BINAURAL INTERACTION IN
HEARING IMPAIRED LISTENERS
by
Kaigham Jacob Gabriel
¢1
B.S.
University of Pittsburgh ( 1977 )
S.M. Massachusetts Institute of Technology ( 1979 )
SUBMITTED TO THE DEPARTMENT OF ELECTRICAL
ENGINEERING AND COMPUTER SCIENCE IN PARTIAL
FULFILLMENT OF THE REQUIREMENTS
FOR THE DEGREE OF
DOCTOR OF SCIENCE
at the
MASSACHUSETTS INSTITUTE OF TECHNOLOGY
August 30, 1983
Signature of Author
-
r
-
Dedrt6ýnt oi/Electrical ingineering
ad Computer Science
August 30, 1983
Certified by
H. Steven Colburn, Thesis Supervisor
Accepted by
W
-mACIHUSESTTINSTITUT-
OF T-CH~InLOGY
4 1983
Archives
C'T
LIBRARP.!
BINAURAL INTERACTION IN
HEARING IMPAIRED LISTENERS
by
Kaigham Jacob Gabriel
The binaural hearing of four hearing impaired listeners
in
interaural
time
discrimination,
interaural
discrimination, interaural correlation discrimination
detection
experiments.
All
tests
was
intensity
and
4000
Hz.
pattern
techniques.
narrowband
model
By
of
interaural-differences
of
loss
as
augmenting
the
results.
suggests
2000
binaural
averager,
correlation
measured
by
interaction
the
current
a simple, representative,
results
time and intensity discrimination tests were
relate
1000,
In general, the pattern of loss in binaural hearing
was independent of the
audiometric
binaural
were conducted on each subject
using third-octave bands of noise centered at 250, 500,
and
tested
discrimination
an
from the interaural
used
and
with
to
predict
binaural
and
detection
For both hearing impaired and normal listeners, this study
that
detection can
narrowband
be
correlation
characterized
by
a
discrimination
listener's
interaural time and intensity differences.
THESIS SUPERVISOR: H. Steven Colburn
TITLE: Principal Research Scientist
Research Laboratory of Electronics
and
NOS'rf
sensitivity
to
Acknowledgment
I always have trouble with this part.
It's been four years
since I last had to write an acknowledgment to a thesis. Let's hope
I never have to write another one. I'm feeling sort of emotional
right now, so before this gets real soppy, I thank you all for your
friendship, your guidance, your enthusiasm and your patience.
Success in all your endeavors.
Table of Contents
Chapter 1
Introduction
Motivation ......................... 1-3
Chapter 2
Previous Work
A. Normal Listeners ................ 2-5
Interaural Time Disc.........
Interaural Intensity Disc ...
Interaural Correlation Disc. .
Binaural Detection ...........
i)
ii)
iii)
iv)
B. Hearing Impaired Listeners ......
2-5
2-7
2-8
2-9
2-10
C. Models of Binaural Interaction .. 2-15
Chapter 3
Experiments
A. Subjects ........................ 3-1
B. Stimuli ......................... 3-3
i)
ii)
iii)
iv)
Interaural Time Disc. ........
Interaural Intensity Disc. ...
Interaural Correlation Disc. .
Binaural Detection ...........
C. Procedure .......................
3-7
Sequential Testing Rule .........
Chapter 4
3-3
3-4
3-5
3-6
3-8
Experimental Results
A. Normal Listeners .....
i)
ii)
iii)
iv)
.......
.......
Interaural Time Disc.
...
Disc.
Intensity
Interaural
Interaural Correlation Disc. .
Binaural Detection ...........
4-1
4-1
4-2
4-2
4-2
B. Impaired Listeners .............. 4-3
i)
ii)
iii)
iv)
Interaural Time Disc. ........
Interaural Intensity Disc. ...
Interaural Correlation Disc.
Binaural Detection ...........
4-3
4-5
4-6
4-8
C. Binaural Audiograms ............. 4-9
D. Relationships Among the Tasks ... 4-12
Chapter 5
A Model of Binaural Interaction
A. Outline of the Model ............ 5-1
B. Elements of the Model ...........
5-3
C. Comments ........................ 5-5
D. Estimation of Model Parameters .. 5-7
i) Separate Time and Intensity
........
Differences .....
ii) Sum of Differences (SID) .....
Chapter 6
Characterization of Stimulus
Interaural Differences
A. Analytical Evaluation ..
Chapter 7
5-9
5-9
6-2
· · · · · · · · ·
i) Correlation Stimuli
ii) Detection Stimuli ... · · · · · · · · ·
6-2
6-7
B. Numerical Computation .. · · · · · · · · ·
6-9
Binaural Performance Based on Stimulus
Variability
A. Distribution of Averaged
Interaural Differences ..........
7-2
B. Model Predictor Equations .......
7-4
i) Separate Time and Intensity
Differences .................. 7-5
a)
b)
c)
d)
ii)
Chapter 8
Intensity Alone ...........
.......
Time Alone .......
.......
Sum
of
Diff.
Linear
Optimal Combination .......
7-6
7-8
7-9
7-10
Sum of Interaural Diff. (SID). 7-11
Predictions of the Model
A. Separate Time and Intensity
Differences .....................
8-1
B. Normal Listeners ................ 8-2
i) Correlation Discrimination
Predictions .................. 8-3
ii) NOST( Threshold Predictions .. 8-3
C. Impaired Listeners .......
..
8-6
i) Correlation Discrimination
Predictions ................. 8-6
ii) NOS7f Threshold Predictions .. 8-8
D. Relative Use Of Interaural Cues . 8-9
Chapter 9
Appendix
Appendix
Appendix
Appendix
Conclusions and Remarks
B. Modelling Results ...................
9-5
II Sequential Testing Methods
III Estimation of Model Parameters
IV Predictor Equations for Correlation
Discrimination and NOS1r Detection
Table 3.1
Table 7.1
Figure Captions
Figures
9-1
I Waveform Generation
Footnotes
References
A. Psychophysical Results ..........
CHAPTER 1
INTRODUCTION AND MOTIVITATION
Binaural hearing is the sensory processing of the sounds at the
two
ears
which extracts auditory information not present at either
ear alone.
The utilization of this binaural information enables
us
to locate sounds in the environment, focus on specific sounds within
a
multitude
of
different
masking
sounds,
and
perceive
the
spaciousness of sounds.
The physical differences between
provide
binaural
information
the
include
acoustic
signals
differences in the spectral
characteristics of the sounds, differences in the arrival
sounds
at
the
two
from
different
In natural environments, these
path
geometries
differences in the diffraction of sounds
body,
etc.)
times
of
ears and differences in the intensities of the
sounds at the two ears.
arise
which
involved
in
the
differences
(different
path
caused
the
transmission
by
lengths,
head
and
of the sound from the
source to the two ears.
From an evolutionary point of view, it is clear
hearing
is an advantage.
was
binaural
The degree to which our distant ancestors
were able to distinguish and locate the
prey)
that
sounds
of
predators
directly related to their chances for survival.
(and
Certain
INTRODUCTION AND MOTIVITATION
aspects
of
our
Page 1-2
present-day
interactions
with
the
environment,
although
less exotic and primitive, are still dependent on binaural
hearing.
Warnings about the
objects,
and
perceptions
direction
of
approaching
complex
or
noisy
in
people
or
environments are
greatly enhanced by our binaural hearing.
A substantial number of
normal
listeners
in
binaural information.
experiments
have
been
performed
on
an effort to quantify our ability to perceive
Many of these experiments have
measured
the
ability of human listeners to discriminate interaural differences of
simple
sounds
Although
presented
these
in
controlled
listening
situations.
sounds would not normally be encountered in natural
environments, their interaural differences can be finely
and
extraneous,
example,
by
contaminating
presenting
factors
electronically
can
be
controlled
eliminated.
generated
and
For
controlled
sounds over headphones, arbitrary interaural time differences can be
created with no interaural intensity differences.
Such
a
stimulus
configuration would be difficult, if not impossible, to achieve with
naturally occuring sounds.
In
models
conjunction
of
binaural
with
the
hearing
experimental
in
normal
efforts,
listeners
developed.
Like all succesful models, these provide
framework
within
which
the
different
binaural hearing are organized.
to
an
exposition
which might not
succesful
a
of
relationships
otherwise
model
is
be
at
have also been
an
experimental
This organization
theoretical
economical
results
naturally
in
leads
between the different results
apparent.
organizing
In
data,
addition,
the
more
the
more
binaural
performance in many different binaural tasks can be characterized by
INTRODUCTION AND MOTIVITATION
a
set
of
model.
the
Page 1-3
experiments which specify the parameter values of such a
Most of thesq models have been
processes
functional
descriptions
of
presumed to be performed by the physiological system
and imply no specific correspondence between physiological processes
and a model's elements.
Motivation
Hearing impairments at the peripheral level (the portion of the
auditory
neural
system
which
firing
transduces acoustic signals at the ear into
patterns)
neurophysiological
level
or
(or
at
both)
a
higher,
can
result
degradation of binaural hearing (Durlach
everyday
et
al.,
more
central
in a significant
1980).
In
life of an impaired listener, the degradation can manifest
itself as an inability to localize sound sources or an inability
function
in complex auditory environments.
consequences in situations such as work
where
the
auditory
warnings are important.
deficits
can
impaired
listeners
have
social
avoid
and
or
to
This can have dangerous
environments
and
traffic,
Moreover, binaural hearing
psychological
consequences
when
are uncomfortable in situations with
many speakers because their binaural impairments make
it
difficult
to focus on a single speaker.
With few exceptions, current clinical procedures do not include
measurements of binaural capabilities in hearing impaired listeners.
Because the standard audiometric evaluation of
involves
separately
testing
hearing
impairments
each ear, little or no information is
provided about the effect of an impairment on binaural hearing.
In
INTRODUCTION AND MOTIVITATION
fact,
some
Page 1-4
multiple sclerosis patients show audiometrically normal
hearing and yet
exhibit
severe
degradation
in
binaural
hearing
(Hausler and Levine, 1980).
The lack of any
primarily
binaural
tests
interaural
intensity
detection) should
time,
of
be
it
capabilities.
variety
clinical
due to not knowing what to measure.
aspect of binaural hearing (e.g.,
testing
in
is
interaural
discrimination,
tested.
to
It is not clear what
time
discrimination,
test
due
to
only
constraints
a
relating
The ability to characterize binaural performance in a
different binaural tasks with a few, representative set
the
different
be
capable
successful
types of binaural phenomena.
none of the current models of binaural interaction have
to
on
minimum set of
of tests, requires a description of binaural interaction
at
is
or binaural target-in-masker
Moreover,
necessary
evaluations
To date,
been
shown
of relating even the above four phenomena in normal
listeners under the same set of assumptions
(Colburn
and
Durlach,
1978).
A way to determine the
characterize
impaired
to
(a)
obtain:
experiments,
subset
of
measurements
necessary
to
binaural hearing in an individual subject is
results
from
a
number
of
different
binaural
each performed on every impaired subject in the study;
and (b) a model of binaural interaction which can simulate simply
given
impairment's effect on binaural hearing.
a
Such a model should
focus on the use of binaural information to effect performance
(and
hence, on the relations between the different tests), rather than on
any detailed assumptions about how such information is obtained.
INTRODUCTION AND MOTIVITATION
Page 1-5
The first requirement is a consequence of
binaural
hearing
abilities
encountered
the
differences
in
across different impaired
listeners, even for listeners with the same audiological description
(Durlach
al.,
et
Hausler and Colburn, 1981).
1980 ;
assumption in the modelling of normal listeners
have similar binaural hearing.
different
subjects
and
integrated
and
on
considered
is
An implicit
that
they
all
Results from different studies (with
different
equivalent
binaural
to
phenomena)
results
For
from
impaired
are
a single
extensive study on one normal
listener.
listeners,
this assumption is not valid.
Thus, the different types of binaural
experiments must all be performed on each impaired listener used
a
study
if
any
in
valid model of impaired binaural hearing is to be
developed.
The requirements on the model are made because different
of
impairment
origins.
between
have
varying, complicated, or unknown physiological
Thus, in a model intended
binaural
phenomena,
it
to
is
explore
more
interrelationships
general (and easier) to
describe the overall effect an impairment has on the
binaural
information
types
is
processed,
description of the impairment.
rather
than
way
in
which
on any specific
Although models with
more
detailed
descriptions of the impairments are possible, it is not evident that
such modelling will necessarily improve our ability
to
relate
the
different binaural hearing phenomena.
This study presents an attempt to define
measurements
required
to
characterize
binaural
restricted, but representative, set of binaural
variety of impaired listeners.
the
minimum
set
of
performance in a
experiments
for
a
INTRODUCTION AND MOTIVITATION
The
experiments
in
dependence
of
structure)
discrimination,
binaural
masked
four
Page 1-6
this
study
binaural
phenomena:
interaural
detection,
These four binaural
descriptive
the
functional
the
frequency
intensity
time
discrimination,
interaural
tests
(fine
were
correlation
chosen
as
being
aspects of the binaural hearing as
described earlier in this chapter.
chapter,
on
interaural
and
discrimination.
of
focused
As will
be
seen
in
the
next
interaural time and intensity discrimination is related to
localization ability, binaural masked detection to focusing ability,
and
interaural
correlation
discrimination
to
the
perception of
spaciousness or.extent of the acoustic image.
Our interest in the frequency dependence of
hearing
is
generated
by
several
signals it is generally accepted
binaural
factors.
that,
in
impaired
One,
binaural
for narrowband
normal
listeners,
the
system is most sensitive to interaural time differences at
low frequencies (less than 1500 Hz) and roughly equaly sensitive
interaural
intensity
differences at all frequencies.
narrowband stimuli, performance in
to
As such, for
different binaural tasks (with
both interaural time and intensity cues available) is believed to be
mediated by
interaural
which
interaural
processing
at
low
frequencies
intensity processing at high frequencies.
this
intensity
time
frequency
processing
delineation
exists
in
and
The extent to
between
interaural
impaired
listeners
time
can
and
be
an
important factor in determining the nature of the impairment and can
have
consequences
for
both the type of interaural information and
the way in which interaural information
hearing aids.
is
processed
in
binaural
Page 1-7
INTRODUCTION AND MOTIVITATION
Two, comparison of binaural
hearing
to
impairments
current,
audiometrically defined monaural losses would be more meaningful and
facilitated by a frequency dependent measure of binaural hearing.
Finally, the auditory
organized
up
system
is
known
to
be
tonotopically
to the level of the VIIIth nerve bundle (Kiangt4,1965)
and at least as far as the superior olivary complex (Guinanetl.,1972).
Thus,
a
frequency
dependent
measure of binaural hearing loss may
also delineate regions of physiological loss in the
peripheral
and
central portions of thA auditory system.
Because of our interest in the frequency dependence of binaural
hearing,
we
have
chosen to use narrowband (one-third octave wide)
noise at five different center frequencies.
instead
of
pure
tones
for the following reasons.
theoretical thrust of this
different
binaural
We used noise waveforms
study
phenomena.
is
an
attempt
One, the basic
to
As such, we wanted to use the same
stimuli in both the detection and discrimination tasks.
narrowband
noise
used
in
in
chapter
2,
Thus,
the
the discrimination experiments were the
same noise waveforms used in the detection experiments.
discussed
four
relate
certain
binaural
apparent when testing with wideband stimuli and
Two, as
impairments
are
are
apparent
is
not
only
when a narrowband stimulus is used (Hausler et al., 1985).
Chapter 2 reviews a selection of binaural phenomena and
relevant
hearing in
binaural
to
this
normal
study.
models
This includes a description of binaural
listeners,
a
general
description
of
current
interaction models, and a brief review of past research on
binaural hearing in impaired listeners.
INTRODUCTION AND MOTIVITATION
Page 1-8
Chapter 3 describes the experiments, stimuli and subjects
in
the
study.
used
A new, general method of psychophysical testing was
developed, which has been particularly
useful
in
the
testing
of
hearing impaired listeners.
In Chapter 4 the results of the experiments are
discussed
in
relation
normal listeners'
presented
and
to the impaired subjects' audiograms and to
performance.
In
addition,
we
present
a
new
description
of binaural performance (" binaural audiograms ") which
reveal some
interesting
patterns
of
loss
not
apparent
in
the
traditional representations of binaural performance.
Chapter 5 presents a model of binaural interaction for a single
frequency
band
which
uses
only
intensity differences of narrowband
binaural
information.
interaural
stimuli
time
as
magnitudes
of
the
variables
of
Moreover, this model limits the performance
of normal listeners and simulates the effects of
the
and interaural
noise
terms
added
to
the
an
impairment
by
ideally processed
interaural time and intensity differences of the stimuli.
In Chapter 6, a characterization of the
binaural
experiments
is
given
(time) and intensity differences.
two
difference
simplified
variables
second-order
distributions.
are
stimuli
used
in
the
in terms of their interaural phase
Probability distributions for the
presented along with an approximate
statistical
description
of
the
Page 1-9
INTRODUCTION AND MOTIVITATION
results
In Chapter 7, the model discussed in Chapter 5 and the
given
6 are combined to estimate the parameters of the
Chapter
in
This
noisy binaural information processing.
binaural
narrowband
for
equations
leads
experiments
to
prediction
in which stimulus
interaural time and intensity characteristics are known.
predictions
Chapter 8 presents the
the
class
of
models
by the model of chapter 5) under different assumptions
(represented
combination
the
concerning
of
of
interaural
time
and
intensity
An argument is made for a weighted linear combination
differences.
of the two differences as a near-optimal combination scheme and
one
best
which
agrees
with
the
normal and impaired binaural hearing
results.
Finally, Chapter 9 discusses the results of the tests
model in relation to:
impaired
listeners,
interaction
hearing aids.
and
the
(1) clinical and academic research on hearing
(2)
testing
and
modelling
of
binaural
in normal listeners and (3) the development of binaural
In addition, generalizations and possible
of the model to other binaural phenomena are discussed.
extensions
CHAPTER 2
PREVIOUS WORK
We begin with a review of
binaural
phenomena
in
normal
and
hearing impaired listeners which are of particular relevance to this
study.
Specifically,
narrowband
binaural
we
consider
phenomena.
the
In
studies which used narrowband noise
frequency
dependence
of
general, we cite results from
stimuli
similar
to
the
ones
which were used in this study.
In addition, we review past models of binaural interaction
suggest
a
refinement
to
such
and
models which unify predictions for
lateralization and detection phenomena.
The
majority
characterized
different
of
the
cues
ability
just-noticeable-difference
difference
(along
studies
sensitivity
interaural
Discrimination
the
some
by
is
discussed
of
the
binaural
performing
often
(jnd).
jnd
e.g.,
intensity) between a reference stimulus and a
corresponds
to
some
specified
level
in
a
signal-
plus-noise
chapter
system
is
in
to
interaural
test
of
as
a
the
time
stimulus
of performance.
the
tests.
terms
defined
detection capability is characterized in terms of a
ratio
this
discrimination
described
A
dimension,
in
or
which
Similarly,
signal-to-noise
stimulus which is just noticeably
PREVIOUS WORK
Page 2-2
different from a stimulus with only noise present.
