were shaped by
the raised—cosine window. The variation of the interaural parameters can be seen in
Figure 20.

Figure 21 shows the distribution of interaural phase and level fluctuations for one-

hundred 2394—Hz bandwidth noises. The corresponding values for Experiments 1 and

44

 

I U V I r U ‘ fi' 1 T I U ' I U U U l V r U V

15 20 25 30 35 40 45
I
I

 

 

 

 

(D
a) .-
0) ' .
3, I . 2
«I f ‘ 1
‘3 : :
'3' I- -Z
,3 Z 2
J" L BW = 2394 Hz .1
o =_ u(s,[A<I>]) = 13.5 55 _:
"‘ : u(SI[AL]) = 1.76 ;
; a(sf[A<l>]) = 1.70 :
m :- o(s,[AI.]) = 0.11 1
’ ' corr = 0.27 .1
o l I I L l l I l I l I 4 J I l 1 l I l I I A I l d
0 1 2 3 4 5

SI[AL] dB

Figure 21: Fluctuations of IPD versus fluctuations of ILD for the collection of 100 re-
producible noise-pairs having a 2394-Hz bandwidth, as used in Experiments 3. Each
noise-pair is labeled by a serial number indicating only the order of creation. The
means, standard deviations, and IPD-ILD correlation of the distributions are re-
ported. The small black dots represent the 14—Hz bandwidth noise—pairs from the
collection in Experiment 1. The large black dots represent the 108-Hz bandwidth
noise-pairs from the collection in Experiment 2.

2 are shown by the small black dots. The mean of the distribution remained about
the same as in Experiments 2 in that the ensemble average phase fluctuation was
about 13 degrees and the level fluctuation was about 1.7 dB. However, the standard
deviations of the phase and level fluctuations over the collection of 100 noise-pairs
decreased dramatically when the bandwidth was increased to 2394 Hz, as shown by

the a values in Figure 21, respectively 1.07 degrees and 0.11 dB. The correlation

between level and phase fluctuations decreased to 0.27.

1.3.2 Results

The results of the incoherence detection experiments, expressed as Pc and CAS values,

are shown in Figures 22—25 for the phase and level sets. Listeners D and M, the

45

st[A<l>] degrees

 

 

10.95 1 1.87 15.63 16.34
I l T I I I I I l I
100 I: O : .:
p \ q
C X : O Listener D I
90 1' \\ .0“ | O Listener M j
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so 1 i I x .‘
I I I I I A’ I I I I

 

 

 

97 32 73 17 52 039 57 75 74 93
Noise-Pair Number

Figure 22: The PC data for the 2394-Hz phase set.

listeners with consistently the highest values of Pc in the previous experiments, are
near the ceiling for only a few noise-pairs with a 2394-Hz bandwidth.

With four listeners and two sets there were eight possible significance tests, and
Table 8 shows that only one of them led to a significant difference at the 0.05 level
for PC; none for CAS. Further, Table 9 shows inter-listener correlations comparable
to those in Experiment 2. However, Table 10 shows an overall negative inter-listener

correlation, mainly because of Listener W.

46

CAS

CA8

70
65
60
55
50
45
40
35
3O
25
20

15-
10*-

70
65
60
55
50
45
4O
35
30
25
20

15-

10

Sf[A¢] degrees

10.95 1 1.87 15.63 16.34

 

I I I I I I I I I

O Listener D
O Listener M

.0..- 9
s I ‘ ” I) _ _
‘ 31* -o-’---0’ ~13: 9‘0

 

 

O Listener P
O Listener W

\ ,’D\
\ I \
‘ ‘3
-J
\\ u\>".‘ll ~‘s" \
\ I \ I
V U

__---_?:-----_____--_-
P
6 7b

1 l I L l L I l l

 

 

97

32 73 17 52 29 57 75 74 93
Noise-Pair Number

Figure 23: The CAS data for the 2394-Hz phase set.