Localization (the apparent source position for an
signal)
and lateralization (the phenomena related to the laterality
of an auditory image perceived to be within the
been
by
tested
sensitivity
measuring
to
head)
ability
interaural
has
time (fine
Lord Rayleigh was
structure) differences and intensity differences.
the
externalized
first to suggest that different types of binaural cues are used
effect
at different frequencies to
theory
of
localizes on
the
frequencies
and
of
basis
In
his
duplex
he proposed that the binaural system
hearing,
binaural
localization.
time
interaural
at
differences
low
at
high
To a first order, this description is still valid today.
Mills
interaural
differences
intensity
frequencies.
(1960)
compared
jnds
tones,
relative
to
reference,
to
in
a
interaural
diotic
he
was
signals)
minimum audible angles (MAAs) measured from directly
able
For
below
frequencies
6000
to predict the MAAs obtained from the interaural
phase (or equivalently, interaural time) and
frequencies
identical
(interauraly
in front of a listener in free-field.
Hz,
and intensity of pure
phase
intensity
jnds.
For
below approximately 1500 Hz, interaural phase jnds were
consistent with observed
MAAs,
while
above
1500
Hz,
interaural
measured
interaural
intensity differences predicted the observed MAAs.
More recently, Domnitz and Colburn (1977)
time
and intensity jnds for a 500 Hz tone at various reference time
and intensity differences.
In
addition,
they
also
measured
the
subjective lateral position of a 500 Hz tone (with position matching
PREVIOUS WORK
Page 2-3
experiments) for the same set of subjects and
differences.
The
interaural
reference
interaural
time jnds were predicted by a simple
model of lateralization which used a Gaussian position variable
mean
of
which
was determined from the lateralization data and the
variance of which was determined from the
results.
In
later
work,
Stern
succesfully predict the same set
model
that
activity.
the
explicitly
and
of
included
intensity
discrimination
Colburn (1978) were able to
lateralization
a
description
This model, referred to as the
data
using
a
of auditory-nerve
position-variable
model,
will be discussed in more detail later in this chapter
The increased detectability of
maskers
sounds
in
the
background
due to binaural interaction have been tested in the past by
measuring the binaural masking level difference
different
interaural
signal-to-noise
(MLD)
the
presence
of
a
masker
for
in
configuration.
defined as the difference between the threshold of a
in
of
some
The
MLD is
target
signal
"reference"
configuration and the threshold of the same signal
several,
in
interaural
a
different
interaural configuration.
The largest such difference in thresholds
occurs between
(interaurally identical)
presence
of
a
a
diotic
diotic
masker
(usually
signal
in
the
termed NOSO) and the same
signal 180 degrees out of phase between the two ears in the presence
of the same diotic masker (NOST ).
We chose to test this particular
difference in our experiments because (1) it
difference
produces
the
in signal thresholds and hence, one which we presumed to
be the easiest difference to detect by impaired listeners
it
has
largest
recently
and
(2),
been tested on a large number of hearing impaired
listeners by several investigators (Lynn et al.,
1981 ;
Jerger
et
PREVIOUS WORK
al.,
1982
;
Page 2-4
Noffsinger, 1982).
In further discussions, when the
term MLD is used, it is with reference to this
difference
measured
in decibels.
Interaural correlation discrimination, while not a
frequently
measured
classic
or
binaural phenomenon, tests discrimination of a
"pure" binaural difference.
There
stimuli
the measurement of binaural capability.
which
contaminate
are
no
monaural
In the detection experiments, the presence of the
the
energy
of
the
target
in
small
possible
impaired
for
for
normal
signal
the
increases
total stimulus at the target frequency.
these increases are
that
cues
While
thresholds,
it
is
listeners (with increased thresholds)
these monaural cues would play a larger role in
binaural
detection
experiments.
In addition, Pollack and Trittipoe (1959
the
interaural
cross-correlation
perceptual fusion of binaural
(1982)
has
proposed
that
a,b)
ears
provide
a
stimuli.
More
interaural
recently,
Lindemann
cross-correlation functions
received
at
the
measure of the acoustic "spaciousness" of the
sounds.
Finally, a large
compute
as
their
that
provides a direct measure of the
(computed in different frequency bands) of sounds
two
suggested
number
binaural
of
binaural
processor
output
interaction
models
a function which is
essentially the interaural cross-correlation of the signals (Colburn
and Durlach, 1978).
Note that for all four
conditions
were
diotic
experiments
stimuli.
performed,
the
reference
Sensitivity to interaural time,
intensity and correlation differences are best (smallest jnds)
when
PREVIOUS WORK
reference
Page 2-5
conditions
are
diotic
(Domnitz
and
Colburn,
1977
;
Kearney, 1979 ;
Pollack and Trittipoe, 1959alBecause discrimination
performance
best
is
at
this reference condition, we thought that
impaired listeners (with interaurally symmetric losses)
this
task
easiest
to
perform.
Moreover,
interactions with the environment, the
(corresponding
to
in
diotic
would
terms
find
of natural
reference
condition
straight-ahead sound sources) is the one usually
encountered.
A.
Binaural Phenomena in Normal Listeners
To date, there exists in the literature a substantial amount of
data
from
experiments
related
to
the
frequency
binaural interaction in normal-hearing listeners.
review
of
these
studies
up
Durlach and Colburn (1978).
to
the
dependence
A
of
comprehensive
early 1970s is available in
In this section, we focus on
the
four
experiments introduced above.
i) Interaural Time Discrimination
Klumppand Eady (1956) measured interaural
bands
of
narrowband
using
several
noise at various center frequencies.
Using a
2-second duration signal presented at levels
(total
time
of
60
-
80
dB
SPL
noise power), they measured an average jnd of 14 usecs for a
band of noise ranging from 425 - 600 Hz and a jnd of 62 usecs for
band of noise ranging from 3056 - 3344 Hz.
a
PREVIOUS WORK
Page 2-6
Interaural time jnds
for
normal
listeners
using
narrowband
noise at center frequencies of 500 Hz (100 Hz wide) and 4000 Hz (500
Hz)
were
reported
listeners.
At
a
by
Hawkins
(1977)
in
a
study
of
impaired
stimulus level of 85 dB SPL (total noise power),
average time jnds were 17 usec for the 500 Hz noise and 61 usecs for
the 4000 Hz noise.
McFadden
and
Pasanen
(1976),
using
narrowband
waveforms
centered at 500 Hz (100 Hz wide) and 4000 Hz (500 Hz wide), measured
average time jnds of 17 usec at 500 Hz and 42 usecs at 4000 Hz.
A relatively small time jnd at high frequencies was measured by
Henning
Hz.
(1974)
using
a 600 Hz wide band of noise centered at 3900
He reported average time jnds of approximately 20
usecs.
The
discrepency between the high-frequency results of the latter two and
former two studies
are
most
likely
due
to
differences
in
the
low-frequency energy of the different stimuli.
In a more
low-frequency
recent
energy
experiment
in
concerned
high-frequency
Bernstein and Trahiotis (1982) measured
narrowband
noise
centered
at
low-frequency-skirt slopes of the
tested
(24
dB/octave,
and
4000
with
the
time
discrimination,
interaural
Hz
noise.
as
a
At
the
effect
time
of
jnds
for
of
the
function
steepest
slope
thus the condition which had the least
amount of low frequency energy)
the
average
jnd
obtained
stimulus level of 70 dB SPL) was approximately 80 usecs.
(at
a
PREVIOUS WORK
As is seen
reviewed
here),
Page 2-7
in
Figure
2.1
sensitivity
(an
to
aggregation
interaural
time
of
the
results
differences for
normal listeners is best in the frequency region between 250 Hz,
gradually increasing to approximately 80 usecs at 4000 Hz.
1000
The
jnds observed for narrowband noise are consistent with low-frequency
time jnds observed for tonal stimuli at frequencies corresponding to
the center frequencies of the noise waveforms (Klump and Eady,
;
1956
Durlach and Colburn, 1978).
ii) Interaural Intensity Discrimination
Hawkins (1977), in an ancilllary experiment, measured intensity
jnds
(using the same narrowband noise as in the time discrimination
experiment) for one normal-hearing listener.
intensity
jnd
was
measured
for
the
At 85 dB SPL, a 0.9 dB
500-Hz
noise
and a 0.6 dB
intensity jnd was measured for the 4000-Hz noise.
Zurek and Leshowitz (1975), in
intensity
jnds
and
frequency
a
study
selectivity,
comparing
interaural
measured
interaural
intensity jnds for a 250 ms, 100-Hz wide noise centered at
At
60
dB
500
Hz.
SPL (total noise power), they measured average intensity
jnds of 1.5 dB, about a factor of two larger than the jnds
reported
by Hawkins.
We have not been able to find any other studies which
interaural intensity jnds of narrowband noise waveforms.
measured
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Page 2-8
The results presented by Hawkins are consistent with
discrimination
bursts
in
of
tonal stimuli.
normals
frequencies
is
between
approximately 0.6
dB
Intensity discrimination of tone
approximately
200
at
intensity
and
1000
4000
Hz
constant
Hz,
at
0.8
grasually
(Durlach
and
dB
for
decreasing
Colburn,
to
1978).
Results from the two narrowband studies are presented in Figure 2.2.
iii) Interaural Correlation Discrimination
Compared to
interaural
time
discrimination,
sensitivity
to
differences in interaural correlation has received relatively little
attention.
we
Due to the paucity of correlation
discrimination
data,
review wideband correlation data in addition to the single study
which has measured narrowband correlation jnds.
Despite the importance of interaural correlation processing
models
of
binaural
Trittipoe, 1959 a,b;
reported
on
the
correlation.
the
hearing,
Gabriel
ability
of
only
and
three
Colburn,
papers
1981)
have
to
which
the
a
a
reference
directly
measure
of
signals at the two ears are similar, is
varied and a subject is asked to distinguish changes in
between
and
listeners to discriminate interaural
In this type of task, the correlation,
degree
(Pollack
in
correlation
value
correlation
and some test correlation
value.
Pollack and Trittipoe (1959 a,b) measured the
of
wideband
correlations.
(6800
Hz)
Gaussian
At a reference
correlation
jnd
noise for a variety of reference
correlation
of
unity
(interaurally
PREVIOUS WORK
identical
Page 2-9
stimuli), they measured a jnd of approximately 0.04, i.e.
discrimination performance was 75% correct
perfectly
correlated
noise (
= 0.96).
noise
No definitive studies
function
of
frequency.
(
=
have
when
and
correlation
Colburn
interaural correlation jnds for a 500 Hz narrowband
as
a
function
of
compared
1) to a slightly decorrelated
measured
Gabriel
subjects
the noise bandwidth.
jnds
as
a
(1981),
measured
noise
waveform
At a bandwidth of 115 Hz,
they reported an average correlation jnd of 0.008
and
a
value
of
0.03 for wideband (0 - 4kHz) noise.
iv) Binaural Detection
Although
experiments
many
(see
researchers
have
performed
Durlach and Colburn, 1978),
individual thresholds obtained in the NOSO
configuration.
Since
the
focus
of
NOS7r
study
signal-noise
is the binaural
"unmasking" ability as evidenced by NOSrT thresholds, the
data
are
discussed
(not
MLDs).
following
threshold
As noted above, NOSO results are
measured for comparison and as an upper bound
the
MLD
few have reported the
and
this
binaural
on
performance.
In
sections, detection results are reported in units of
10log(E/No).
Hirsch and Webster (1949), measured NOSO
and
NOSqT
thresholds
using
waveforms.
For a 50-Hz wide masker centered at 250 Hz, the
NOSO
threshold
a
was
detection
250 Hz target masked by three different masker
found
to
be
6.0
dB
and
average
the average NOST
PREVIOUS WORK
Page 2-10
threshold was -5.0 dB.
Bourbon (1966), in a study on the effects of
on
MLDs,
target.
masker
bandwidth
measured NOSO and NOSIT detection thresholds for a 500 Hz
Using a
stimulus
duration
of
150
msec
(with
25
msec
rise/fall times) he measured an average NOSO threshold equal to 8 dB
and an average NOSIT
threshold
equal to - 9 dB, for a noise
masker
bandwidth equal to 130 Hz (approximately equal to a one-third octave
noise).
Wightman (1971), in a similar study on the
bandwidth
on
the MLD, reported NOSO and NOSTr
for an 800 Hz target.
reported
an
average
With
NOSO
the
"heavily
threshold
of
effects
masker
detection thresholds
filtered"
10
of
stimuli,
he
dB and average NOS-7
thresholds of -4 dB for an 800-Hz target masked by a
200
Hz
wide,
800-Hz centered noise masker.
Most recently, Zureketfl.(•,t)
for
a
4000
Hz
measured NOSO and NOS7r
tone with various masker bandwidths.
thresholds
For a masker
bandwidth of 1000 Hz, he obtained average NOSO thresholds of
14
dB
and average NOS1T thresholds of 9.0 dB.
These results are plotted together in Figure 2.3.
the
results
are in agreement with wideband MLD results reported in
other studies (Durlach and Colburn, 1978).
tonal,
In generall,
target
signal
frequency
in
As
a
function
of
the
the background of a broadband
masking noise, the MLD shows a maximum of approximately 15 dB in the
region between 250 to 500 Hz, remaining constant up to approximately
1000
Hz.
For
frequencies
above
1000
Hz
monotonically to approximately 4 dB at 4000 Hz.
the
MLD
decreases
PREVIOUS WORK
B.
Page 2-11
Binaural Phenomena in Impaired Listeners
In contrast
listeners,
to
the
experimental
on
listeners,
and
even
dependence of binaural interaction.
1978) on binaural interaction
reviewed in Durlach et al.
in
of
hearing
less
about
hearing
impaired
separately,
listeners
tests
are
employed
versus
tone
pure
tone
thresholds
example,
flat-loss
in
audiogram.
relative
frequency.
Impairments
categorized on the basis of the frequency dependence
For
are
the
impairments (Davis and Silverman, 1970), the
thresholds are obtained at frequencies spaced one octave
plotted
frequency
(1981).
most common description of impaired hearing is the
ear
the
Results from experiments (up to
Although many different clinical
each
normal-hearing
relatively little is known about binaural interaction in
hearing-impaired
diagnosis
results
listeners
are
impaired
are
of
to
For
normal
apart
and
sometimes
the
loss.
listeners
whose
threshold levels are elevated by a relatively constant amount at all
frequencies, and hence have a relatively flat audiogram.
Current clinical tests can also classify losses in terms of the
general
underlying
physiological impairments.
two such descriptions:
conductive losses and sensori-neural losses.
Conductive losses are impairments of the
ear
function.
These
There typically are
external
and
middle
two portions of the auditory system transmit
the acoustic signal from the environment to the cochlea (the site of
PREVIOUS WORK
transduction
Page 2-12
from
mechanical
Conductive losses are
bone-conducted
(commonly
clinically
hearing
refered
conductive-loss
energy into neural firing patterns).
defined
thresholds
to
as
by
and
the
differences
air-conducted
air-bone
gap).
between
thresholds
Typically,
listeners show normal bone-conducted thresholds but
air-bone gaps of approximately 40 -
60
dB
(Davis
and
Silverman,
1970).
Sensori-neural losses are impairments
cochlear-losses)
and
neural
pathways
in
of
the
the
inner
ear
auditory
Sensori-neural losses are difficult to describe in general
(or
system.
and
can
result in complicated and different impairments.
Hawkins (1977), measured interaural time discrimination from
reference
delay
and
Hz.
4000
of zero usec for narrowband noises centered at 500
Their
impaired
subjects
were
bilaterally symmetric, sensori-neural losses:
listeners,
2
listeners.
low-frequency-loss
Hawkins
found
that
all
listeners
simply
particular,
and
2
the
flat-loss-listeners
high-frequency-loss
had
larger
frequency narrowband
noise.
measured
intensity
found
no
intensity
flat-loss
impairments there was a
that
relatable to the magnitude of the audiometric loss.
both
interaural
correlation
In
between
discrimination.
For
than
listeners
and
was
In
the
normal time jnds for the low
addition,
jnds
with
2 high-frequency-loss
listeners,
for
6
substantial degradation of interaural time discrimination
not
a
Hawkins
and
Wightman
for two of their subjects and
interaural
time
and
interaural
example, at 4000 Hz, the flat-loss
subject with a very abnormal time jnd (approximately 622 usec) had a
normal intensity jnd (approximately 0.8 dB).
PREVIOUS WORK
Page 2-13
Subjects for the survey conducted by
Hausler
et
al.,
(1983)
included 39 normals, 17 unilateral or bilateral conductive losses, 7
bilateral sensori-neural losses with good speech discrimination, and
7
bilateral
sensori-neural losses with poor speech discrimination.
Furthermore,
auditory
in
conjunction
with
evoked
potentials,
the
another
study
on
brain
stem
survey also included 26 multiple
sclerosis patients, all of whom had
normal
audiograms
and
better
than 88% speech discrimination.
All of the hearing-impaired subjects (aside from
the
multiple
sclerosis patients) had moderate to severe hearing losses (> 35 dB).
The stimuli for all the tests were 1-sec bursts
-
(0.25
10
of
wideband
noise
kHz ) presented at a level of 65 dB SPL for the normal
listeners and 85 dB SPL for the hearing-impaired listeners.
Although most of the tests performed on the
study
used
wideband
additional
tests
listeners
using
on
stimuli,
Hausler
bilaterally
in
this
and Colburn also performed
symmetric,
one-third-octave
subjects
bands
sensori-neural
of
noise
at
loss
center
frequencies of 500 and 3300 Hz.
They found that the listener with good speech discrimination (>
92 %) had normal time jnds at both 500 Hz (20 usecs) and 3300 Hz (30
usecs).
gave
In contrast, the person
very
abnormal
time
with
poor
speech
discrimination
jnds at 3300 Hz (> 500 usecs) but a near
normal time jnd at 500 Hz (30 usecs).
PREVIOUS WORK
Page 2-14
Since the wideband time jnds were near normal (< 40 usecs)
the
majority
listeners;
above
of
bilaterally
symmetric,
regardless of their speech
result
sensori-neural
discrimination
scores,
for
loss
the
suggests that there are frequency regions of impaired
binaural activity which are apparent only the non-impaired frequency
regions are not stimulated.
Each MS subject showed abnormal localization in
localization
had normal
Another
at
audiograms
finding
the
one
test -- a significant result since all the MS subjects
and
normal
(consistent
speech
with
the
discrimination
binaural
system's
interaural intensity.
processing
scores.
findings of Hawkins, 1977)
obtained from testing the MS patients was the apparent
of
least
of
independence
interaural
time
There were MS subjects with normal
and
intensity
jnds but abnormal time jnds, abnormal intensity jnds but normal time
jnds, and subjects with both time and intensity jnds abnormal.
suggests
(but
This
does not require) different physiological mechanisms
for the processing of interaural time and intensity differences.
In addition to these studies, many clinical investigators
have
tested the efficacy of the MLD as a diagnostic tool for neurological
disorders (Noffsinger et al., 1975 ;
al., 1981).
Olsen et al., 1976 ;
a
wideband
noise
bilateral, sensori-neural loss subjects.
for
180
unilateral
of
the
and
Results showed that 46% of
the cochlear-loss subjects had abnormal MLDs (defined by
MLDs
et
In a recent study, Noffsinger (1982) measured MLDs of a
500 Hz tone masked by
as
Lynn
Noffsinger
less than 8 dB) while 76% of the subjects with impairments
VIIIth
sensori-neural
nerve
had
abnormal
MLDs.
This
suggests
that
impairments have a significant effect on the MLD and
Page 2-15
PREVIOUS WORK
supports the notion
of
using
binaural
experiments
detection
as
diagnostic tests.