47

100

90

80

70

60

50
100

90

80

70

60

50

s,[AL] dB

 

 

 

 

 

1.45 1.59 1.98 2.16
.- I I I I I I I I I I
b I 1
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. t1 1 I Listener D .
f : C1 Listener M j
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f : El Listener W 1
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: 5.--.- 1 \x “I U 1
D ' " ‘
- I .,
I I I J I I I I I I
28 12 73 62 3 49 15 38 29 20
Noise-Pair Number
Figure 24: The Pc data for the 2394-Hz level set.

48

CAS

CA5

70
65
60
55
50
45
4O
35
30
25
20
15
10

70
65
60
55
50
45
40
35

30-

25
20
15
10

$f[AI-] dB

1.45 1.59 1.98

2.16

 

I I T I T T I I I

I
I ‘\
\

-‘I\
-4. ‘

I
\ I
\ ---I----I*"' N- ,
lit-"‘0: EVD-HdHQ‘ 1,1
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I \ I,

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I”

I
I

I

I Listener D
D Listener M

P

.1

I

 

 

I Listener P
D Listener W

 

 

2512 73 52 3 4915 35 29
Noise-Pair Number

Figure 25: The CAS data for the 2394-Hz level set.

49

Table 8: The p—values from a one—tailed t-test for 108-Hz bandwidth data.

 

 

 

 

 

PC Phase Level CAS Phase Level
Listener Set Set Listener Set Set
D 0.772 0.230 D 0.907 0.375
M 0.981 0.049 M 0.981 0.080
P 0.683 0.633 P 0.683 0.654
W 0.964 0.753 W 0.947 0.866

 

 

 

 

 

 

Table 9: Inter-listener correlations for 2394-Hz bandwidth phase set.

 

 

 

 

 

 

 

 

 

 

PC D M P W
D 1 0.585 0.161 0.103
M — 1 0.165 0.363
P — — 1 —0.125
W — — — 1
Average 0.208
CAS' D M P W
D 1 0.572 .—0.059 0.426
M — 1 0.165 0.377
P — — 1 0.031
W — — — 1
Average 0.252

 

 

 

 

1.3.3 Discussion

Experiments 1, 2, and 3 clearly show trends in the nature of interaural incoherence de-
tection. For narrow bands, detection depends on the details of interaural fluctuations,
and it is not possible to predict detection performance if one knows only the value
of coherence. As the bandwidth increases, the coherence becomes a better predictor
of detection performance. The wideband limit, where the coherence statistic itself
becomes adequate to predict performance for all stimuli, was apparently reached for

the bandwidth of 2394 Hz because no systematic differences appeared between those

50

Table 10: Inter-listener correlations for 2394-Hz bandwidth level set.

 

 

 

 

PC D M P W

D 1 0.364 0.024 —0.153

M - 1 0.042 —O.439

P — — 1 -0.474

W — — — 1
Average ——0. 106

 

 

 

 

CAS D M P W

 

D 1 0.253 0.136 0.130
M — 1 0.043 -0.683
P — — 1 —O.488
W - - — 1

 

 

 

 

Average -0.105

 

noise-pairs with the largest fluctuations and those noise-pairs with the smallest.
The above interpretation, however, is not flawless. The noise-pairs for Experiment
3 were chosen on the basis of fluctuations computed for the entire band of noise, as
presented to the listeners. However, it is possible that listeners do not perform the
incoherence detection experiment by listening to the entire band. Instead, they may
listen to a narrower portion of the band - perhaps one critical band width wide. If
so, then the choices of noise—pairs were inappropriate for the band actually used, and
further, one would have no way of knowing a priori which band to examine when
selecting stimuli based on large and small fluctuations. If this were true, then the
reasoning by which it was concluded that the wideband limit is reached in Experiment
3 would be circular reasoning. One piece of evidence in favor of this view is found
in the MLD experiments by van de Par and Kohlrausch (1999) which suggested that
listeners detect an S7r sine in noise by listening to a critical band around the tone.
It is believed that the above criticism is incorrect and that in a wide band in-
coherence detection task - perhaps unlike a wideband MLD task - listeners do not

attend to only a portion of the band. The evidence for that belief is that the listeners