Jerger et al.
of
649
impaired
measured the MLD for a 500 Hz tone masked by a broadband
listeners,
noise.
in an exhaustive test
(1982)
MLDs for 71 bilaterally symmetric
(symmetric
9
within
dB
interaural threshold differences), sensori-neural loss subjects were
The reduction
obtained.
in
the
MLD
found
was
no
significant
(approximately
equal
reduction
to 11 dB).
was
observed
of
40
-
directly
in
the
MLDs
For losses in the range from 20 -
40 dB, MLDs were reduced to approximately 7 dB.
range
be
For hearing losses of
proportional to the threshold loss at 500 Hz.
0 - 20 dB,
to
For losses
in
the
60 dB, MLDs were essentially non-existent (about 1
dB).
Unfortunately, in both the Jerger and Noffsinger
studies,
the
individual thresholds for the NOSO and NOST' configurations were not
reported and it is hard to determine whether normal MLDs
to
normal
NOSO
and
NOST(
thresholds.
Moreover, it is not clear
whether abnormal MLD were a result of increased NOSIT
normal
NOSO
thresholds
correspond
thresholds and
or differential increases in both the NOSO
and NOSW thresholds.
C.
Models of Binaural Interaction
Most models of binaural interaction can be described by a block
diagram
from
one
of
the form shown in Figure 2.+.
another
in
the
detailed
Individual models differ
assumptions
about
(1)
the
PREVIOUS WORK
peripheral
Page 2-16
processing
of
the
signals,
and
(2)
the form of the
binaural interaction mechanism.
The peripheral transduction of the stimuli usually
critical-band
over
which
Moreover,
the
peripheral
peripheral
imperfectly, and
is
auditory
system
transduction
generally
degraded
and
assumed
by
some
physiological
an
stimuli.
to
form
be
of
done
noisy
This noisy processing reflects psychophysical evidence
neural activity.
from
combines
is
of internal "noise" limiting performance in
tasks
a
filter, the narrow (1/3 octave wide) frequency region
the
processing.
includes
recordings
of
monaural
the
and
binaural
intrinsically random
The embodiment of this noisy processing has varied
additive
noise
term
(Osman,
1971)
a
to
physiologically consistent description of the stimulus
detailed,
transduction
into neural firing patterns (Colburn, 1973).
The
computes
binaural
interaction
portion
of
typically
in
different
The
models
from a functional description (either explicitly (Sayers and
Cherry, 1957 ;
the
model
the cross-correlation of the signals at the two ears.
embodiment of the cross-correlation operation
varies
the
energy
Osman, 1971) or implicitly (in
the
calculation
of
in the difference between the interaural signals in the
EC model, Durlach, 1963) to a presumed neural coincidence
mechanism
which effects an interaural correlation measurement (Jeffress, 1949;
Colburn, 1973).
The decision mechanism is assumed to have available to
two
monaural
channel
interaction mechanism.
outputs
and
For stimulus
the
output
of
configurations
the
in
it
the
binaural
which
the
Page 2-17
PREVIOUS WORK
output of the binaural mechanism provides information which improves
performance, the decision mechanism is presumed to use the
stimulus configurations in which the
for
Similarly,
information.
binaural
binaural output provides less information
than
the
monaural,
the
decision process is assumed to use the better monaural channel.
These
models
in
predictions
mainly
have
binaural
performance
to
applied
been
detection and lateralization experiments.
Colburn and Durlach (1978) have extensively analyzed the predictions
of
the
different models and the dependence of these predictions on
the different modelling assumptions.
this
study,
instead
of
With regard to the purpose
concentrating
on
the
success
predictions in any one of the tasks, we focus on
past
of
attempts
of
the
at
relating
discrimination and detection tasks within the framework of
a single
model.
determine
to
Our
what
characterized
ability
extent
results
by
to
relate
different
from
a
these
binaural
small
two
tasks
phenomena
will
can
be
number
of
"elementary"
followed
by
Jeffress
experiments.
Starting with
al.,(1956),
many
of
detectability
differences
is
Webster
(1951)
researchers
signals
directly
have
in
suggested
Specifically,
improvements
binaural
to
Webster
detection
differences resulting from the addition
signals and maskers.
that
processes
(1951)
are
of
due
interaural
which
hypothesizes
to
et
the increased
with
configurations
related
lateralization.
in
and
effect
that
interaural time
interaurally
different
PREVIOUS WORK
Thus,
Page 2-18
given
differences
a
(for
measure
of
example,
a
sensitivity
to
measure
the
of
interaural
time
just-noticeable
interaural time difference) and a description of the interaural time
differences resulting from the addition of a signal to a masker, one
can predict that
required
to
the
produce
signal
level
at
threshold
is
that
level
the just-noticeable amount of interaural time
difference.
Hafter (1971), in relating a lateralization model
to
binaural
signal-in-noise detection, assumed a binaural decision variable,
, which was weighted sum of the instantaneous
intensity
differences.
No
internal
interaural
binaural
detection
configurations.
between
of
signal-to-noise
for values of
(9
(1976)
out
point
because
contribution
of
MLD
as
interaural phase configuration, S
ranging from 0 to
T
.
Domnitz
and
a
,
Colburn
that such a fit is not dependent on the specific
model assumed but is a.function
addition,
the
Using such a model,
Hafter was succesful at predicting the dependence of the
function
and
noise was explicitly assumed
since Hafter was primarily concerned with the relation
different
time
of
the
stimulus
parameters.
In
his binaural decision variable also included the
interaural
intensity
differences,
Hafter's
lateralization model, like the model presented by Durlach (1964), is
capable of predicting high-frequency MLDs.
used
only
(Jeffress
interaural
et
al.,
high-frequency MLDs.
phase
1956)
differences
were
Previously, models which
as
the
unsuccesful
binaural
at
cues
predicting
Page 2-19
PREVIOUS WORK
Note however, that the
binaural
decision
(a sort of compound interaural time difference) calculated
variable
at
Hafter's
of
value
the
in
threshold
signal-to-noise
NOS7i
is
configuration
Clearly, if such a model were to be applied
approximately 90 usecs.
both
to localization and detection, it would not be able to predict
the
observed
10-20 usec time jnds and the observed signal-to-noise
thresholds in an NOS7r paradigm.
Another, more recent, model which also combines interaural time
and
intensity
differences is the position-variable model mentioned
in the beginning of this chapter (Stern and Colburn, 1978).
conception, this model generated a binaural timing display
original
of neural coincidence counts after a fixed
between
interaural
delay,
of
fibers
an
Stern included
with
a
units
width,
fixed
the
W
on
position
function,
L ('Z), was
lateralization,
P
was assumed to be
a
and
interaural
dependent
intensity
function,
of interaural delay so that the two
L (•r)
function
L (( ) and L ( C).
interaural
analogous
to
transformed
relative
is obtained.
functions could be combined.
form
This
the assumed interaural delays and a timing
with
function (designated L (z))
L (T_ ),
,
'
pairs of fibers of the same characteristic frequency.
distribution of coincidence counts is then weighted by the
number
its
In
then
Gaussian
"mean" equal to M (1:
intensity
formed
difference.
in
), a
A
from the product of
The binaural decision variable used in effecting
,
was
obtained
this resultant position function.
by calculating the centroid of
PREVIOUS WORK
Page 2-20
To date, this model has not been applied to detection data, but
has
been
quite succesful at predicting subjective lateral-position
data and interaural discrimination of time in the presence of
noise
(Stern and Bachorski, 1983)
In general , if the parameter values of any model of
discussed
in
this
these two tasks are related
processes,
identical tasks
experiments,
value
20
dB
the observed thresholds (Colburn and Durlach, 1978).
identical
of
experiments
for
the
the
it
variables
may
be
lower
Although
effected
by
not necessarily true that the two are
is
mechanism.
In
lateralization
looking based on shifts in the mean
variable,
correlation
decision is based on changes in
binaural
performance
decision
decision
in
and
is
the
binaural
(and
type
section are chosen to fit interaural time jnds,
the predicted binaural detection thresholds are 15 to
than
the
the
distribution.
while
in
binaural
detection
discrimination experiments), the
width
In
the
(or
variance)
analysis
to
of
the
follow,
important consequences can be seen to follow from these differences.
CHAPTER 3
EXPERIMENTS
We tested four hearing-impaired listeners in
binaural
experiments
intensity
interaural
;
(1)
interaural
discrimination,
fundamental
time discrimination, (2)
interaural
(3)
discrimination and (4) binaural detection.
four
correlation
The same stimuli and the
same paradigm were used for all the subjects in all the experiments.
A.
Subjects
The
symmetric
two
criteria
(within
subject
for
were
bilaterally
5 dB), sensori-neural hearing loss with no known
differences in physiological damage
simplified
selection
between
the
two
ears.
This
the issue of signal level presentations (see Durlach, et
al., 1981) and allowed us to present signals of equal
SPLs
at
the
two ears.
The subjects used
in
this
study
were
three
subjects
with
moderate-to-severe bilaterally symmetric hearing losses diagnosed as
sensori-neural in origin and a Multiple Sclerosis (MS) patient
no
hearing
high-frequency
loss.
losses
Two
of
(both
these
subjects
subjects
had
been
had
with
noise-induced
regular
pistol
Page 3-2
EXPERIMENTS
shooters) and had audiograms which matched within plus or minus 5 dB
at all
48
were
subjects
as
diagnosed
These
3.2).
and
3.1
Figures
and 65 years old, had good speech discrimination
wear
not
scores and did
(cf.,
tested
frequencies
having
hearing
The
aids.
presbycusis
of
subject
third
type
strial-atrophy
the
(Schucknecht, 1974) and showed a relatively flat loss
3.3)
(Figure
This subject
with slightly larger losses at the higher frequencies.
regularly
scores,
was 62 years old, had poor speech discrimination
was
a hearing aid in her everyday life, but did not wear it during
wore
The
the experiments performed in this study.
as
hearing
normal
measured
audiological tests, but had
been
in
(cf.,
diagnosed
subject
fourth
Figure
as
3.4)
having
had
standard
MS.
This
subject.was 30 years old, did not wear a hearing aid, and had normal
speech discrimination scores.
In addition to the impaired
of
one
listeners,
a
subset
of
we
tested
the
respectively.
conditions
These subjects
this
normal
were
tested
tested with the hearing-impaired
listeners in order (1) to provide a comparison of the
in
two
whom was the author, the other an undergraduate
student , aged 28 and 19
in
subjects,
methods
used
study by comparing our normal results to previous data and
(2) to fill in "gaps" in the normal data, particularly in interaural
intensity and interaural correlation experiments.
B.
Stimuli
Page 3-3
EXPERIMENTS
Stimuli for
of
bands
noise
discrimination
the
five
around
centered
tests
were
one-third-octave
of the frequencies usually
Stimuli
the
for
noises (as maskers) and
experiments were synthesized on
amplitude,
random
phase
at
tones
pure
the
the same narrowband
a
computer
(see
cosines
from
Appendix
of
sums
I).
(at
a
10
random
The digital
waveforms were stored on disk and were reconstructed over
channels
center
corresponding
All the noise stimuli used in the
(as target signals).
frequencies
were
experiments
detection
Hz).
4000
tested in pure-tone audiometry (250, 500, 1000, 2000 and
dual
D/A
kHz sampling rate) followed by lowpass filters
with 4.5 kHz cutoff frequencies.
In all the
stimulus
experiments,
interval durations of 300 msec (rise-fall times of 15 msec;
of 270 msec) and interstimulus interval durations of 100
on-time
msec
were
used.
Stimulus levels at each frequency were held constant across the
different
subject,
binaural
but
were
tests.
These
above
threshold
levels
and
were different for each
within
the
range
of
comfortable listening (generally 30 dB above a subject's threshold).
Table 3.1 lists the stimulus levels for each
subject
at
the
five
testing frequencies.
The stimulus waveforms presented to the left and right ears
each
of
the
the
experiments
methods described below.
i) Interaural Time Discrimination
were
constructed
in
according to the
Page 3-4
EXPERIMENTS
Interaural time differences less than 100 usecs were created by
16
of
sets
synthesizing
independent
waveforms,
each
with time
differences (relative to the zero-standard set) ranging from 2.5
steps
47.5
usec
in
sets
were
generated
of 5 usecs.
at
each
of
to
Thus, a total of 11, 16-waveform
the
five
center
different
frequencies.
Interaural time differences greater than 100 usecs were created
by delaying presentation in one D/A channel.
This was done for ease
of presentation since it was easier to delay the waveform outputs by
multiple
sample
values
(at
large
generate sets of delayed waveforms.
waveform
(envelope
(onset)
interaural delays) rather than
Note that this causes
and fine structure) delay.
a
total
For delays
less than 100 usec, only a delay of the fine structure was created.
For any one presentation, the delayed waveform was presented to
either
the
left or right ear in the first interval and then to the
opposite ear in the second interval
or
where '
or ni(t) is one
is the interaural time difference and n-(t)
L
J
of
16
the
waveforms chosen at random.
The ear to which the delay
was first presented was chosen randomly with equal probability.
ii) Interaural Intensity Discrimination
Page 3-5
EXPERIMENTS
Interaural intensity differences were
and
amplifying
one
created
by
of 64 uncorrelated waveforms chosen at random.
For any one presentation, the attenuated waveform was
the
either
attenuating
presented
to
left or right ear in the first interval and then to the
opposite ear in the second interval
L=-&X=
A~±
-vYyL()
or
where A and B are the waveform amplitudes
4A</2 and
such
that
we
to
one
ear
also attenuated the signals at both ears in each interval
by a common, random amount (0 - 10
intensity
=
6• is equal to the interaural intensity difference in dB.
Since it is possible to perform this task by listening
only,
20log(B/A)
cues.
to
confound
any
monaural
A roving level over this range makes it impossible
to use monaural
discrimination
dB)
intensity
cues
to
perform
interaural
intensity
for intensity differences less than 6.0 dB.
The ear
in which the lesser amplitude waveform is first presented is
chosen
at random with equal probability.
iii) Interaural Correlation Discrimination
Different interaural correlations were created by
varying
the
relative amount of a common signal in one of the two intervals
or
where n,(t) and n-(t) are uncorrelated waveforms chosen from
C
i
a
set
Page 3-6
EXPERIMENTS
of
uncorrelated
64
correlation.
in
ear
each
power.
is
and
waveforms
, the average
Note that regardless of
interaural
test
the
power
noise
is equal since all n 's had the same ensemble average
The interval in which the test correlation appears is chosen
at random with equal probability.
iv) Binaural Detection
A tonal target signal was added to an in-phase noise masker
one
two
of
signal
phase
interaural
the first
In
conditions.
interaural
configuration (NOSO), the tone was added to each ear (an
phase
in
difference of 0 radians) in one of the two intervals as shown
below
or
and
where s(t) is the tone target
uncorrelated
waveforms
used
discrimination experiments.
the
tone
was
added
to
in
In the
n(t)
the
is
the
from
correlation
second
set
and
configuration
of
64
intensity
(NOS7-),
one ear and subtracted from the other (an
interaural phase difference of
'7-
radians)
in
one
of
the
two
intervals
or
In both configurations, the interval which contained the target tone
was chosen at random with equal probability.
Page 3-7
EXPERIMENTS
C.
Procedure
Subjects responded via push-button response boxes with no fixed
two-interval,
a
in
duration
response-interval
two-alternative-forced-choice (21,2AFC) paradigm with feedback.
such
a
paradigm, temporally ordered pairs of stimuli are presented
an
and the subject is asked to indicate in which interval
"event"
In
appeared.
auditory
For discrimination experiments, such an event is
the test difference along some dimension which must be distinguished
from
a
difference.
reference
For detection experiments, such an
event is the presence of a target sound which must be
from
a
masking
sound
alone.
distinguished
Typical runs of such presentations
lasted from 15 to 20 minutes.
Hence,
condition,
for
a
a
plot
particular
of
percent
and
reference
correct performance versus several
different test conditions was obtained.
in
attribute
stimulus
Percent correct was plotted
logit units and a weighted, minimum-chi-square fit (see Appendix
II) was
used
subject's
to
discrimination
just-noticeable
difference
characterize
the
curve.
ability
difference
between
the
(jnd),
reference
From
was
which
capability
was
signal-to-noise ratio, which
was
condition
defined
and
defined
test
by
as
a
a
the
condition
Similarly, a subject's
characterized
was
plots,
characterized
corresponding to 75% correct discrimination.
detection
such
as
by
the
ratio which corresponds to 75% correct detection.
a
threshold
signal-to-noise
Page 3-8
EXPERIMENTS
Representative psychometric
functions
and
normal
both
from
impaired listeners are presented in Figures 3.5 - 3.&.
Sequential Testing Rule
in
The method outlined in this section and discussed in detail
Appendix II (a draft of a paper) was motivated by a desire to reduce
to performance levels substantially different
corresponding
values
(stimulus
values
stimulus
extreme
at
the number of observations
from a desired performance level) in a fixed-number-of-trials (FNOT)
procedure.
impaired
hearing
with
testing
method of
listeners.
several stimulus values.
of
Performance estimates are usually obtained
throughout
fixed
presenting a specified, fixed number of trials, recording
run,
pyschometric
function
is
then
constructed
from
estimates at several stimulus values bracketing the
corresponding
clear to the
to the desired performance level.
experimenter
what
stimulus
suitably sampled psychometric function.
there will necessarily be
trials
cases
to 5 such
3
value
stimulus
It is not a priori
will
produce
a
Hence, in a FNOT procedure,
a
considerable
number
of
are used to estimate performance at extreme stimulus values.
This uncertainty about the range
testing
where
values
run.
the
responses and calculating a percent correct at the end of
A
at
level
performance
by selecting a particular stimulus value which is
the
particularly
A typical experiment with this
estimation
requires
efficient,
not
generally
The FNOT procedure is
of
hearing
is
especially
important
in
the
impaired listeners since the range of suitable
Page 3-9
EXPERIMENTS
significantly
stimulus values can vary
requiring
a
new
stimulus
from
subject
determination
range
for
to
subject,
each subject
tested.
Extreme stimulus values correspond to nearly perfect or
performance.
In
each
after the first 5 to 10 trials it is
case,
used
is
either
very
stimulus
value
discern.
Intuitively, in order to save time
vitality,
the
experimenter
the remaining trials.
continued
presentation
the
that
usually apparent to both the subject and the experimenter
being
chance
easy or very hard to
and
preserve
subject
should stop the run without presenting
However,
the
FNOT
procedure
requires
of all the trials in the run.
the
Practically,
an experimenter often implements an arbitrary criterion (e.g., if
a
subject has 10 consecutive correct responses, then stop) in order to
terminate such runs early.
In Appendix II, we formalize the above intuitive notions
reducing
experimental
data
collection
well-defined, objectively implemented rule.
into
a
about
systematic,
CHAPTER 4
EXPERIMENTAL RESULTS
Results from the four binaural experiments
discussed
in
relation
are
presented
and
to individual subject's hearing impairments
and to normal binaural hearing.
A.
Normal Listeners
i) Interaural Time Discrimination
Average results for the two listeners at 250, 1000 and 2000
are
presented
in
Figure
reviewed in Chapter 2.
250
Hz,
15
usecs
at
Hz
4.1, along with results from the studies
Observed interaural time jnds (20
usecs
at
1000 Hz and 70 usec at 2000 Hz) are in good
agreement with results from previous work.
ii) Interaural Intensity Discrimination
Page 4-2
EXPERIMENTAL RESULTS
Average interaural intensity jnds versus noise center frequency
are presented for the two listeners in Figure 4.2 along with results
from the studies reviewed in Chapter
For
2.
both
the
subjects,
interaural intensity jnds obtained (0.8 dB at 250 Hz, 0.9 at 500 Hz,
Hz)
0.8 at 1000 Hz, 0.7 at 2000 Hz and 0.6 at 4000
with
values
dependence
obtained
by
consistent
Hawkins (1977), as well as the frequency
intensity
smaller
(slightly
observed
are
jnds
at
high
frequencies relative to intensity jnds at low frequencies).
iii) Interaural Correlation Discrimination
Figure 4.3 presents average interaural correlation jnds from
reference
correlation of unity versus noise center frequency.
Hz
obtained
from
the
study
a
Also
by
plotted is the one point at
500
Gabriel and Colburn (1981).
Interaural correlation jnds are best at
low frequencies (approximately 0.01), increasing gradually
to
0.05
at 4000 Hz.
iv) Binaural Detection
Figure 4.4 presents average NOSO and NOS7T
versus
target
(or
noise center) frequency, along with the results
from the studies reviewed in chapter 2.
NOS71
detection thresholds
Except at 500 Hz, where the
threshold reported for our normal listeners are approximately
5 dB higher than the threshold obtained in
a
threshold
with
measurements
detection thresholds.
are
consistent
previous
study,
previous
our
binaural
Page 4-3
EXPERIMENTAL RESULTS
Generally, the normal data from this study is in agreement with
results from past studies on narrowband, binaural discrimination and
It is important to note that due to constraints on time,
detection.
the
testing of normal listeners was not as extensive as the testing
of the impaired listeners and was only
results
from
and
studies
previous
intended
provide
to
gaps
fill
in
consistency check
a
between past results and the results of this study.
B.
Impaired Listeners
i) Interaural Time Discrimination
Results from the two high-frequency loss subjects are shown
Figures 4.5 and 4.6 .
Despite their audiometric similarity (Figures
3.1 and 3.2), they had different sensitivities
differences.
to
interaural
on
the
order
of
60
-
frequencies (2000 and 4000 Hz),
100
usec
time
At low frequencies (250 - 1000 Hz) subject FG had time
jnds ranging from 30 - 50 usecs (Figure 4.5), while subject
jnds
in
while
DH
showed
100
usecs (Figure 4.6).
DH
had
At higher
subject FG had time jnds of
80
and
a marked loss of sensitivity with jnds
equal 550 and 600 usecs.
Note that subject FG has near-normal (Figure
to
4.1)
sensitivity
interaural time difference at high frequencies where his loss is
most severe.
In contrast to FG, subject DH has degraded
time sensitivity at both low an high frequencies.
interaural
Page 4-4
EXPERIMENTAL RESULTS
Results from the subject with a flat hearing loss, subject
(Figure
4.7) show no sensitivity to interaural time differences (up
to 1 msec, the largest time difference
where the jnd is 100 usec.
500
Hz
Subsequent detailed measurements of this
from
to
400
are consistent with her audiogram (Figure 3.3) and show no
Hz)
such region of good monaural hearing in either
to
appears
at
except
tested)
subject's thresholds near 500 Hz (at 10 Hz increments
600
VF,
have
an
"island"
of
ear.
sensitivity
This
subject
to interaural time
differences at 500 Hz.
Finally, results from the MS listener, subject
sensitivity
(up
to
1
CS,
showed
no
msec) to interaural time differences at any
frequency tested (Figure 4.8).
Recall
that
this
subject
two
high
frequency
had
a
normal audiogram at all frequencies.
The
listeners
time
jnds
obtained
for
listeners,
Hawkins
reports
time
using the 4000 Hz centered noise.
at
loss
are in good agreement with the results of Hawkins (1977),
except for subject DH at 4000 Hz.
usecs
the
4000
Hz,
a
For his two
high-frequency
loss
jnds ranging from 85 to 123 usec
Subject DH has a time jnd of
600
factor of 6 worse than the average time jnd
reported by Hawkins at this frequency.
The time jnds of subject VF are similar to the time jnds of the
two low-frequency loss listeners (no observable time jnds) tested by
Hawkins.
time
The two flat-loss listeners in Hawkins's study had smaller
jnds than those of subject VF (43 usecs at 500 Hz and 600 usec
at 4000 Hz).
Page 4-5
EXPERIMENTAL RESULTS
ii) Interaural Intensity Discrimination
Interaural intensity jnds measured from the two
loss
subjects
shown
are
similar sensitivities to
subjects
larger
had
in
high-frequency
They indicate
Figures 4.9 and 4.10.
interaural
intensity
Both
differences.
than normal intensity jnds ranging from 2.5 -
3.0 dB at low frequencies (< 1000 Hz), decreasing to 2.0 - 2.5 dB at
the
frequencies.
higher
The
low
frequency intensity jnds are a
factor of 3 - 4 worse than normals (Figure 4.2),
subjects
had
normal
hearing
those
at
though
even
frequencies, where both subjects have severe losses,
higher
At
frequencies.
the
both
intensity
jnds were a factor of 4 - 5 worse than normal.
Results from the flat-loss listener are shown in
This
dB.
4.11.
Figure
subject's low-frequency intensity jnds are between 3.0 and 4.5
At high frequencies, her intensity jnds increased to a
of 8 dB at 4 kHz.
maximum
At all frequencies, this subject's intensity jnds
were significantly worse (a factor of 6 - 10 larger) than normal.
Intensity discrimination results for the MS subject
in
Figure
4.12.
In
contrast
differences
at
500
Hz
sensitivity
and 1000 Hz.
to
interaural
Since the jnds at
other frequencies are near 6.0 dB, it is possible that this
used
monaural
(see below).
cues
shown
to interaural time discrimination,
subject CS, the MS patient, showed some
intensity
are
subject
to perform interaural intensity discrimination
Thus, despite a normal audiogram, subject CS has
poor
(a factor of 6 - 8 larger than normal) interaural intensity jnds.
Page 4-6
EXPERIMENTAL RESULTS
of
The random, 10 dB roving level added to each interval
experiment
the uses of monaural intensity information to
precluded
an
to
effect performance up
At and above
75%
this difference, it is possible to perform better than
correct
intensity changes even with the 10 dB roving level.
monaural
using
of
difference
intensity
interaural
dB (assuming a 21, 2AFC paradigm).
6.0
approximately
this
Thus, except at 4000 Hz for subject VF and at 250, 2000 and 4000
for
Hz
CS, interaural intensity discrimination could not have
subject
been mediated by monaural intensity cues.
Unfortunately, Hawkins did not measure the
his
loss
high-frequency
listeners.
intensity jnd for one of his flat
near-normal
waveform.
(0.8
This
intensity
However,
loss
jnds
of
he did measure the
listeners
and
obtained
a
intensity jnd using the high-frequency noise
dB)
result
is
not
consistent
with
our
flat
loss
listener's 8 dB intensity jnd at 4000 Hz.
iii) Interaural Correlation Discrimination
Results from the two high-frequency loss listeners are shown in
Figures
4.13
and
4.14.
Despite their audiometric similarity, the
two high-frequency loss subjects exhibited dissimilar
to
interaural
correlation
differences.
sensitivities
Subject FG has relatively
constant jnds equal to approximately 0.25 (a factor of 5 - 10 larger
than
normal)
at
the
middle
frequencies (500, 1000 and 2000 Hz),
decreasing to a near normal 0.05 at 250 Hz and to 0.1
Subject
DH
has
no
at
4000
Hz.
sensitivity to interaural correlation (subject
could not distinguish between correlated and uncorrelated noise)
at
Page 4-7
EXPERIMENTAL RESULTS
Moreover, this subject's sensitivity is worse
250 Hz (Figure 4.14).
at the low frequencies and best at the high
not
does
which
a
frequencies,
result
seem to be consistent with either his audiogram or
his time discrimination data.
As in the time discrimination experiment, subject VF showed
to
sensitivity
interaural
correlation
may
be
processing
at 500 Hz where we
interaural
a
that
This suggests
measured a jnd of 0.7 (Figure 4.15).
mechanism
except
no
correlation
and
time
common
differences at low frequencies.
As in interaural time
to
sensitivity
interaural
correlation
at
any
differences
further support the notion
that
no
frequency (Figure
interaural
to
The results from this subject
any frequency.
at
showed
CS
subject
Recall that subject CS showed no sensitivity
4.16).
time
discrimination,
interaural
time
correlation
and
processing are related.
In general correlation discrimination proved to be a
for
task
subjects
to
perform.
The
training for this task took
longer than in other tasks and this task was reported as
and
at
times confusing by all of the subjects.
by
Gabriel
and
Colburn
This is consistent
as
(1981) and Widjadja (1982).
It
should be noted that in the latter study, one
unable
"annoying"
listeners
with reports of correlation discrimination by
reported
difficult
normal
normal
listener
was
to discriminate perfectly correlated noise from uncorrelated
noise at 500 Hz even after a considerable amount of training.
vi) Binaural Detection
Page 4-8
EXPERIMENTAL RESULTS
Detection thresholds for both the NOSO and NOS7r conditions are
10
-
(5
elevated
dB
than
higher
FG
subject
are
approximately 7 - 8 dB higher than normal and
NOSTi thresholds are approximately 8 - 10 dB higher
an
unexpected
subject
had
subject
DH
are
are the NOSTr
thresholds,
monaural
normal---
than
at low frequencies where this
particularly
result,
normal,
thresholds
More precisely, NOSO
elevated by roughly equal amounts.
for
all
at
thresholds
normal)
the NOSO and NOSY thresholds are
both
Furthermore,
frequencies.
Both show
and 4.18 for subjects FG and DH.
4.17
Figure
in
shown
NOSO
thresholds.
for
thresholds
also approximately 8 - 10 dB higher than normal as
As with subject
thresholds.
particularly
Hence, subjects FG and DH
at
low
the
have
normal
FG,
the
elevated
NOSO
frequencies, is surprising.
or,
MLDs
equivalently,
a
normal amount of advantage in listening to a target plus masker with
interaural differences, even though
they
have
elevated
detection
thresholds.
As shown in Figure 4.19, results from subject VF, the flat-loss
listener,
show a different pattern of threshold elevation.
She had
near normal NOSO thresholds (within 2 - 3 dB) but elevated (a
12
dB
increase
above
normal)
frequencies (and hence, no MLDs).
NOS 1
thresholds
at
almost
The one frequency which
largest difference between the NOSO and NOST7j
had
10
all
the
thresholds was 500 Hz,
but this appears to be due to an elevated NOSO threshold rather than
a
reduced
NOSW threshold.
If we had been measuring only the MLD,
we might have incorrectly attributed the presence of the MLD to
the
Page 4-9
EXPERIMENTAL RESULTS
of
"island"
interaural time sensitivity this subject seems to have
at 500 Hz.
The results from the above three subjects are in agreement with
the
results
MLDs (albeit
hearing
at
of Jerger (1982).
500
elevated
to
due
Hz
(Figures
Both subjects FG and DH have normal
near-normal
and
thresholds)
NOSO
3.1 and 3.2), while subject VF has a
abnormal MLDs and monaural threshold loss greater than 40 dB at
all
frequencies (Figure 3.3).
Finally, as is
elevated
seen
in
advantage
detecting
4.20,
Figure
NOSO thresholds and NOS7r
the high-frequency loss
signals.
in
listeners,
out-of-phase
has
both
furthermore, unlike
thresholds;
subject
CS
subject
CS
showed
almost
no
signals relative to in-phase
Given the lack of any sensitivity to time and the degraded
sensitivity
to intensity differences, it is not surprising that the
NOST' configuration offers no listening advantage to subject CS.
C.
Binaural Audiograms
In this section, we present a
new
method
of
displaying
the
results of interaural discrimination experiments on hearing impaired
listeners.
descriptions
audiograms.
This
and
method
is
similar
to
current
audiometric
hence, we will refer to the new plots as binaural
Page 4-10
EXPERIMENTAL RESULTS
interaural
Binaural audiograms are plots of observed
decilog
Figures 4.1 - 4.3 display the normal
units re normal jnds.
discrimination jnds used in
in
jnds
the
We
development.
following
have
chosen a log scale in order to conveniently plot the increased range
(typically 1 to 2 orders of magnitude larger than
and
correlation
encountered
jnds
in
testing
normal)
of
time
hearing
impaired
listeners.
audiogram
For interaural time discrimination, the binaural
is
constructed by plotting
Figure 4.21 plots
versus the center frequency of the stimulus.
the
interaural time audiograms for all the subjects tested in our study.
Note that the time audiogram clearly illustrates features which
not
In particular, subject
readily apparent in the previous plots.
FG has a
low-frequency
time
"loss"
(in
are
his
region
of
normal,
monaural hearing) and normal, high-frequency time discrimination (in
the region of
his
loss).
In
contrast,
subject
DH
(the
other
high-frequency loss subject) has an approximately constant time loss
as a function of frequency, a
characteristic
not
easily
seen
in
expressed
in
Figure 4.6 .
Since
decibels
interaural
and
intensity
binaural
jnds
are
already
audiograms are plots of "dB loss" re normal
jnds, the intensity audiogram consistent with the time and
monaural
audiograms is a plot of
(aO/,
00
-
versus the stimulus center
intensity
(A
;?)OJAtL
frequency.
Figure
4.22
presents
audiograms for the four subjects of this study.
the
Note the
Page 4-11
EXPERIMENTAL RESULTS
relatively constant intensity loss of the
two
high-frequency
loss
subjects.
Furthermore, subjects VF and CS exhibit a high-frequency
interaural
intensity
"loss",
discrimination
a
pattern
of
loss
highlighted by the intensity audiogram.
Finally, Figure 4.23 presents the correlation audiograms of the
subjects.
four
Interaural correlation jnds were converted to dB re
normal jnds by the transformation
Note that subjects FG and DH show a low frequency correlation "loss"
which resembles their time loss at low frequencies.
In summary, binaural audiograms (1) highlight patterns of
which
are
not
apparent
readily
in
conventional
displays,
loss
(2)
incorporate the increased range of jnds observed in hearing impaired
listeners
and
(3)
provide
which is similar to current
a
description of binaural performance
audiometric
of
descriptions
monaural
hearing loss.
Clearly, binaural audiogram descriptions are dependent on
However, the basic utility of the binaural
is termed "normal" data.
audiograms in exposing patterns
independent
of
what
of
impaired
binaural
hearing
any specific set of normal data assumed.
is
Hence, we
feel that binaural audiograms are an informative display of binaural
discrimination
"loss"
in
hearing
become a standardized method of
impaired
reporting
results.
D.
Relationships Among the Four Tasks
listeners
impaired
and should
discrimination
Page 4-12
EXPERIMENTAL RESULTS
Scatter plots (Figures 4.24 - 4.29) of
four
Each scatter plot combines data from
for
the
from
results
the
tests are presented for all possible combinations of
binaural
pairs.
and
the
different subjects.
different
frequencies
Only measured data points (i.e.,
correlation jnds less than unity and time jnds less than 1000 usecs)
are plotted and used in the calculation of the sample correlations.
The sample correlations, r, calculated for
the
various
pairs
are presented below :
r(.AT , 4( ) = -0.28
r(
e"
, 4
) = -0.03
, n = 11
,
n = 10
r(
,iotl.a5)
r(Q(
, 6
r(Ao(
,toh/.) = -0.38
, n = 11
r(A4
.,Lo.)
, n = 10
= 0.60
)=
0.41
= -0.20
, n = 11
,n
10
For n = 10, the critical values of
are
Y
<
-0.63 and
and
r
>
0.60.
r
Thus,
> 0.81.
none
`Y at 95% confidence levels
For n = 11, they are
of
the
sample
f
< -0.60
correlations
are
significantly different from 0 at the 95% confidence level.
The low (and negative) sample correlation
jnds
and
believed
NOS¶r
between
correlation
detection thresholds is surprising in light of the
dependence
of
processors (see Chapter 2).
binaural
interaction
on
However, if we express ( 4
correlation
). in units
Page 4-13
EXPERIMENTAL RESULTS
causes
of a signal-to-noise ratio which
amount
of
a masker for an NOS7? signal configuration by the
in
decorrelation
equivalent
an
transformation :
(A
)
=
log(WT) + 10log-----------
we compute a new sample correlation equal to 0.67.
not
larger
is
it
but
significant,
This
still
is
than what it was before (and
positive instead of negative).
The above analysis suggests that correlation values
expressed
in
This
not
is
need
only
based
on
correlation obtained above by such a transformation.
discrimination experiments from a reference
one
presents
typically
be
similar to signal-to-noise ratios in detection
units
experiments.
should
test
correlation
the
increased
In correlation
correlation
unity,
of
values ranging over two
orders of magnitude (0.9 to 0.999) in order to sample a psychometric
The
function.
range
spanned by the transformed correlation value
(see equation above), is less than a factor
Pollack
and
of
three.
Note
that
Trittipoe (1959 a,b) plotted their results in terms of
equivalent common-to-uncommon noise ratios rather than correlation.
Scatter plots of the results from the four binaural
monaural
threshold
losses
are
presented
subjects.
and
in Figures 4.30 - 4.33.
Each scatter plot combines data from different frequencies
different
tests
and
for
Only measured data points are plotted and used
in the calculation of the sample correlations.
Page 4-14
EXPERIMENTAL RESULTS
The sample correlations, r, calculated for
the
various
tests
are
, HL
r(
HL
r(
) =
0.50
Sn= 11
) = -0.10
Sn = 15
, HL- ) =
4
r(to % ,
-0.08
Sn = 10
0.29
, n = 20
) =
For n = 15, the critical values of
levels
values are
four
Y
are
r
binaural
<
-0.59 and
< -0.19 and
tests
C
appear
monaural hearing losses.
r
Yr > 0.45.
> 0.66.
to
be
at
the
95%
confidence
For n = 20, the critical
None of the results from the
correlated
with the measured
CHAPTER 5
A MODEL OF BINAURAL INTERACTION
interaction
in
an
introduce
we
In this chapter
attempt
to
:
general
a
model
of
binaural
unify interaural time and
(1)
intensity discrimination phenomena with binaural detection phenomena
in
normal
and
and
listeners;
impaired
(2)
a
provide
simple
characterization of binaural hearing on the basis of interaural time
and
interaural
intensity
processing.
With this goal in mind, the
model presented in this study is not a final model and is
in
a
described
way that allows alternate assumptions to be investigated.
It
is a working hypothesis that serves as basis for the development and
modification of existing models of binaural interaction.
A.
Outline of the Model
The basic thrust of
interaction
time
model
is
to
characterize
process
and
is
interaural
assumed
intensity
differences.
The
to be intrinsically stochastic (or
noisy) and limited in its temporal tracking capability.
these
binaural
as decisions based on imperfect estimates of interaural
differences
estimation
the
The use
of
imperfect difference estimates is assumed to be ideal subject
Page 5-2
A MODEL OF BINAURAL INTERACTION
to a specific combination rule.
performance
The parameters of the model are estimated from the
of the individual impaired subjects in interaural time and intensity
discrimination experiments.
either
continuous
Although the model can be formulated in
time or discrete time, we have chosen a discrete
has
attempt
No
time formulation in order to simplify the calculations.
been made to address bandwidth effects and individual frequency
bands are assumed to be processed separately.
problem
As discussed in Chapter 2, a general
binaural
interaction
lateralization and
parameter
is
their
detection
values.