51

performed much less well for the wide band in Experiment 3 compared to the 108-Hz
band of Experiment 2. Comparing CA5 values in Figures 17 and 23 (phase sets)
and comparing values in Figures 19 and 25 (level sets) show that the most successful
listeners, D and M, had higher scores even for the most difficult (lowest values of
PC) noise-pairs at 108 Hz than for any noise-pairs with wide bands. Listeners P and
W also scored consistently better at 108-Hz for the level sets. If listeners were able
to take advantage of the slower and potentially larger fluctuations in a critical-band
portion of the wide hand one would have expected that some listener would have
scored well for some one of the noise-pairs, contrary to the results of Experiment 3.
Consequently it is believed that Experiment 3 reached a wideband limit wherein the

relevant interaural fluctuations are completely characterized by the coherence value.

1.4 EXPERIMENT 4: THE ROLE OF BANDWIDTH

Experiments 1, 2, and 3 demonstrated that, as the bandwidth increases, two effects
occur. First, the ranges of fluctuations in IPD and ILD become narrower. Second,
the ability of listeners to detect incoherence depends less on the individual noise-
pairs and is better determined by the value of coherence itself. According to the
hypothesis of this chapter, the second effect is the direct result of the first, and the
main effect of a variation in bandwidth is to alter the distributions of interaural

variances. Experiment 4 was designed to test this idea.

1.4.1 Method

To test the hypothesis, a subset of noise-pairs was assembled from a new collection of
1000 more pairs with a bandwidth of 14 Hz to make a “matched set” whose members
were selected to best match the fluctuations in the noise-pairs from Experiment 2,
which had a bandwidth of 108 Hz. Experiment 2 included 20 noise-pairs, ten for the

phase set and ten for the level set, as determined by the five largest and five smallest

52

 

 

 

 

m U'I'V'VTV'T—IUII'V'TIV'I'I'U'T1I'I'V'I'U'I'UT'IV'V
N ‘ . ‘ ' "
. .1, ‘-
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3 L ' . ..
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Ln- ', ,. . . _,
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0.5 l 1.5 2 2.5 3

Sf[AL] dB

Figure 26: The matched set for Experiment 4. The 17 noise-pairs from phase set 1
and level set 1 in Experiment 2 were matched in fluctuations of IPD and fluctuations
of ILD by the closest noise-pairs from Experiment 1, which are shown as black dots.
fluctuations. However, phase and level fluctuations tend to be correlated and five of
the noise-pairs were common to the phase and level sets. Therefore, there were only
15 different noise-pairs in Experiment 2. For each of these 108-Hz bandwidth noise-
pairs a 14-Hz bandwidth noise-pair was selected that best matched the fluctuations
in phase and level. The selection is illustrated by the 15 open and filled circles in
Figure 26. Phase and level sets using the matched noise-pairs formed the stimuli for

Experiment 4, which was otherwise identical to the other experiments of this chapter.

1.4.2 Results

According to the working hypothesis, the detection scores for the matched 14-Hz sets
from Experiment 4 ought to be identical to the detection scores in the 108-Hz sets
from Experiment 2. The results of the comparison are shown in Figures 27—30 for

the phase and level sets, and for the PC and CAS values. The phase set data in

53

Figures 27 and 28 show that the values of PC and CAS are comparable for the two
bandwidths when the IPD fluctuations are matched for Listeners D and M. However,
for Listeners P and W performance is better for the 14-Hz bandwidth than for the
108-Hz bandwidth.

The level set data in Figures 29 and 30 show comparable PC and CAS values for
the two bandwidths for all the listeners, though Listeners P and W still tend to show
better performance at the smaller bandwidth - better on 15 of 20 possible comparisons
for PC and 14 of 20 possible comparisons for CAS. Therefore, the raw data, shown
in Figures 27—30, offer modest support for the hypothesis that bandwidth should be
unimportant if the sizes of fluctuations are matched.

The hypothesis can be further tested by examining the relative detectability of
the noise-pairs with the largest interaural fluctuations vs. the noise—pairs with the
smallest interaural fluctuations. These are, respectively, to the right and to the left
of the vertical dashed line in Figures 27-30. A t-test of the hypothesis that PC and
CAS scores are higher for the five noise-pairs on the right led to the p-values in Table
11.