A
inability
performance
possible
with
resolution
to
with
to
predict
the
same
without
changing
the
mean
value
of
both
set
of
this problem is an
additional mechanism which reduces the variability of
statistic
models
the
binaural
of the statistic.
A
mechanism which achieves this is an averager (or lowpass filter)
differences.
binaural
As
will
be
seen
in
this
chapter,
of
the
incorporation (or inclusion) of this mechanism in a general model of
binaural
interaction
appears
to
make
predicted NOS7T
thresholds
consistent with predictions based on observed discrimination jnds.
Evidence for such a mechanism is
(Blauert,
1972
;
Perrot
present
in
several
studies
and Musicant, 1977), most recently in a
series of papers by Grantham (1980) and Grantham and Wightman (1980)
concerned
follow
with
time
the measurement of the binaural system's ability to
varying
interaural
differences.
For
interaural
correlation differences about zero correlation, they measured cutoff
frequencies of 5-8 Hz for a 500 Hz-centered narrowband noise.
At
a
Page 5-3
A MODEL OF BINAURAL INTERACTION
frequency of 1000 Hz, they measured an 8-15 Hz cutoff
center
noise
frequency, and at 2000 Hz,
18-25
approximately
The
Hz.
roughly proportional to
they
the
a
measured
center
of
cutoff frequencies is
in
increase
frequency
cutoff
the
of
frequency
noise
and
suggests a constant ratio of peripheral-filter bandwidth to low-pass
filter cutoff frequency.
B.
Elements of the Model
of
Figure 5.1 illustrates a block diagram
section
of
the
one
binaural portion of the model.
frequency-band
The assumptions of
the model are:
1.
The stimulus waveforms at each
ear
are
filtered
with
a
rectangular, 1/3-octave bandpass filter of width Wcb ;
2.
The binaural system processes only a 300
the
signal for each decision.
msec
segment
of
Equivalently, the effective
duration of the stimulus is limited to 300 msec.
3.
A temporal sequence of instantaneous
interaural
intensity
samples
(
'-
interaural
time
and
and k; ) are obtained
from the filtered stimuli at time intervals
equal to
).
bandwidth (Wcbinverse of the peripheral filter
inverse of the peripheral filter bandwidth (Wcb
).
the
Page 5-4
A MODEL OF BINAURAL INTERACTION
4.
by
corrupted
are
The interaural time and intensity estimates
independent, zero-mean additive Gaussian noise terms of
deviations of the noise (
and
r
),
each
standard
the
by
specified
are
difference
interaural
and
band
each
in
levels
noise
The
fixed level.
the
only
estimates
are
are
and
free parameters of the model.
5.
corrupted
of
sequences
Both
interaural
over K samples.
Individual estimates
separately
averaged
of Z.
0- are not available nor are running
Each
and
average
and
estimate,
parameter
of
the
parameter
in
each
consider
different
it
model,
frequency
for
Ks
is
(available every K
on
samples) is independent of the others.
Although
K
At
most,
is
a
a free
considered
not
band.
averages.
we
will
interaural time and intensity
averaging.
6.
The two averaged interaural estimates can
as
be
approximated
Gaussian random variables and are available as separate
inputs to an ideal decision mechanism.
7.
Two monaural channels are available to the
mechanism
which,
in
the
limit the predicted NOS1f
the monaural thresholds.
ideal
decision
context of this study, serve to
thresholds to be
no
worse
than
Page 5-5
A MODEL OF BINAURAL INTERACTION
C.
Comments
The first four elements are not
the
of
sort
included
assumptions
in
most
interaction (Colburn and Durlach , 1978).
are
different
significantly
of
models
from
binaural
The first two assumptions
to the present study (we used only one-third-octave
irrelevant
bands of noise and a duration of
300
msec),
made
on
and
stated
are
for
completeness.
The
is
assumption
third
basis
the
of
the
characterization of a narrowband signal n(t) of bandwidth W by
S*-
=
A (-t)
c.os
t?- t
T.
7c-e)
1
where A(t) is equal to the envelope function, C (t) is equal to
phase
and
function
fo
the center frequency of the narrowband
is
signal (Wozencraft and Jacobs, 1965).
When n(t) is a Gaussian noise
A(t) is a stochastic function with time samples which are
function,
Rayleigh distributed random variables
function
the
with
time
time
q (t)
is
a
stochastic
samples which are uniformly distributed in the
interval between 0 and 271
independent
and
samples
(Davenport and Root, 1958).
of
Furthermore,
both A(t) and q (t) occur every W-1
seconds (the first time instant when the
autocorrelation
functions
of A(t) and (f(t) equal zero) and completely describe the stochastic
functions A(t) and YC(t) (Van Trees, 1968).
the interaural time (phase) difference
and interaural intensity difference
Thus,
the
samples
of
Page 5-6
A MODEL OF BINAURAL INTERACTION
AJ&)
L
(where
=
t
completely
to
assumed
are
i/Wcb)
the
describe
interaural time and intensity difference functions (Footnote 1).
characterization
This
processing.
of
assumption
is
both
types of hearing impairments.
various
time and intensity
interaural
imperfect
the
independent
allow
to
order
The fourth assumption is made in
and
simple
applicable
to
Moreover, the additive noise
term is presumed to characterize the combined
noisy
processing
of
the peripheral and central portions of the auditory system.
The fifth, key assumption is the
for
in
Chapter
2,
variability of the
detection
and
additional
An averaging mechanism reduces the
Section C.
difference
interaural
correlation
argued
mechanism
statistics
discrimination
in
binaural
experiments
without
affecting the predictions of the interaural difference statistics in
interaural
time
and
intensity
discrimination
experiments.
Initially, for ease of presentation calculation, we assume equal
Ks
(or equal temporal tracking capability) for both interaural time and
interaural intensity processing.
different
averaging
Ks
for
the
In chapter 8, we
interaural
will
time
and
show
that
intensity
estimates provide a better fit to observed results.
The last assumption allows us to explore various
including
the optimal combination, of interaural time and intensity
differences.
normal
combinations,
This exploration is not only relevant to modelling
listeners,
but
is
in
particularly important in modelling the
binaural hearing of impaired listeners, where one of the
interaural
Page 5-7
A MODEL OF BINAURAL INTERACTION
measures
difference
so degraded as to be of little use in
be
may
the
separates
which
interaural
model
a
Without
providing binaural information about the stimuli.
time and intensity processing and
defines the combination of-the two interaural differences, it is not
clear
observed
from
interaural
and intensity jnds what the
time
relative usefulness of the two cues are in a given binaural task.
Ito
This model is similar to the one proposed by
(1982)
that
Their
a study of masked interaural time discrimination.
in
they
assumed
no
intensity
interaural
specific linear combination of the
interaural
here
presented
model can be considered a special case of the model
in
et al., (1982)
processing and a
phase
observations.
Moreover, the averaging of their interaural phase difference samples
was explicitly performed since
they
assume
that
mean
interaural
phase differences are used in forming the decision variable.
Similarly, Hafter's lateralization model (described in
2)
can
also
be
considered a special case of the general model in
that he assumed no temporal averaging of the interaural
and
a
specific
Chapter
linear
of
combination
the
differences
interaural
time and
intensity differences.
D.
Estimation of the Model Parameters
As
stated
independent
earlier,
interaural
the
difference
number, K, of these samples.
K
seems
to
averager
reduces
samples
by
the
number
averaging
From the Grantham studies, the
of
a fixed
number
be constant across different center frequencies and is
Page 5-8
A MODEL OF BINAURAL INTERACTION
Thus the only
approximately equal to 20.
single-critical-band
6
gZ and
are the internal noise levels,
model
the
of
parameters
free
, in each of the binaural difference processors.
The most direct
way
estimating
of
interaural time discrimination
two
any
by
however,
could be used to estimate the
binaural
other
results
general,
In
experiments.
experiments
binaural
parameters;
model
parameters. is
model predictions to results from interaural intensity and
matching
from
these
(e.g.
experiments
discrimination and detection) generally produce changes
correlation
in both the interaural time and intensity differences
chapter
(see
6).
using
Further,
differences
?ý and
in
stimuli
with
fixed
(non-random)
interaural
interaural discrimination experiments of this type,
the
can be considered as statistics with means equal to
k
interaural differences and variances equal to zero.
Thus,
the only limitations on performance are the additive internal
noise
stimulus
terms.
In
the
following
sections,
using
standard
techniques
of
communication theory (Van Trees, 1968), we will relate ez and
to the interaural difference jnds, (AT)o
this
and
relationship
intensity
depends
difference
and (A.X ) .
The
form
of
on the way in which the interaural time
estimates
are
decision mechanism.
i) Separate Time and Intensity Differences
combined
prior
to
the
Page 5-9
A MODEL OF BINAURAL INTERACTION
With the
assumption
(
estimates
difference
each
that
)
,
ideal decision mechanism
Figure
of
averaged
the
interaural
is individually available to the
5.2
(a),
it
follows
that
(see
Appendix III)
Sl
( 5.1 a)
and
d
where
V
=(
5.1 b)
cý
= number of independent samples of
L
or
obtained
during the stimulus duration, T, (or 300 msec, whichever is shorter)
and is given by
K
ii) Weighted Sum of Interaural Differences (SID)
As an illustration of the
way
in
which
these
relationships
change for different mixing assumptions, one combination rule (which
has
been
perception,
suggested
see
as
Chapter
interaural differences
represented
here
the
by
variable
2)
is
(Figure
the
a
5.2
underlying
lateralization
fixed, weighted sum of the two
(b)).
parameter
b
The
and
fixed
turns
weight
out
to
((•)/((T) ), the inverse of the time-intensity trading ratio.
is
be
A MODEL OF BINAURAL INTERACTION
Page 5-10
Given this assumption, there
is
effectively
only
one
noise
term, which is related to the interaural intensity jnd by
+
2
14 .
-
(4
)
( 5.2 a )
or, equivalently, from the interaural time jnd by
+ 6
-
( 5.2 b )
Since the left-hand-sides are the same in
clear
that
b
must
be
equal
to
these
equations,
((AC).o)((r,)•),
6
values of
6
decision
and
(
assuming
This
no
combination
SID
rule
is
still
band, we must specify b and
prior
by
predicting
a two-parameter model.
z
tested.
Thus,
we
the
the
noise
now
have
that
For each critical
.
z
can
be
level estimates from observed
interaural time and intensity jnds at each
bands
to
In addition, note
The parameters of each narrowband portion of the model
specified
the
has consequences for the predictions of
the two assumptions presented in chapter 8.
the
Moreover,
in this sort of combination is less than the
and 6,
mechanism.
is
the ratio of the
interaural intensity jnd to the interaural time jnd.
values of
it
a
of
simple
the
five
model
frequency
of binaural
interaction which allows us (1) to match the frequency dependence of
interaural time and intensity jnds in normal and impaired listeners,
and (2) to predict performance in other binaural hearing tasks
with
Page 5-11
A MODEL OF BINAURAL INTERACTION
no additional assumptions or parameter choices.
It is important to realize that the theoretical predictions are
independent
of (1) whether the averaging mechanism is placed before
or after the noisy processing and (2) that in the case of
for
interaural
time
independent
of
whether
differences
occurs
and
intensity
the
before
averaging,
combination
or
after
of
the
predictions
two
the averaging.
the
order
Ks
are
interaural
Although the
values of the processing noise variances would change for
orders,
equal
different
of the operations is not important (because the
operations following the extraction
estimates are linear).
of
the
interaural
difference
CHAPTER 6
CHARACTERIZATION OF STIMULUS INTERAURAL DIFFERENCES
According to the
intensity
differences
are
averaged, and then
used
mechanism.
given
Thus,
in
model
5,
Chapter
interaural
time
and
extracted from the stimulus, corrupted,
as
observations
a
for
an
ideal
decision
specification of the corruption (i.e.,
of
the
from
the
interaural intensity and time (or phase) differences present in
the
additive noise terms) and the
model
for
a
given
binaural
the
averaging,
task
can
be
predictions
calculated
stimuli at the two ears.
In this
intensity
chapter,
and
we
present
the
statistics
of
interaural
interaural phase differences for the stimuli used in
the correlation discrimination and binaural
detection
experiments.
Using the method outlined by Domnitz and Colburn (1976), we obtained
analytic expressions for the instantaneous interaural intensity
and
interaural
too
phase
intractable to
correlation
the
and
numerical
differences
ratio.
at
differences.
evaluate
The
analytically
signal-to-noise ratio;
calculations
limiting
and
for
expressions
at
intermediate
proved
values
of
however, they were used in
characterizations
of
the
values of correlation and signal-to-noise
CHARACTERIZATION OF STIMULUS INTERAURAL DIFFERENCES
A.
Page 6-2
Analytic Evaluation of Interaural Differences
i) Correlation Discrimination Stimuli
In the correlation discrimination experiments, the
the
left
ear,
Re[EXt+f)],
and
at
stimuli
at
the right ear, Re[r(t)], can be
described as complex waveforms of the form
XCjt) = N(e)
Ie
( 6.la
(
6.lb
where fo is the center frequency of the noise, N( (t)
Rayleigh
stochastic
distributed
sample
stochastic
time
time
functions (i.e.,
values),
functions
distributed sample values).
and
(i.e.,
(t)
and
N (t)
are
functions with Rayleigh
and
(t)
are
functions
The correlation time
with
(i.e.,
uniform
uniformly
the
time
instant at which the autocorrelation function first equals zero) for
all the functions is equal to the inverse of the noise bandwidth.
Forming the interaural complex ratio of the two
get
waveforms,
we
Page 6-3
CHARACTERIZATION OF STIMULUS INTERAURAL DIFFERENCES
(t) are both
Since (, (t) and
from
interval
that
(e(t)
(6.2
fit.
-
)
in
distributed
uniformly
we have
to 77- and the phase is circular in 2'77,
- 7
- Y(t)=
(t),
where
C(t)
is
uniformly
the
distributed
from - 7t to 7 .
I(ti)
Thus, at any time instant,
=
I
is
a
complex
random
variable given by
3
C
where N I and N2 are independent,
variables
random
in the interval -7T
and
(fis
(
6.3 )
identically
distributed
Rayleigh
a uniformly distributed random variable
to ?7 .
the
The magnitude of I, or equivalently
interaural
magnitude
ratio at any instant in time, is given by
47
/(6.4 )
thus
the
difference in decibels is equal to zero.
For
1 this magnitude ratio is identically unity and
= 1,
For
interaural
=
,
intensity
CHARACTERIZATION OF STIMULUS INTERAURAL DIFFERENCES
Since N
and N
variables
of
S2
are
degree
identically
2,
their
distributed
ratio
variable, usually represented by F(v:
of freedom.
is
2)
,= =
Thus,
0.4-333
)
F]
L
From Johnson and Katz (1970), we have
S
:L
F
= o
( 6.7a )
V
L"- F
0
Z-2
( 6.7b )
It then follows that,
E
and
2•o ,Iti
0-
chi-squared
random
an F-distributed random
with
(6.6
Page 6-4
(6.8 )
2
degrees
CHARACTERIZATION OF STIMULUS INTERAURAL DIFFERENCES
Vo-4
2.o~o
Page 6-5
( 6.9
(Tjz
in dB
Therefore, the interaural intensity difference (201logIIl)
=
at
0
has an expected value of zero and a standard deviation
equal to approximately 7.9 dB.
Eqn.
in
shown
is
Furthermore, as
6.3, the amount of variability in I (and in III) is modulated by
L-$
1.
hence,
Clearly, the maximum variability occurs
7.9
dB
is
0,
and
intensity
waveforms
correlated
the
difference fluctuations possible for
ý =
interaural
of
amount
maximum
the
at
of
6.1 .
Eqn.
The phase of I, the interaural phase difference at any
instant
in time, is given by the expression
22
,ctp
is
satisfied
multiples of 2
a
of
Since the above equation (the angle
plane)
( 6.10
by an infinite set of
, we restrict the values
be in the principal-value range of -11
<
)
4
we
have
chosen
symmetric about zero, and hence,
the
for
near
to
.
< TF
above
complex
development
._I in our
.I
the
I values differing in
Although any continuous range of length 2i7(
principle-range,
in
vector
could serve
range
diotic
as
a
because it is
stimuli
(small
CHARACTERIZATION OF STIMULUS INTERAURAL DIFFERENCES
interaural
phase.
near
Page 6-6
differences), the phase distribution clusters about zero
Since the stimulus conditions of interest in this study
are
diotic (near-zero interaural intensity and phase differences),
the above principal-value range is appropriate.
f = 1i,we have
For
difference.
I = 0, and
hence,
no
interaural
phase
= 0,
For
( 6.11 )
3
As in the case of III,
the
distributions is modulated by
amount
of
1 -
2
variability
in
the
phase
=
and the variablility at
0 represents the maximum amount of variability in the stimulus phase
difference.
To
realize
that
this
represents
the
variability, it is helpful to consider the probability
maximum
distribution
of the phase difference to be defined over a circular abscissa, with
-Ti and 7[
near
being the same point on the circle.
For
values
of
1, all the probability is clustered around the 0 point.
decreases to 0
,
the
probability
becomes
distributed
As
uniformly
around the circle.
Finally, it is important to note that III and 41 are functions
of
the
random
these variables
waveforms.
variables, N2 /N
are
independent
I
and
of
@ .
the
The statistics of both
power
in
the
stimulus
Thus, for correlated waveforms of the form in Eqn.
the interaural difference statistics depend only on
.
6.1,
Page 6-7
CHARACTERIZATION OF STIMULUS INTERAURAL DIFFERENCES
ii) Binaural Detection Stimuli
Just as in
the
in
waveforms
stimulus
described
as
correlation
the
discrimination
binaural
waveforms.
complex
the
experiments,
detection experiments can be
For
the
NOSO
detection
configuration (in-phase noise added to an in-phase signal) we have
( 6.13a )
L
L
where N(t) is a
uniform
( 6.13b )
+A
At)4= e
,/)
stochastic
Rayleigh
time
function,
L
(t)
the
a
stochastic time function, fo is the center frequency of the
noise as well as the frequency of the target signal, and A is
to
is
signal
amplitude.
equal
Hence, for all signal-to-noise ratios,
I(t) = 1 which implies 201loglII
= 0 and
.I = 0.
For the NOSWT detection configuration (in-phase noise added
an out-of-phase signal) we have,
5)
e-1[J
-=A(4e-)
?C§-t= AJC-)e
where N(t), ( (t),
)
( 6.13c )
-
Ae
6.13d )
fo and A are as defined above.
to
CHARACTERIZATION OF STIMULUS INTERAURAL DIFFERENCES
Page 6-8
Forming the interaural complex ratio, we get
c+
• C>
÷
( 6.14 )
Hence, at any instant of time, I(ti) = I is a random variable
given
by
A
-
WC
711
( 6.15 )
A
-f
fQe,
The magnitude of the interaural intensity ratio is given by
0Sce
_
N~cse
IT-(
A
-
I-k
K~ L
=
ZAA6.16 )
SI'
For the case of no signal present (A/N = 0),
implies
201logIII
=
0.
we have III =
1
which
In the limit as the signal-to-noise ratio
approaches infinity, III again approaches 1 and 201logII
0.
The phase of I is given by
-'•a,,v
L
cz 5.
approaches
Page 6-9
CHARACTERIZATION OF STIMULUS INTERAURAL DIFFERENCES
L-a
ta~6 -I
-
-)I
M
( 6.17
For A/N = 0, we have 4
In
difference.
I
=
and
0,
hence,
)
no
limit as the signal-to-noise ratio approaches
the
infinity, the argument of the first term of Eqn.
from
a
negative
value
while
the
approaches 0 from a positive value.
?'t- o
B.
phase
interaural
argument
6.17 approaches
of
0
second term
the
Therefore, we have
= 7
Numerical Computation of Interaural Differences
At intermediate values of
distributions
of 201loglII
computer simulations.
variables
were
techniques and
signal-to-noise
ratio,
the
and LI were empirically obtained through
phase
Rayleigh amplitude and uniform
generated
a
and
by
pseudo-random
inverse
number
cumulative
generator
random
distribution
(Dahlquist
and
Bjork, 1974).
Using equations 6.4, 6.10, 6.16, and 6.17,
and
second-order
density
histograms
statistics of interaural intensity and interaural
phase differences were obtained from 10,000 samples of
from a uniform distribution in - 'i
to T7
CP
(chosen
) and N, ,N7 (chosen from a
Rayleigh distribution corresponding to a unit-normal Gaussian,
i.e.
CHARACTERIZATION OF STIMULUS INTERAURAL DIFFERENCES
&
= (2 -
))
Example
at each value of
distributions
differences
at
intensity
Figures
6.1
Figures
(PDFs)
0.995, 0.80
and
interaural
and
phase
r and signal-to-noise ratio
through
-
6.1
for
0.0.
6.3
6.12.
illustrate
interaural
Figures
intensity
6.4
phase differences at
-
In
each
figure,
signal-to-noise
ratios
illustrate
PDFs
of
-26.0,
for
6.6
probability
density
differences
at
illustrate
PDFs
= 0.995, 0.80 and 0.0.
6.7 - 6.9 illustrate PDFs for interaural
6.12
differences
density is plotted versus interaural intensity or phase
difference.
functions
and signal-to-noise ratio.
intermediate values of
are illustrated in
probability
of
Page 6-10
intensity
-21.5 and 0 dB.
interaural
phase
=
for
Figures
differences
at
Figures 6.10 differences
at
signal-to-noise ratios of -26.0, -21.5 and 0 dB.
In the correlation
(Figures
case
for
values
of
equal
that
unimodal,
0.995
6.1 and 6.4), 0.8 (Figures 6.2 and 6.5) and 0 (Figures 6.3
and 6.6) both difference distributions are unimodal and
Note
to
as
mean.
approaches zero, both distributions retain their
zero-mean
distribution
zero
characteristics
becoming
increasingly
with
uniform
the
phase
difference
(as predicted by Eqn.
6.11) and the intensity distribution reaching its maximum width.
For
the
detection
(Figures
6.7
and
6.10),
case
at
signal-to-noise
ratios
also
zero
Although it is not apparent in each figure, the distributions
of both differences are also bimodal.
phase
dB
-21.5 dB (Figures 6.8 and 6.11) and 0 dB
(Figures 6.9 and 6.12) both difference distributions are
mean.
-26
The bimodal structure of
the
distributions (Figures 6.10, 6.11, and 6.12) is more apparent
Page 6-11
CHARACTERIZATION OF STIMULUS INTERAURAL DIFFERENCES
than that of the intensity distributions, particularly at the higher
signal-to-noise
ratios
where
the double peaks are more pronounced
and separate.
The detailed functional forms of these difference distributions
are not important from the modelling point of view but are presented
here for completeness.
averages
Since
approximately
the
model
Chapter
chapter
random
Gaussian
5
variables
Such averaging must be carefully defined for the
7).
interaural phase estimates since phase is a circular
this
in
20 such difference estimates, the resulting
averaged samples can be approximated by
(see
presented
In
function.
study, we assume that (as a result of the averaging), the PDFs
of the phase distributions are circularly convolved
average
resultant,
distribution.
distributed phase (
phase
does
not
In
the
to
case
obtain
of
the
uniformly
and 10log(S/N) equal to zero), averaging
result
the
in convergence to a Gaussian distribution.
However, since most of the predicted correlation jnds
in
the
next
chapter are less than 0.7 (correlation values greater than 0.3), the
uniform phase distribution does not appear in our predictions.
Given the Gaussian assumption, a sufficient characterization of
the
stimuli
which
is
useful
for
second order description of the
dependence
the modelling predictions is a
difference
estimates.
Thus,
of the standard deviations of 20logIII and 4-I versus
and signal-to-noise ratio are plotted in figures 6.13 through
For
all
values of
of
intensity
6.16.
and signal-to-noise ratio, the expected value
of both 201logIIl and 4I were equal to zero.
values
the
In addition,
for
all
and signal-to-noise ratio, the interaural phase and
measures
appeared
to
be
uncorrelated
(numerically
CHARACTERIZATION OF STIMULUS INTERAURAL DIFFERENCES
calculated
correlations
Page 6-12
were always a factor of 10
-3
less than the
product of the individual standard deviations).
In the correlation case, for both difference
is
a monotonic increase in standard deviations as
unity to zero.
deviation
rises
Specifically,
the
intensity
sharply at values of
of 5.6 (ordinate values divided
by
variables,
f decreases from
difference
the
maximum
phase difference standard deviation showed
near
unity
(a
normalized
slope
standard
near 1, a normalized slope
ordinate
a
value),
= 0.6 .
reaching a constant value of approximately 7.0 dB at
rise
there
relatively
The
shallower
of 3.7) and increased at a
linear rate of 1.25 radians per unit decrease in
for
less than
0.9
In the detection case, as with the correlation waveforms, there
is
a
monotonic
increase in standard deviations as signal-to-noise
ratio increases up to
approximately
0
dB.
However,
unlike
the
correlation waveforms, the intensity difference and phase difference
standard deviations rise at approximately the same
(0.018
Moreover,
approximatly
at
higher
signal-to-noise
and
ratios
(up
to
0 dB), both difference standard deviations increase at
a linear rate of 0.4 dB intensity difference per dB
ratio.
rate
for intensity and 0.013 for phase) for small signal-to-noise
ratios.
ratio
normalized
0.07
signal-to-noise
radians of phase difference per dB signal-to-noise
CHAPTER 7
BINAURAL PERFORMANCE BASED ON STIMULUS VARIABILITY
We have presented experimental results from normal and impaired
listeners
in
four
binaural
experiments
narrowband noise center frequencies.
simple,
narrowband
at
several
In chapter 5, we
different
presented
a
model of binaural interaction which facilitates
the exploration of relationships between the four different binaural
tasks.
The
major
goal of this model is to unify the relationship
between interaural time and intensity discrimination and the ability
to
discriminate
interaural
correlation
and
detect
targets
in
binaural signal configurations.
In chapter 6, we characterized
time
(phase)
differences
for
the
interaural
intensity
the stimuli used in the correlation
discrimination and binaural detection experiments of this study.
this
and
In
chapter, we derive the equations for predicting performance in
the correlation discrimination and binaural
detection
experiments.
These predictions are obtained from the model presented in chapter 5
in conjunction with the stimulus characterization discussed
6.
chapter
BINAURAL PERFORMANCE BASED ON STIMULUS VARIABILITY
Depending
assumed,
on
the
the
interaural
model
differences
predicts
performance
relationship between the time and
intensity
noise
)
parameters
of
the
model
variability in the stimulus ( the
).
model
Thus,
given
the
and
interaural
time
and
The
the
a
(
intensity
available
in
difference
internal
and
of
to
the
the correlation
terms
of
distributions,
under
rule
particular
the
time
stimuli
estimate performance in these two tasks
assumptions.
from
jnds
characterization
intensity
combination
"information"
discrimination and binaural detection
Page 7-2
various
their
we can
combination
results of the formulations which are derived in
this chapter are presented and discussed in chapter 8.
A.
Distribution of Averaged Interaural Differences
In the derivations that follow, we
interaural difference observations, '
assume
and
that
the
averaged
c/ , are Gaussian random
variables with means equal to the mean of the corresponding stimulus
interaural
of
the
differences
corresponding
and variances proportional to the variances
stimulus
interaural
differences
plus
the
processing noise variances ( see Figure 5.1 ).
Figures 7.1 through 7.8 illustrate plots of the log-probability
distributions for twenty (20) averaged values of
Y' and
C<, along
with Gaussian distributions which have the same means and variances.
Averaged
interaural
intensity
distributions (Figures 7.1 and 7.2)
and phase distributions (Figures 7.3
correlation values of 0.995 and 0.80.
and
7.4)
are
presented
for
Averaged interaural intensity
distributions (Figures 7.5 and 7.6) and phase distributions (Figures
BINAURAL PERFORMANCE BASED ON STIMULUS VARIABILITY
7.7
and
7.8) are also presented for for NOSr1
detection stimuli at
signal-to-noise ratios of -26.0 dB and -21.5 dB.
differences,
from the
Page 7-3
Note that for both
the'variability seen in these figures comes completely
external
variability
of
the
stimulus;
the
Gaussian,
internal noise is not included.
As can be seen in
discrimination
and
these
figures,
binaural
for
detection
both
the
waveform
correlation
statistics,
Gaussian assumption is supported out to more than 2
or
3
the
standard
deviations.
Furthermore,
critical
to
because
the
the
predictions
variance
of
these
estimates
presented
in
this chapter, we were
concerned about the effect of a small number of very
on
the
variances
important
for
"natural"
limiting
computed
the
in
chapter
interaural
intensity
occurs
in
as
differences ( the natural limiting
phase
in
2 r
).
Therefore,
clipped the interaural
absolute
intensity
6.
case
being
the
of
circularity
no
of
the
hard-limited or
samples
values of 5, 10, 15, 20 and 30 dB.
where
interaural phase
symmetrically
difference
samples
This is particularly
differences
the
we
large
is
at
maximum,
From Figures 6.5 - 6.8
it is clear that the variance of the interaural intensity difference
is
largest
at
a
correlation
Hence, clipping would
variances
near
Therefore, in the
computed
this
have
the
and
largest
correlation
following
signal-to-noise ratio of zero.
and
discussion,
effect
on
the
signal-to-noise
the
differences
computed
value.
in
the
variances at the various clipping maxima are presented for
a correlation and signal-to-noise ratio equal to zero.
differences
decrease
The reported
to zero as the correlation increases to unity
BINAURAL PERFORMANCE BASED ON STIMULUS VARIABILITY
Page 7-4
and the signal-to-noise ratio decreases.
We found that for clipping bounds greater than or equal
dB,
the
decrease
unclipped noise.
were
decreased
15
in the computed variances was at worst 5% of the
For clipping bounds less than 15 dB, the variances
by
more
than 5% ;
however, for bounds of
this decrease was at most 10% of the unclipped value.
a
to
10 dB,
The effect of
5 - 10 % decrease in the variance on the predictions proved to be
less than the variability of the predictions
variability
in
the
measured
time
due
to
the
observed
and intensity jnds.
predictions in this chapter are based
on
the
Thus, the
unclipped
variances
computed before averaging in chapter 6.
The
above
intensity
results
differences
suggest
greater
that
than
processing
of
approximately
provide any significant, additional information about
interaural
15 dB does not
the
variance
or width of the interaural intensity distribution in the correlation
and detections tasks.
value
It is interesting to note that the "critical"
of the hard limiting of the intensity difference ( r-
is close to
the
value
observed
which
results
in
a
15 dB )
completely
lateralized image ( Durlach and Colburn, 1978 ).
B.
Model Predictor Equations
For
a
correlation
configuration,
differences
interaural
are
the
zero
discrimination
mean
and
values
the
or
of
variances
an
the
are
NOS7r
detection
stimulus
interaural
functions
correlation or the signal-to-noise ratio.
of
the
Therefore, in
BINAURAL PERFORMANCE BASED ON STIMULUS VARIABILITY
these experiments,
the
( 't
observations
only
and
DC
aspect
of
the
Page 7-5
binaural
difference
) which changes between the test and
reference stimulus conditions is the variance of the
two,
averaged
interaural differnces.
The just-noticeable change in variance will correspond to
stimulus
parameter
value
(
?
or signal-to-noise ratio ) which
so
produces just enough additional stimulus variability
just
noticeable
from
that
as
to
the variance of the noisy processing.
be
Given
the stimulus presentation structure of the form described in chapter
3,
Interval
Sl
R = reference stimulus
S2
T = test stimulus
and assuming a reference condition
variability
(
with
no
interaural
difference
reference correlation of unity or masker alone in an
NOSW7 paradigm ), we obtain prediction equations under the following
combination rules.
i) Separate Time and Intensity Difference Observations
In this section, we assume that interaural time
differences
and
intensity
are separately available to an ideal decision mechanism
( Figure 5.2 a ).
Given this assumption,
predictions
four
for
possible
we
combinations
can
of
investigate
the
the
interaural
BINAURAL PERFORMANCE BASED ON STIMULUS VARIABILITY
differences :
alone,
(3)
(1) intensity differences alone, (2) time differences
weighted, linear sum of the interaural differences ,
a
and (4) the optimal combination of the two
By
testing
interaural
differences.
the predictions of these four combinations, we are able
to explore :
time
Page 7-6
and
(1) how the optimal
intensity
compares
combination
to
a
rule
difference
interaural
lateralization-like,
combination rule of interaural time and intensity,
interaural
of
and
linear
(2),
which
cue is important in effecting performance at
different frequency regions.
It is important to note that for all
the
processing
noise
estimates
are
four
made
combination
on
the
separately available differences ( Equations 5.1
such,
the
a
rules,
assumption of
and
b
).
As
linear sum considered in this section is not the same as
the weighted, fixed linear sum considered
Figure 5.2 b ).
in
the
next
section
(
The linear combinations are different in two ways :
(1) the processing noise estimates are different ( Equations 5.1 and
5.2 ) and (2) the combination weight in section B-i is assumed to be
the ratio of
the
interaural
lateralization-type
models
difference
)
whereas
jnds
in
(
section
consistent
B-ii
chapter, the weighting is constrained to be the ratio of
of
with
this
interaural
difference jnds.
a) Interaural Intensity Difference Alone
Assuming the use
performing
a
of
interaural
likelihood
ratio
intensity
test,
differences
alone
and
the optimal decision test (
based on a minimum probability-of-error criterion, Van Trees, 1968 )
BINAURAL PERFORMANCE BASED ON STIMULUS VARIABILITY
Page 7-7
results in a decision rule of the form ( see Appendix IV )
S,
II
2-5
or equivalently
2-
W
where
>
, is
the
interaural
intensity
observation
L
interval.
Combined
in
the
ith
with the processing noise estimate of equation
5.1 a, the above equation implies the just-noticeable change in
test
stimulus
interaural
variability (
the
&T
) is satisfied by the
an
F-distribution
equation
d'0('r
(Loo~l
where K = 20 and
7.1)
ý
is equal to
and F (1 ,
) is the critical
.z•
probabililty of 0.25 with
value
-1 =
for
=
9
right-hand
side
of
equation
stimulus.
b) Interaural Time Differences Alone
a
degrees of freedom.
Hence, the test-stimulus value corresponding to 6r which
the
at
satisfies
7.1 is the just-noticeable test
Page 1-8
BINAURAL PERFORMANCE BASED ON STIMULUS VARIABILITY
Similarly, using interaural time alone, we
rule
obtain
decision
a
S
2.
>
Combining the above decision rule with the processing noise estimate
we get that the just-noticeable change in the
b,
5.1
equation
of
stimulus interaural phase variability (
) is satisfied by
T
6'C
(7.2
)
C A-r\
where C ,
the
band
critical
of
usec/radian ( fo is the center frequency
= 0,/
), a conversion factor from interaural
filters
phase difference to an interaural time difference.
To compute the prediction at any one frequency, we use the time
and
jnds
intensity
measured
for that critical band and scale the
6.16
interaural differences standard deviations ( Figures 6.13 by
1/C(A)r
and Cy /Cy)
)
We then find the scaled standard deviation
equal to the expression on the right appropriate for that frequency.
The
stimulus
value
corresponds
which
that
to
standard
scaled
deviation is the just-noticeable stimulus value.
to
Because the rate of independent difference samples is equal
the
is
bandwith of the stimulus and the bandwidth of the critical band
proportional
independent
to
the
center
frequency,
rate
at
which
stimulus differences samples are available is higher at
high frequencies than at low frequencies.
independent
the
averaged
and therefore, a larger
Hence,
there
are
more
difference samples available to the processor
.
This
increase
is
reflected
in
a
BINAURAL PERFORMANCE BASED ON STIMULUS VARIABILITY
smaller
"threshold". for
the
Page 7-9
variability as seen in the
stimulus
expression to the right of the equality in Equations 7.1 and 7.2
Since this threshold expression will appear once again
and
is
of importance in the predictions to follow, we have tabulated values
narrowband
of the expression in Table 7.1 for the different
center
frequencies tested in this study.
c) Linear Sum of Differences
Assuming a linear combination of the form,
+I
=
forming an LRT and using the processing noise estimates of equations
5.1
a
and
b, we find that the just-noticeable test stimulus value
corresponds to interaural difference variances which satisfy
(
see
of
the
Appendix IV )
7IFr
(,2fe-7
c"C.
has
elements
Equation
7.1
Note that the above variance expression
interaural-intensity-alone
expression
(
interaural-time-alone expression ( Equation
7.2
).
time or intensity processing is severely degraded (
much greater than 6C
ý
fI- or
6
),
then
the
)
and the
Moreover,
(~
if
)o or (4? )
left-hand
side
of
BINAURAL PERFORMANCE BASED ON STIMULUS VARIABILITY
equation
7.3
reduces
to the left hand side of equation 7.1 or 7.2
reduced by a factor of /Fi
is
if
sub-optimal
Page 7-10
the
.
Clearly, the
interaural
linear-sum
combination
are
differences
separately
available.
d) Optimal Combination of Interaural Differences
i.e,
With no a priori combination assumptions,
assuming
both
interaural time and intensity difference observations are separately
available, we form an LRT and obtain a decision rule of the
form
(
see Appendix IV )
S2
where
~2
-14
d =t
i
is
a
variable
processing
binaural
noise
terms
seems
to
mixing
and
the
coefficient
stimulus
dependent
interaural
on
the
difference
variances.
There
be
no
tractable
or
expression for the performance of this rule.
enlightening
analytic
Hence, the predictions
of this rule were numerically obtained by Monte Carlo simulations of
the decision rule.
One thousand sample values of
I
'z
2,
, and
BINAURAL PERFORMANCE BASED ON STIMULUS VARIABILITY
Page 7-11
-- were generated ( as detailed in chapter 6 ) at each value of
and 10log(S/N), and used to calculate a percent correct based on the
above decision
rule.
Jnds
and
detection
thresholds
were
then
estimated from the correlation value and signal-to-noise ratio which
corresponded to 75% correct.
Predictions
of
this
rule
2
that
lateralization
will
be
discussed in chapter 8.
ii) Fixed Sum of Interaural Differences
We know from
phenomena
the
suggest
review
the
interaural
differences
variable.
Moreover,
of
chapter
binaural processor weights and sums the two
and
from
forms
the
a
single
analysis
weighting coefficient, b, must equal the
binaural
of
chapter
ratio
of
the
difference
5,
a fixed
interaural
difference jnds.