There, it can be seen that two of eight p-values are significant at the 0.05 level
for the 14-Hz matched sets PC values, and that two of eight p-values are significant
at that level for the targeted 108-Hz sets. It can also be seen that three of eight
p—values are significant at the 0.05 level for the 14-Hz matched sets CAS values, and
that six of eight p-values are significant at that level for the targeted 108-Hz sets. By
comparison, seven of eight p—values were significant at the 0.05 level for the 14-Hz
bandwidth PC data and all eight p-values were significant at the 0.02 level for the 14-
Hz bandwidth CAS data in Experiment 1. Only one of the p-values were significant
even at the 0.05 level for the wide bandwidth Pc data and none of the p-values were
significant even at the 0.05 level for the wide bandwidth CAS data in Experiment 3.

Thus, the matched phase and level sets appear to have approximately matched the

54

relative difference in performance between the noise-pairs in the Experiment 2 sets,
consistent with the hypothesis that the size of interaural fluctuations determines the
detection of incoherence.

However, there are differences between the results of Experiments 2 and 4. As
noted above, there is a tendency for listeners P and W to score better on the 14-Hz
bandwidth sets (Experiment 4). More impressive, a comparison of the inter-listener
correlations in Tables 12 and 13 show that all twelve of the correlations are higher
for the 14—Hz matched sets than for the correlations in Tables 7 and 9 for the 108-
Hz bandwidth sets. Averaged over listener pairs and over phase and level sets, the
inter-listener correlation was 0.601 for the 14-Hz bandwidth and only 0.171 for the
108-Hz bandwidth for the Pc results. Likewise, the averaged inter-listener correlation
was 0.700 for the 14-Hz bandwidth and only 0.329 for the 108-Hz bandwidth for the
CAS results.

Table 11: The p—values from a one-tailed t-test for matched phase and level data.

 

 

 

 

 

 

 

 

 

PC Phase Level CAS Phase Level
Listener Set Set Listener Set Set
D 0.428 0.111 D 0.103 0.077
M 0.408 0.421 M 0.384 0.315
P 0.025 0.050 P 0.006 0.038
W 0.163 0.308 W 0.042 0.117

 

1.4.3 Discussion

 

Experiment 4 attempted to construct a set of noise-pairs with a 14—Hz bandwidth
that would lead to the same patterns of detection performance that had been seen
in Experiment 2, which used noise-pairs with a 108-Hz bandwidth. This was done

by best matching the values of st[A<I>] and st[AL] of the Experiment 2 noise-pairs

55

24.26

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Noise-Pair Number

Figure 27: Matched phase set Pc data.

56

2426

2L5!

s+[A<l>] degrees
5.50

621

 

 

 

 

 

54 54 73 9 4o 32 75
Noise-Pair Number

10

93

49

 

 

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7 6 5 4 3 2 7 6 5 4 3 2 7 6 5 4 3 2 7 6 5 4 3 2

Figure 28: Matched phase set CAS data.

57

 

256

250

SJAL] degrees
1J5

 

 

 

 

 

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on. Un_ Un_ Ml

47 100 92 80 32

Noise-Pair Number

19
58

5

79

81
Figure 29: Matched level set PC data.

61

 

2.66

2.50

1.15

sf[AL] degrees

0.91

 

 

 

 

 

 

 

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an 79 5 19 47 tOO 92 so 32
Noise-Pair Number

61

Figure 30: Matched level set GAS data.

59

Table 12: Inter-listener correlations for matched phase set.

 

 

 

 

Pc D M P W

D 1 0.681 0.599 0.750

M — 1 0.644 0.783

P — — 1 0.804

W —- — — 1
Average 0.710

 

 

 

 

CAS D M P W

 

D 1 0.708 0.737 0.808
M — 1 0.661 0.799
P — — 1 0.912
W — — — 1

 

 

 

 

Average 0.771

 

with noise-pairs having a 14-Hz bandwidth. Experiment 4 was partially successful in
that the number of significant p—values was comparable in Experiments 4 and 2, and
quite different from Experiments 1 and 3. It is clear that the fluctuation matching
procedure caused the 14-Hz bandwidth noise-pairs of Experiment 4 to behave more
like the 108—Hz noise-pairs of Experiment 2 than like 14—Hz noise-pairs of Experiment
1.