Thus, assuming the model is
forced
to
use
a
fixed,
linear
combination of the form ( see Figure 5.2 b )
and performing an LRT , we obtain a decision
Appendix IV )
rule
of
the
form
(
S
2.-
S
Combined with the processing noise estimate of equation 5.2 ( recall
that
under
the
fixed,
linear sum assumption there is essentially
only one noise term in the model ) we find that the
test
just-noticeable
stimulus value corresponds to interaural difference variations
Page 7-12
BINAURAL PERFORMANCE BASED ON STIMULUS VARIABILITY
which satisfy
"
e7. =C
r
Jar
(
differences
is
combination
)
SID
of
sum
Note that the prediction equation of the fixed,
interaural
to the expressions
related
Specifically,
obtained for either interaural difference alone.
if
the processing of either interaural intensity or time differences is
or (dt).
severely degraded ( (4)
much
than
larger
stimulus
the
difference variations ), the fixed linear sum predictions approaches
the predictions of the separate, non-impaired interaural
(
7.1
Equations
).
7.2
and
section
B-i-c,
in
Furthermore,
Equation
difference
to the
contrast
optimal
predicts
7.4
development
in
performance
given the assumption of the fixed, SID combination rule
( see Figure 5.2 b ).
In the next chapter, we present the values predicted
for
equations
both
normal
listeners in this study.
listeners
and
hearing
the
these
by
impaired
Not only do we investigate the predictions
of different interaural difference combinations, but in addition, by
comparing the values of the time and
stimulus
variability
to
the
other
intensity
components
expressions
of
at threshold, we
assess the relative importance of the two interaural differences
effecting
impairment.
the
in
performance for a given binaural task and a given hearing
CHAPTER 8
COMPARISONS OF PREDICTIONS WITH OBSERVATIONS
The equations of chapter 7 were used in
performance
binaural
obtained
characteristics
stimulus
in
the
detection
in
correlation
interaural
experiments.
chapter
compare
them
with
to
the
predict
and
Below, we present the predictions
observed
the
6
discrimination
of the four combination rules investigated in the
and
with
conjunction
previous' chapter
correlation
jnds and NOS
detection thresholds of chapter 4.
correlation
For the graphs presented in this chapter, observed
jnds
detections
and
thresholds
are
plotted
with
connecting-lines along with the predictions of the model
connected
by
solid lines.
dashed
which
are
In addition, vertical bars representing
the range of predicted values obtained due to the variability of the
observed
time
and
intensity
jnds (approximately 10 - 15 % of the
observed jnds and thresholds) are included with the predictions.
A.
Separate Time and Intensity Difference Observations
Page 8-2
COMPARISONS OF PREDICTIONS WITH OBSERVATIONS
None of
rules
combination
four
the
considered
this
under
assumption, including the optimal, non-linear combination rule, were
both
Specifically,
frequencies.
all
the weighted linear sum and
optimal combination rules predicted correlation thresholds and
detection
that
thresholds
at
thresholds
able to predict correlation jnds and NOS7T detection
NOS7I
larger than the observed jnds and
were
detection thresholds (Figures 8.1 and 8.2).
Moreover, the predictions of the model
(Chapter
section
7,
of
B-i-c)
interaural
optimal
combination
rule.
predictions
the
of
As can be seen in Figures 8.1 and
8.2, the difference between the predictions of
within
sum
intensity
and
time
differences is not significantly different than the
the
linear
the
using
two
the
rules
are
range of predictions due to the observed variability of
the observed time and intensity jnds.
the
Thus, in
predictions
model.
alone
of
the
remainder
weighted,
of
this
chapter,
will
present
sum-of-interaural differences (SID)
The time alone component of the SID rule and
the
intensity
component of the SID rule are presented for comparison and to
show the relative usefulness of the interaural
the different frequency bands.
B.
we
Normal Listeners
i) Interaural Correlation Predictions
difference
cues
at
COMPARISONS OF PREDICTIONS WITH OBSERVATIONS
Page 8-3
Predictions of the SID rule for normal listeners
in
Figure
8.3.
The
functional
form
frequency curve is correctly predicted
(Figure
8.4)
and
intensity
differences
differences at
at
high
low
presented
of the observed jnd versus
and,
from
the
time
alone
alone (Figure 8.5) predictions, it is
apparent that the SID rule predictions are
time
is
frequencies
frequencies.
effected
and
However,
by
interaural
interaural
intensity
note
the
that
high
frequency (2000 and 4000 Hz) jnds are significantly smaller than the
observed jnds.
ii) NOS'W Detection Thresholds
Figure 8.6 presents the predictions of the SID rule for
listeners
along
with
observed average data.
normal
The predicted values
are close to the observed thresholds at 250 and
1000
Hz,
but
significantly different (> 5 dB) at 500 Hz, 2000 Hz and 4000 Hz.
in the correlation jnd predictions, the
mediated
8.7)
and
by
threshold
predictions
are
As
are
interaural time differences at low frequencies (Figure
interaural
intensity
differences
at
high
frequencies
(Figure 8.8).
Part of the discrepancy between the predicted and observed jnds
and
thresholds
is
almost
time, interaural intensity,
and
binaural
listeners.
rather
than
detection
certainly
interaural
results
from
due to not having interaural
correlation
the
same
discrimination
set
of
normal
For example, at 500 Hz, if a 20 usec time jnd were
a
used
10 usec jnd, the predicted threshold would be -7 dB
rather than -10 dB -- which is only 1 dB
lower
value and well within experimental variability.
than
the
observed
Page 8-4
COMPARISONS OF PREDICTIONS WITH OBSERVATIONS
However, the SID rule appears
Predictions
thresholds at high frequencies (2000 and 4000 Hz).
the
frequencies
high
at
model
be
could
the value of the variance "threshold" terms derived
increase
would
correlation
in chapter 7, and hence, the model would predict larger
8.9 plots the value of this
Figure
thresholds.
higher
and
jnds
frequency,
threshold (the expression tabulated in Tabel 7.1) versus
K
with
parameter.
a
as
Note
the
large
relatively
effect of
compared
increasing K on the threshold values at low frequencies as
to
threshold values at high frequencies.
the
8.10 -
plot
8.13
threshold
K's
Larger
bands.
of
assuming
by
improved
different averaging K's at different frequency
detection
and
jnds
discrimination
correlation
observed
than
lower
predict
consistently
to
the
predictions
correlation
for
time
In addition, Figures
and
discrimination
detection
alone (Figures 8.10 and 8.12) and
intensity alone (Figure 8.11 and 8.13) for the corresponding
values
of K.
K's
In terms of the model's complexity, allowing different
frequencies
high
begins
trivializes the predictions.
would
equivalent
an
have
to
A
detract
from
modification
effect
of
of
and
simplicity
its
the
increasing
model
the
which
predicted
correlation jnds and detection thresholds at high frequencies is
have
different
averaging.
by
to
K's for the interaural time and intensity estimates
Since the predictions of the model appear to be mediated
interaural
time processing at low frequencies (frequencies less
than or equal to 1000 Hz) and
high
at
frequencies,
interaural
intensity
processing
at
a larger K for intensity estimate averaging will
not affect predictions of the model at low frequencies, but it
will
COMPARISONS OF PREDICTIONS WITH OBSERVATIONS
increase
the
predictions
high frequencies.
interaural
both
for
equal K's
at
Page 8-5
and
time
The assumption of
was
samples
intensity
originaly made to simplify calculations.
The value for interaural intensity averaging (to be denoted
K
)
which
best
by
fit
both
the correlation jnds and the detection
thresholds at 2000 and
4000
Hz
Predictions
of
was
found
to
8.16.
a
=
K
40.
the different-K's SID rule, Figure 8.14 (henceforth
refered to as simply the SID rule), are presented
and
be
As
expected,
the
predictions
in
Figures
8.15
at low frequencies are
unaffected by the increased K for intensity sample averaging.
More
importantly, the predictions of the SID rule at high frequencies are
in
good
agreement
with
discrimination and NOSnT
observed
results
and
b
,
the
both
correlation
detection.
Note that by assuming a different K
averaging,
for
for
interaural
intensity
number of independent estimate averages (
) is now different for time
and
intensity.
'.
Specifically,
for time estimates we have
and for intensity estimates we have
E,
Thus for the predictions presented in Figure 8.15 and 8.16,
frequencies
(frequencies
less
at
low
than or equal to 1000 Hz) where the
predictions of the model are predominately due
to
interaural
time
Page 8-6
COMPARISONS OF PREDICTIONS WITH OBSERVATIONS
processing,
we
used
a threshold value computed from a K = 20.
At
value
as
high frequencies (2000 and 4000 Hz) we used
threshold
a
computed from a K = 40 (see Figure 8.9).
The analysis above suggests that different K's
interaural
for
time and intensity processing result in predictions which are closer
Specifically,
to the observed results.
jnd
and
NOS'7
detection
predictions
high-frequency
(both
predominantly due to
interaural intensity processing in this model)
observed,
normal
results.
correlation
are
to
closer
the
Hence, we now compare the different K's
rule to observed results from the hearing impaired listeners.
C.
Impaired Listeners
In this section, we present the predictions
with
the
different
averaging
of
the
SID
rule
K's for time and intensity samples.
Consistent with the assumptions of the model as presented in chapter
5, the total effect of the hearing impairment on binaural hearing is
and
presumed to be described by an increased variance in
the
time
In
the
following
intensity
processing
noise
(Figure
5.1).
predictions, we have assumed the same "normal" K's (K', = 20 and K,
= 40) for all of the impaired subjects.
i) Interaural Correlation Predictions
COMPARISONS OF PREDICTIONS WITH OBSERVATIONS
Page 8-7
Predictions of the SID rule for subject FG is shown
8.17.
Note
that
the
in
Figure
functional form of the observed frequency
dependence is correctly predicted and that predicted jnds are
most,
a
factor
of
2
-
3
Moreover, from Figures 8.18
intensity
alone
different
and
predictions),
8.19
from
(plots
time
of
alone
and
it is clear that the predictions of
time
low
processing
and
at
the observed values.
the SID model is essentially due to interaural
frequencies
,
interaural
intensity
processing
at
at
high
frequencies.
Predictions of the SID rule for
Figure
8.20.
The
observed
subject
frequency
DH are
presented
dependence
is generally
predicted and the predicted jnds are within a factor of 2 or
at all frequencies except 500 Hz.
in
better
From the time alone and intensity
alone predictions (Figures 8.21 and 8.22), it seems as if subject DH
is
predominately
using interaural intensity information at all the
frequencies, even at 500 Hz where there is useful information in the
interaural time difference.
Predictions of the SID rule for
Figure
8.23.
The
observed
subject
frequency
VF
is
dependence
presented
is
in
correctly
predicted as is the jnd at 500 Hz where she was able to discriminate
correlation.
It
(Figure 8.24)
nor
correctly
predict
intensity
jnds,
is
interesting
intensity
this
one
alone
point.
would
to
have
note that neither time alone
(Figure
From
VF's
8.25)
were
interaural
incorrectly
able
time
attributed
correlation sensitivity solely to her time sensitivity at 500 Hz.
to
and
her
COMPARISONS OF PREDICTIONS WITH OBSERVATIONS
Page 8-8
For subject CS (the MS patient) the SID rule,
intensity
alone
frequencies.
all
As such,
predicted
the
jnds
predictions
greater
of
all
time
alone
and
than
1
at
all
rules
are
three
presented in Figure 8.26 for this subject.
ii) NOS7r Threshold Predictions
Figure 8.27 shows the predictions of the SID rule
FG.
subject
predicted thresholds are close to the observed thresholds
The
at
except
for
predictions
2000
Hz.
As
in
the
case
of
the
jnd
correlation
for this subject, the SID predictions are primarily due
to time processing at low frequencies (Figure
8.28)
and
intensity
processing at high frequencies (Figure 8.29).
Predictions of the SID rule for subject DH (Figure 8.30) show a
reasonable
fit to the observed thresholds at 500 Hz and 1000 Hz but
are too high at 250 Hz and too low at 2 and 4 kHz.
From
the
alone
8.31
and 8.32)
and
intensity
neither time
although
nor
alone
intensity
predictions
seems
to
(Figures
dominate
the
time
predictions,
the functional form of the frequency dependence (except at
250 Hz) is close to that observed in the time alone predictions.
For subjects VF and CS, the SID rule predicted NOSW
thresholds
higher than their observed NOSO thresholds at all frequencies except
at 500 Hz.
(Figure
Hence, except at 500 Hz for subject
8.33 and 8.34) predicted NOSTr
thresholds, i.e.
signal
VF,
At
500
Hz,
SID
rule
thresholds equal to the NOSO
no binaural advantage between the
configurations.
the
the
SID
two
rule
interaural
predicted
a
Page 8-9
COMPARISONS OF PREDICTIONS WITH OBSERVATIONS
threshold of 10 dB when the observed threshold is about 6 dB.
again,
Once
as in the correlation discrimination predictions for subject
VF, neither time nor intensity alone was individually sufficient
to
predict the 10 dB threshold.
D.
Relative Use of Interaural Difference Cues
While the ratio of the
time
and
jnds
intensity
provides
a
measure of the relative sensitivity to interaural time and intensity
differences, it does not provide a
the
ratio
7.1)
(Equation
to
of
the
intensity-alone
their
relative
measure
of
the
variance
By
component
time-alone variance component of (Equation
the
and C
7.2) the SID rule at threshold values of 0'
a
of
in- effecting performance for a given binaural task.
importance
plotting
description
usefulness
relative
of
the
cr
, we
two
obtain
interaural
differences.
For normal listeners, Figure 8.35 shows the expected dependence
of
this
ratio
(plotted
on
a
dB
discrimination and NOSW -signal detection.
1000
Hz),
for
scale)
At low
both
correlation
frequencies,
interaural time differences account for more than 90% of
the SID rule predictions (a ratio of approximately -10 dB).
Hz,
(<
At 1000
both differences contribute equally to the SID rule predictions
(a ratio of 0 dB).
differences
account
greater than 20 dB).
At
for
higher
more
frequencies,
interaural
intensity
than 95% of the predictions (ratios
COMPARISONS OF PREDICTIONS WITH OBSERVATIONS
Subject FG,
despite
his
Page 8-10
low-frequency
time
loss,
shows
a
near-normal dependence interaural time differences (Figure 8.36).
Interestingly, subject DH shows a close to normal dependence on
the
two
interaural
differnces (Figure 8.37) despite a significant
amount of loss in both time and intensity.
Moreover,
although
the
and observed correlation jnds and NOSj -- signal thresholds
predicted
for subjects FG and DH were quite different, the ratios of
relative
usefulness are very similar except at 2 kHz.
Plots for the remaining two subjects were not
no
since
presented
thresholds were predicted except at 500 Hz, where subject VF had
a ratio of 7.2 dB, which is approximately 17 dB higher than
Hence,
time
for
predictions
interaural
account
differences
time
this
only
account
10%
for
whereas
subject,
differences
for
of
normal.
the SID rule
normal
listeners,
for more than 90% of the SID
rule predictions.
It is generally accepted that the binaural system is unable
make
use
of
narrowband
(Durlach
interaural
signals
waveforms
(fine
frequencies
Colburn, 1978).
and
structure)
at
time
discrimination
structure)
above
approximately
1500
Hz
tasks
with
complex,
high
frequency
is believed to be mediated by processing of low frequency
processor
of
the
model
being
Since the interaural
considered
assumed to be processing fine-structure
time
technically
stimulus
differences
for
Performance in interaural time (fine
differences in the envelopes of the waveforms.
time
differences
to
incorrect
in
the
in
using
predictions
the
of
the
in this study is
differences,
model
interaural
at
the
we
are
phase
higher
Page 8-11
COMPARISONS OF PREDICTIONS WITH OBSERVATIONS
frequencies
(2000
frequencies
are
and 4000 Hz).
essentially
due
However, the predictions at these
to
the
interaural
differences in the stimuli (see Figures 8.25 - 8.27).
the time jnds larger at 2000 and 4000
model
Hz
intensity
Hence, making
(effectively
making
the
have no sensitivity to fine-structure time differences) has a
negligible effect on the predictions of the model.
CHAPTER 9
CONCLUSIONS AND REMARKS
The discussion in this
divided
is
chapter
parts.
two
into
First, we evaluate the impaired binaural phenomena with attention to
for
future
hearing
in
directions
binaural
and
clinical
impaired
academic
introduced
in
chapter
5,
of
Second, we evaluate the
listeners.
essential features of the augmented model
investigations
of
interaction
binaural
not only as a predictive tool, but as a
generally applicable modification to
existing
models
of
binaural
interaction.
A.
Conclusions from the Psychophysical Results
The conclusions we draw from the
observed
binaural
phenomena
are
1.
The audiogram tells us very little about the impairments in
binaural
hearing.
This
is
true for both describing the
frequency regions in which impaired binaural hearing
and the extent or amount of binaural impairment.
occur
6.0- Iý I. .- ýW % ..
2.
60 .ý. %_
. . 6 .4 . ýW. 6, .ý._6 b
4. 6-4'.J
~lj--
Noise-induced, high-frequency loss
audiograms
and
presumed
subjects
etiologies
with
~
similar
can have significant
differences between their binaural hearing abilities.
includes
differences
in
the
u
frequency
This
regions of their
impaired binaural hearing and the extent of the impairments
in their binaural hearing.
3.
Impairments
in
interaural
independent
of
impairments
discrimination.
(subject
VF
time
in
discrimination
interaural
intensity
one
frequency
at
Except for one subject
at
500
are
there was no clear correlation
Hz),
between the impairments in the two tasks.
4.
Interaural correlation discrimination, although
to
be
difficult
low
(at
high
intensity
proved
for subjects to discriminate, provides a
direct and simple measure of
(at
it
interaural
time
sensitivity
frequencies) and interaural intensity sensitivity
frequencies).
discrimination
Moreover,
and
unlike
NOS7r-signal
interaural
detection, it
cannot be mediated by monaural cues.
5.
The MLD alone is not a good indicator of
loss
in
hearing impaired listeners.
binaural
Although the absence
of an MLD implies a loss in binaural hearing ( see
for
subject
VF and CS),
hearing
results
the presence of a normal MLD does
not necessarily imply normal binaural hearing ( subjects FG
and
DH
).
-Future
investigations of the MLD in impaired
listeners should report the NOSO and NOS7F thresholds along
with the MLD.
Page 9-3
CONCLUSIONS AND REMARKS
6.
Our results also suggest that studies with large numbers of
hearing
listeners are not as useful in modelling
impaired
on
hearing impairments as as series of complimentary tests
a
Our two, matched high-frequency
few impaired listeners.
loss listeners ( FG and DH )
significantly
different
is almost certainly due to the detailed
This
loss.
time
had
the
differences in their physiological loss not exposed by
Thus, while an average can be useful
audiogram.
monaural
as a descriptive measure of binaural hearing impairment, it
is
little
of
value
the
assessing
in
loss
of any one
individual listener within that class.
7.
A useful representation of impaired binaural discrimination
is the binaural audiogram.
jnds
These plots of dB loss re
normal jnds are similar to monaural audiograms in structure
and
are capable of displaying patterns of binaural hearing
loss not readily apparent in
the
traditional
of
methods
representation.
8.