Although the values of Pc and CAS for the 108-Hz bandwidth (Experiment 2)
and the 14-Hz bandwidth (Experiment 4) were interleaved for two of the listeners,
the values of PC and CAS were higher for the 14-Hz bandwidth for the other two, and
inter-listener correlations were higher overall for the 14-Hz bandwidth. Thus, there
seems to be an advantage for the smaller bandwidth, whether the fluctuations are large
or small. An advantage for smaller bandwidth was also found by Gabriel and Colburn
(1981) where the jnd for detecting incoherence decreased with decreasing bandwidth.
It is conjectured that the slowness of the fluctuations at the smaller bandwidth plays
a major role in improving detection. Fluctuation speed was identified as an important

factor in the MLD experiments by Zurek and Durlach (1987).

60

Table 13: Inter-listener correlations for matched level set.

 

 

 

 

 

 

 

 

 

 

PC D M P W
D 1 0.256 0.681 0.752
M — 1 0.115 0.758
P — — 1 0.387
W — — — 1
Average 0.491
CAS D M P W
D 1 0.714 0.659 0.679
M — 1 0.561 0.691
P - — 1 0.464
W — — — 1
Average 0.628

 

 

61

 

 

1.5 EXPERIMENT 5: EFFECT OF MONAURAL CUES

During the course of the numerical study of interaural fluctuations it was decided to
compare the interaural fluctuations in noise-pairs with the envelope fluctuations in
the left-ear signal itself. (Left and right signals were so similar that it did not matter
which was chosen.) A pn'orz' it seemed possible that noise-pairs with especially large
(small) interaural fluctuations might often be derived from individual noise tokens
with especially large (small) envelope fluctuations.

To make the comparison the envelope fluctuation was calculated,

 

ME] = (J11; t‘élEU) - F12 (12)

where E (t) is the envelope defined in Eq. 7, and E is the average over the time of the
stimulus. Calculations with 1000 noise-pairs with 14-Hz bandwidth - stochastically
identical to the pairs of Experiment 1 - showed a positive correlation between en-
velope fluctuations and interaural fluctuations. Specifically, the correlation between
st[E] and s¢[AL] was 0.48. The correlation between s¢[E] and st[A<I>] was 0.43. Since
the level difference is calculated from the envelope, the first correlation seems intu-
itive. The latter correlation would be hard to understand were it not for the strong
correlation between the standard deviations of interaural phase and level differences,
as shown in Figs. 6, 15, and 21.

Next, the same calculations were made for the 20 noise—pairs actually used in Ex-
periment 1. The interaural phase fluctuations and the interaural level fluctuations
correlated with the monaural envelope fluctuations at levels of 0.59 and 0.65 respec-
tively. Evidently, those waveforms with interaural fluctuations that are especially
large or small particularly owe their binaural character to the envelope of the original
generating noise token.

Given the positive correlation between interaural and monaural fluctuations, it

62

seemed possible that there might be information in the monaural signals that was
used by listeners in performing the experiments of this chapter. Because of the
evident importance of fluctuations in Experiment 1, attention centered on the stimuli

used there, with a bandwidth of 14 Hz.

1.5.1 Diotic experiment method

Experiment 5 was identical to Experiment 1 except for the important difference that
the left-ear signal of Experiment 1 was the signal for both ears in Experiment 5. In
a second difference, the listeners in Experiment 5 had all completed Experiments 1
through 4 and therefore were highly experienced. The listeners were given three-
interval sequences as before and were asked to apply the same strategy that they had
used in the previous experiments. There was reason to believe that this approach
might be successful because all the listeners volunteered that in the previous exper-
iments they based their decisions on a sense of width, choosing the interval - either
two or three - with the larger width. It seemed possible that the sense of roughness
or other “action” associated with a diotic stimulus having large fluctuations could be
associated with a sense of width. Consequently, it was expected that each trial of
Experiment 5 would constitute a comparison between apparent “widths” for a par-
ticular identified noise and a different, randomly-chosen, noise from the set of ten.

The stimulus sets were the phase set and level set from Experiment 1.

1.5.2 Results

Listeners made a negligible number of “confident” responses. Apparently the strong
sensation of width elicited by some of the dichotic stimuli did not occur with any of
the diotic noises. Therefore, the CAS had little value and results of Experiment 5
were plotted only in terms of the percentage of the trials on which a given noise was

selected over other noises. The statistic will be called P,, percent selected. It can be

63

 

 

 

 

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20 84 4o 99 as t 44 57 34 ll
Noise-Pair Number

Figure 31: Comparison between Pc and P, data for the phase set of Experiment 1
and the same noise-pairs with just the left channel presented diotically.

compared with PC, the percent correct in the dichotic experiments.

1. Large fluctuation comparison

Particular interest centered on the five noise-pairs for which the interaural fluctuations
were the greatest. By examining the scores from the diotic experiment it was expected
to gain insight into the role that envelope fluctuations may have played in the dichotic
experiment. The average values of P, for those five noise-pairs for listeners D, M, P,

and W were, respectively:

64

100

75

0350

25

100

75

25

l 00
75

(L50

25

l 00
75

(150

25

 

 

 

 

 

 

 

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4o 95 97 58 86 80 32 44 69 57

Noise-Pair Number

5

P

Figure 32: Comparison between Pc and P, data for the level set of Experiment 1 and
the same noise-pairs with just the left channel presented diotically.

65

For the phase set: 54, 61, 54, 63 ‘70

For the level set: 63, 58, 72, 70 ‘70.
Evidently, in the diotic experiment listeners chose the noises that had led to the
largest interaural fluctuations clearly more than half the time. These numbers can
be compared with the values of P, in the dichotic experiment (Experiment 1) which

averaged 88%.

2. Agreement between listeners
The agreement among the listeners was assessed by comparing values of P, against
noise serial number for listeners taken in pairs. Inter-listener correlations for D-M,
D—P, D-W, M-P, M-W, and P-W were as follows:

For the phase set: 0.59, -0.38, 0.38, —0.22, 0.88, 0.17

For the level set: 0.70, 0.53, 0.76, 0.67, 0.89, 0.76.
The strongest correlation was between M and W. Listener P was responsible for the
only negative correlations, both in the phase set. Correlations were clearly larger in
the level set than in the phase set. The strong correlation indicates that listeners

tended to agree about which fluctuations were salient.

3. Comparison with enve10pe fluctuation
A comparison between the listener selection of noises and fluctuation was assessed by
comparing P, with s,[E] as a function of the noise-pair serial number. Correlations
for listeners D, M, P, and W were, respectively:

For the phase set: 0.38, 0.84, —0.03, 0.88

For the level set: 0.85, 0.66, 0.65, 0.70.
Again, P is responsible for the only negative correlation. The positive correlation
indicates that the choices that listeners make can be predicted based on the physical
envelope fluctuations, as measured by the standard deviation of the envelope over

time, especially for the level set.

66

4. Comparison with Experiment 1
A comparison between the results of the corresponding diotic and dichotic experi-
ments was made by comparing P, on Experiment 5 with P, on Experiment 1, both
as functions of the noise-pair serial number. The data can be seen in Figures 31 and
32. Correlations for listeners D, M, P, and W were, respectively:

For the phase set: 0.24, 0.53, —-0.07, 0.44

For the level set: 0.82, 0.66, 0.81, 0.80.

Again, correlations are larger for the level set.

1 .5.3 Discussion

The correlations above are fairly impressive for being so large with possibly some
exceptions for Listener P. These include the correlations between P, in Experiment
5 and P, in Experiment 1 as well as the correlations between P, and monaural and
dichotic fluctuations. There are several possible interpretations of these correlations.

Possibly the correlation between P, and P, scores only represents a chain of stimu-
lus circumstances. For a narrow bandwidth like 14 Hz, every kind of stimulus fluctua-
tion seems to correlate with every other kind. Interaural phase fluctuations correlate
with interaural level fluctuations and both correlate with noise envelope fluctuations.
In a dichotic experiment probing the detection of interaural incoherence listeners at-
tend to the interaural fluctuations. In a diotic experiment probing an evaluation of
roughness or other stimulus action listeners attend to the envelope fluctuations. The
results of the two experiments, as functions of the stimulus serial number, are similar
because the interaural and monaural fluctuations behave similarly with respect to
serial number.

Alternatively, it is possible that the correlation between P, and P, scores arises be-
cause listeners in a dichotic experiment are misled by monaural envelope fluctuations

that are particularly large or particularly small. Given the enormous difference in

67

the average P, and P, values for the five noise-pairs with large fluctuations, as noted
in the results section above, it seems highly unlikely that monaural fluctuations per
se contribute to listener judgements in the binaural experiment when the detection
of interaural incoherence is easy. But when detection of interaural incoherence is
difficult, or impossible, the cues from monaural envelope fluctuations (or the lack
of them) may influence judgements and are probably responsible for P, values in a

dichotic experiment that are less than chance.

1.6 DISCUSSION AND CONCLUSION

Listeners are sensitive to small amounts of interaural coherence in noise. Given diotic
noise as a comparison, listeners can detect a coherence change of 0.01, i.e. they are
sensitive to the difference between 1.00 and 0.99 (Gabriel and Colburn, 1981). The

goal of this chapter was to understand the origins of this remarkable sensitivity.

1.6.1 Detection of incoherence

Experiment 1 selected stimuli from an ensemble of 100 reproducible left-right noise-
pairs, all of which had a bandwidth of 14 Hz and an interaural coherence of 0.9922. It
was found that those pairs that had a large fluctuation in interaural phase diflerence
(IPD) or large fluctuation in interaural level difference (ILD) were much more readily
recognized as not perfectly coherent compared to pairs with small fluctuations. This
result led to the conclusion that, for bandwidths as narrow as 14 Hz, the interaural
coherence is not an adequate predictor of the ability to detect incoherence. Instead,
the size of the interaural fluctuations matters.

Experiments 2 and 3 progressively increased the bandwidth and found that the
ranges of fluctuations in IPD and ILD among different noise-pairs in an ensemble
decreased with increasing bandwidth. (See Appendix B). This observation led to

the expectation that the detectability of incoherence would exhibit less variation for

68

different noise-pairs with these wider bandwidths. Detection experiments similar to
Experiment 1 showed an increasing uniformity in detectability for the incoherence in
noises with increasing bandwidths, as expected.

It was conjectured that the only reason that detection performance for 14-Hz band-
width was different from performance for 108-Hz bandwidth was that more extreme
values of fluctuations (both very small and very large) were available in the ensemble
with the narrow bandwidth. In Experiment 4 a comparison was made between per-
formance on noise-pairs with 108-Hz bandwidth and performance on a matched set
of noise-pairs with 14-Hz bandwidth. Noise-pairs in the matched set were selected
to have approximately the same interaural fluctuations as the pairs of the 108-Hz
set. The comparison showed that detectability differences among diflerent noise-pairs
in the matched set were reduced to about the same level as for the 108-Hz noises,
consistent with the conjecture. The overall performance on the 14—Hz matched set
was approximately equal on the 108-Hz set for two of the listeners; it was consistently
higher for the other two listeners. These two results from the comparison suggest that
differences in interaural fluctuations are responsible for differences in the detectability
of incoherence for different noises, but that fluctuations of comparable size are more
easily detected when the bandwidth is narrow. The most likely explanation for the
advantage of narrow bands is that fluctuations are slower. The role of fluctuation
speed will be addressed in the chapter on binaural modeling.

These conclusions differ from those of Breebaart and Kohlrausch (2001) who dis-
missed a specific role for IPD and ILD fluctuations in binaural detection because the
distributions of those fluctuations, with or without a signal, failed to show a band-
width dependence. By contrast their NpS7r detection experiments did show such a
dependence. It is agreed that the s,[A<I>] and s,[AL] have mean values, averaged across
waveforms, that are insensitive to bandwidth, as n