Finally, studies on large groups of impaired listeners
find
it useful to classify listeners on the basis of their
binaural audiograms and
"binaural"
look
subject
FG
would
be
for
similarities
within
intensity-loss
listeners
be
viewed
but
low-frequency time-loss listener
a
while subject .DH would be a flat time-loss listener.
not
a
Thus, subjects FG and DH would
categorization.
both be classified as flat,
should
may
as
This
a conflicting set of data, but
rather as a verification of the need for an increase in the
number
of
dimensions
which
fully characterize a hearing
CONCLUSIONS AND REMARKS
Page 9-4
impairment.
Given the importance of measuring results from all the tests on
each
impaired subject in a study, we feel the most critical problem
in testing hearing impaired listeners is the duration of the testing
program.
Even
with
the
development
of
our
routines ( which reduced our testing time by
each
subject
that,
unlike
individually tested.
subjects
approximately
40%
),
in our study was tested approximately 16 hrs per week
for almost four months.
fact
sequential testing
The problem is further
normal
listeners,
compounded
impaired
Not only is it difficult
to
by
the
listeners must be
obtain
impaired
willing to participate in studies of the type presented in
this report ( particularly at
academic
institutions
),
but
such
programs are also a drain on the experimenter.
A resolution to this problem would be the development of quick,
simple
and
robust
binaural
tests analogous to Bekesy audiometry.
Standard audiometry can easily be
perform
binaural
detection
(
modified
tasks,
but
equally easy was to test interaural time,
as
Jergereil.1982
yet,
interaural
)
to
there exists no
intensity
or
interaural correlation discrimination.
In chapter 1, we argued for the use of narrowband noise
appropriate
impairments.
chapter
In addition, we introduced the binaural
audiogram
4, a new description of impaired discrimination jnds.
description
an
stimulus for the frequency analysis of binaural hearing
definition of impaired binaural hearing is dependent on an
tasks.
as
of
normal
binaural
hearing
in
in
This
accurate
these discrimination
Thus, given the paucity of data on the frequency
dependence
CONCLUSIONS AND REMARKS
Page 9-4
impairment.
Given the importance of measuring results from all the tests on
each
impaired subject in a study, we feel the most critical problem
in testing hearing impaired listeners is the duration of the testing
program.
Even
with
the
development
of
our
routines ( which reduced our testing time by
each
subject
that,
unlike
The problem is further
normal
individually tested.
subjects
approximately
40%
),
in our study was tested approximately 16 hrs per week
for almost four months.
fact
sequential testing
listeners,
compounded
impaired
Not only is it difficult
to
the
by
listeners must be
obtain
impaired
willing to participate in studies of the type presented in
this report ( particularly at
academic
institutions
),
but
such
programs are also a drain on the experimenter.
A resolution to this problem would be the development of quick,
simple
and
robust
binaural
tests analogous to Bekesy audiometry.
Standard audiometry can easily be
perform
binaural
detection
(
modified
tasks,
but
equally easy was to test interaural time,
as
Jergeret.1.1982
yet,
interaural
)
to
there exists no
intensity
or
interaural correlation discrimination.
In chapter 1, we argued for the use of narrowband noise
appropriate
impairments.
chapter
In addition, we introduced the binaural
audiogram
4, a new description of impaired discrimination jnds.
description
an
stimulus for the frequency analysis of binaural hearing
definition of impaired binaural hearing is dependent on an
tasks.
as
of
normal
binaural
hearing
in
in
This
accurate
these discrimination
Thus, given the paucity of data on the frequency
dependence
CONCLUSIONS AND REMARKS
Page 9-5
of narrowband noise binaural phenomena ( particularly for interaural
intensity and interaural correlation discrimination ), we see a need
for
an extensive study of normal listeners in the binaural tests of
this study to measure the mean and
limits
of
normal
performance.
Ideally, such a study should include older, normal hearing listeners
to reduce differences in ability due to age differences.
Finally, given the apparent independence of interaural time and
intensity
sensitivity,
interaural time
future
and
binaural
we
feel
interaural
studies
of
it
critical
intensity
impaired
to
measure
discrimination
listeners.
Based
modelling results, the inclusion of interaural intensity
appears
to
be
both
in
any
on
the
processing
particularly important to the understanding of high
frequency binaural interaction.
B.
Conclusions from the Modelling Results
The conclusions we draw from
the
modelling
portion
of
this
study are
1.
A mechanism which low-pass filters ( averages )
time
and
detection
models
which
interaural
intensity differences unifies lateralization and
predictions
of
current
binaural
interaction
under the same set of model parameters.
extract
directly,
the
interaural
averaging
time
can
this study.
For models which
time
intensity
and
and
For models
intensity
estimates
be included as presented in
do
estimates,
not
explicitly
a
similar
extract
type
of
CONCLUSIONS AND REMARKS
Page 9-6
modification would be the inclusion of a correlation window
which
temporally
averages
the
computation
cross-correlation ( Sayers and Cherry, 1957 ;
Bachorski,
2.
interaural
time
Stern and
NOS7T
averaging
Ks
)
and interaural intensity differences
appears to be needed to predict observed
and
the
1983)
Different averaging durations ( different
for
of
detection
thresholds
at
correlation
high
jnds
frequencies.
Without a relatively larger K ( a slower, temporal tracking
ability ) for interaural intensity averaging as compared to
interaural time averaging, high frequency
predictions
are
better than observed performance.
3.
Given an augmented model of this sort, it
characterize
detection
binaural
tasks
hearing
from
a
in
is
possible
correlation
description
of
and
to
NOSZW
sensitivity
to
interaural time and intensity differences.
4.
The predictions of the model using the weighted, linear sum
of
interaural
time
and
intensity
differences
significantly worse than the predictions
combination
The
of
difference
combination
variability.
using
is
the
not
ideal
interaural time and intensity differences.
between
rules
are
the
predictions
within
observed
of
the
two
experimental
Page 9-7
CONCLUSIONS AND REMARKS
5.
The general model presented in this
binaural
impaired
characterize
simply
study
us
enabled
hearing
to
four
in
of' hearing
hearing impaired subjects with different types
Although the model is purely functional and includes
loss.
only a gross description of the impairment, it is a
and can expose the essential character
tool
investigative
useful
of relationships between various binaural phenomena without
in
involved
getting
detailed computations typically
the
based
encountered in physiologically
of
models
binaural
interaction.
6.
By having a model with simple and separate descriptions
of
interaural time and intensity processing, we can assess the
importance
relative
differences
interaural
of
intensity
and
time
at a given frequency for a particular binaural
Although a ratio of observed time and intensity jnds
task.
is a necessary component of such an assessment, it can only
the
describe how well each difference is processed and not
of
consequences
task.
binaural
integration
stimuli
of
A
the
with
along
degraded
that
complete
amount
a
processing
assessment
for
a
given
requires
an
of information present in the
description
of
how
well
such
information is processed.
We emphasize the fact that we have not developed a new model of
binaural
interaction
in
this
study.
Rather, we have proposed a
general, additional mechanism to the models presented in chapter
which
allow
those
2,
models to make predictions consistent with both
CONCLUSIONS AND REMARKS
Page 9-8
lateralization and detection data.
For
example,
inclusion
of
an
averager of binaural differences in Hafter's ( 1971 ) lateralization
model
would
enable
lateralization
predicted
data.
value
approximately
variance of
that
Recall
of
90
the
model
A
at
usecs.
With
stimulus
to
predict
that
without
an
would
predict
and
the
averager,
the
threshold
was
added averaging mechanism, the
interaural
'=O,2Z
=Fi .
_K=
detection
signal-to-noise
time
reduced by a factor of 1/Kor the value of
factor of 1/
both
differences
A
a
be
would be reduced by a
Thus, Hafter's
a new threshold value for
would
lateralization
model
approximately equal to
20 usec, a value consistent with his assumed time-intensity
trading
ratio and observed time jnds at low frequencies.
Since the temporal averaging mechanism plays such'critical role
in
enabling the model to predict discrimination and detections data
with the same set of parameter values, further study of the temporal
tracking
ability
of
Grantham ( 1980 )
essential
first
comparison
of
correlations
the
and
Grantham
step,
the
binaural
but
more
temporal
system is needed.
and
Wightman
(
work is needed.
tracking
capability
The work of
1982
)
was
an
Specifically, a
of
interaural
near unity ( recall that they tested fluctuation about
zero ) with interaural time and intensity tracking capability
about
a diotic reference, would help to further identify the relationships
between the three binaural phenomena.
The main
essentially
deficiency
a
narrowband
of
the
model.
current
model
averager
which
that
it
is
One possible modification of the
model so as to include wideband stimuli would be to
additional
is
averages
the
C7s and
incorporate
~is
an
( the time
Page 9-9
CONCLUSIONS AND REMARKS
)
intensity
and
averaged estimates of interaural time
narrowband section across the different frequency bands.
stimulated
would
it
predict
increasingly
1975
)
less
report
than
a
difference
two
of
factor
Leshowitz
and
Zurek
intensity jnds with increasing bandwidth.
time and
interaural
better
noise intensity jnds.
(
between
and
narrowband ( 100 Hz centered at 500 Hz ) noise intensity jnds
wideband
or
noisy
be
Such an averaging processor would necessarily have to
else
each
from
A similar result between narrowband
(
reported
time jnds and wideband time jnds has also been
Durlach
and Colburn, 1978 ).
Given such a
question
resulting
a
averager,
frequency-band
would be how to average the different number of independent Z
5
due
to
Recall
channels.
available from the different frequency
s and
that
the larger peripheral bandwidths at the higher frequencies,
there were more independent averages available at
frequencies
high
than at low frequencies.
model
We feel that the main contribution of the
has
study
this
been
to
the
demonstrate
would
be
better
expended
for
need
in
an
Future modelling
interaural-differences averager or lowpass filter.
efforts
presented
at refining existing models of
binaural interaction to include such an averaging mechanism.
The simple model presented in
situations
this
study
to
be
useful
in
where a quick, rough estimate of the relative usefulness
of interaural time and interaural intensity cues
ability
may
predict
which
are
needed.
The
interaural difference is important at a
given frequency for a particular
binaural
task
can
help
in
the
Page 9-10
CONCLUSIONS AND REMARKS
and
fitting
so
hearing aid could be adjusted
binaural
residual
match
to
as
The binaural
hearing aids.
binaural
of
development
For example, subject VF might be fitted with hearing aids
hearing.
of
characteristics
time
interaural
designed to preserve the
the
stimuli near 500 Hz in order to match her residual time sensitivity.
Moreover, one could also enhance the stimulus interaural differences
in
order
to
possible to magnify the
differential
interaural
match
through
differences
intensity
and
scaling
interaural
It may be
sensitivities.
impaired
for
compensate
an impaired subject's
residual intensity sensitivity.
In addition, although the model was developed
stimuli
of
set
a
of
characterization
a
Specifically,
All that is needed
stimuli used in the experiments in
the
(
time
interaural
terms of the stimulus
differences.
model
phase
)
and
intensity
of this type will be able to
correctly predict masked time discrimination results ( Ito
et
al.,
Stern et al., 1983 ).
1982 ;
Moreover,
subjects
study
certain
and experiments in mind, there is no reason why it
cannot be applied to other binaural experiments.
is
a
with
were
should
intensity
only
although
tested
also
be
in
this
useful
bilaterlly
symmetric
hearing-loss
study, the model developed in this
in
relating
interaural
time
and
discrimination to correlation discrimination and binaural
detection tasks for other types of hearing impairments.
Appendix I
Waveform Generation
Our waveforms are sample functions
process
which
from
is periodic in some interval T.
zero
mean,
Gaussian
The sample function
n(t) of bandwidth W and center frequency fo can be decomposed into a
finite Fourier series in the interval 0 < t < T as shown below ;
~
Cti
I
21
A.
VIcS-szTr( Yý
-Y\)
-L+- f ,
where
7-
-)
'-2
4
Y17-
V
-J Z
z_
r
u
i~
·.
)C
j
c1t
J/
=
JkJ
o
It can be shown ( Davenport and Root, 1958 ) that the
random
variables
and the
S.
ýA
with
I AQ are
a Rayleigh probability density distribution
are uniformly distributed in the interval from - q
to
Below is a Fortran listing of the program used to generate the
noise waveforms used in both the experimental portion of this
and in the waveform analysis section.
study
F'ror
NOL SE. F
fram
k
Generates Gaussian noise wavef'orms of any given
bandwidth and level (< 110 dB SPL) by using sums of
The program
random amplitude, random phase cosines.
also generates the Hilbert transforms of the noise
waveforms by creating corresponding sums of
sines waveforms.
real*4 uniformrayleigh, freq, amp,pha.temp,pimagsq
real*4 arraq(
1023), A,P, F comp
integer*2 cnoise(0:1023),snoise(0:1023),tbuff (0:1023),fileid
1o
integer*4
freq, hi
freq, in _•req, ncomp
integerA-4 seed, idbn,creabn,putbn, index
character"*
f ulrlam
characct. Ler*9 fTi lnamf
charact.er *4
ext
p
i,
3. 141592G54
t e mp =se c nds (0. 0)
se edi j in .(temp)
call
clear
screen
type *, 'Lnter low, high and incremental freq; level
, ave-Form family file name and number'
type
, lo_freq,h i_freqin__freqlevel,fi
accept
:((hi
_freq -- 10o freq)/in_freq)
=10*alog10(float.j(ncomp))
power =2.62*exp(.2303*(level -- comp
ncomp
do
i
= Io
- 30.0))
!
random amplitucde
and random
phase
olat.j
,
( i )
call wavcos(F,A,'.,tbuff{,
j -0,
cn
E,n I d -
10:23
is e ( I ) :
ro i '.
1-7 , 0 ;.3
j
):snji,
Sni ise
10 4.>)! Generate cos component
( j .)+tbu
uaus in ( ,A, ',tbu{{,
call
do
+ 1
Generate
A=r atj 1 e i gh ( un i form, power
P'=2. *p i*ran(seed)
do
nam ,fileld
fr'eq, h i __f req, i nfreq
un 1 form=r an (seed)
V=f
:
and'
e
j
wa,,)e
f - ( j)
Generate
1024)
)+tbuff
sin
component
wa.ve'
j)
tnri
c clo0
Lur
tteC
e
. 1. -U
+ I
e i
Store
r
cos componen
ca
u obn
t n
nu
214
wr 1 te
exL I,1 ) (file
,d+64)
fu I n am = fl nam//ext.
idbn = creabn(fulnaam,2048, 0)
call
putbn( idbn,.snoi e,204•0)
call
c losbn(idbn)
e n cl
"
Store sin component
wave as fi inam. (Wt-64)
real2
)
i les (buf,nfies
getf
subrout ine
t ime,nfileP
integer*;;
buff (2, 0C
1 0 ý 3),
(
)
integer*:4 idbn, creahn openbn, getn, putbn, nbyts, seed
characte.r*9 fi lnam
charactr
Pr',*4 'ext.
character 13 fulnaam
secnds(0.0)
time
ed
seed
10
=
Get seed for the
random # generator
.j nt(time)
ii nt (nfi lesran
ii nt(nfiles*ran
n(1)
n( -2)
if
(
do
i = 1,2
(:
)
.eq.
n(2)
seed)+0.5)
Pick two uncorrelated
noise files from 1--nfiles
(seed)+0.5)
) go to 10
i
I
wrnite(ext,20)
20
n(i)
fTormat
'.
fulnam
=
idbn
nbyts
= openbn(fulnam,1)
getbn(idbn,buff(i),2048)
call
e n d do
r e t.
ur rn
E n dt
13)
filnam//ext
closbn(idbn)
Put file contents into
buff(')
and buff(2)
re a 1 4 amp, f req, I evtl,p
integer*2 buff (0: 103)
ase
len
bff
integer*4 idbn,creabnopenbn,qetbnputbn, nots,closbn
character*30
if Inam
par ameter p i :3. 1,1159.i'E654
data buff
len /10~'2i/
call clear screen
type *,'Enter tone
level
(dB
SPL),
frequency and starting phase'
accept *,levelfreq,phase,filnam
amp
= 1.414*5.12*LXI'(
cal I waucos(freq
. 115* (level
amp,prase,buff
i dbn
= crjeabn(fi lrI am,2048, 0)
call
putbn ( 1 dbn, cno
c alI
closbn(idbn)
end
e
,
2048 )
-
40))
buff len)
Appendix II
Sequential Testing Methods
An essential element of certain psychophysical
the
construction
determination
of
of
experiments
is
psychometric functions and concomitantly, the
thresholds.
Typical
experimental
methods
of
testing require estimation of performance at several stimulus values
which span the full range of performance (chance to correct response
on every stimulus presentation).
Prior to the experiment, it is not
clear to the
stimulus
suitably
experimenter
sampled
performance.
values
to
psychometric
Hence, the
provide
a
coarse
function
function
experimenter
followed by successively
psychometric
what
finer
is
values
completed.
initially
of
divisions
selects
surprising
that
a
considerable
directed towards the development of
a
stimulus
the stimulus range
until
the
final
This can require substantial
amounts of time, effort and cost to the experimenter.
not
produce
over the desired range of
partitioning
grain
will
amount
efficient
of
Thus,
effort
procedures
it
is
has been
for
the
estimation of psychophysical performance (Taylor and Creelman, 1966;
Levitt, 1971).
A.
Previous Work
To date, the procedures developed to reduce the amount of
collection
have
been
varieties
Details of these procedures vary
of
across
stimulus-adaptive
specific
data
methods.
implementations,
Page 2
but, in general, the adaptive methods converge at a single specified
level of performance by using several of the most recently presented
stimulus
values
and
the corresponding subject responses to modify
the stimulus value for the next presentation.
These methods have been and are
considerable
procedures
success.
are
experimentation
In
general,
However,
issues relevant to all
adaptive
used
extensively
measurements
and
efficient
repeatable,
time.
being
there
made
by
significantly
are
a
procedures
with
these
reduce
number of critical
which
restrict
their
generality.
Pollack (1968) in his review of PEST
identifies
(1966)
must
be
specified
applicable
to
by
most
experimenter.
the
adaptive
procedures;
initial stimulus value, and the step size.
assumptions
Taylor
and
Creelman
six parameters of the procedure which
least
at
by
Of
these,
three
are
the exit criterion, the
Thus, in addition to the
all experimenters need to make concerning the selection
of intial stimulus values, the specification of the above parameters
requires
the
experimenter
to make arbitrary assumptions about the
shape and slope of a subject's psychometric function.
Although the efficiency of the stimulus-adaptive methods is not
critically
dependent
on all of the parameters examined by Pollack,
the
mentioned
above
three
efficiency
of
are
a
substantial
effect
on
the
the methods if chosen incorrectly (or, equivalently,
if the initial assumptions
function
have
false).
For
concerning
the
subject's
psychometric
instance, a too fine exit criterion or
step sizes which are too small (i.e., changes in the stimulus
value
Page 3
have
a
small
effect on performance) increase the number of trials
required until convergence, thus reducing the speed
and
efficiency
of the methods.
The above discussion becomes even more critical when applied to
testing
of
hearing impaired subjects.
experiment being performed and the type
hearing
Depending on the particular
of
hearing
impairment,
impaired subject's psychometric function may be (1) normal,
(2) shifted ,(3) have a different slope, (4) both (2)
(5)
have
of
training
procedures,
consecutively
a
for
hearing
single
for
more
impaired
stimulus
than
methods
value
four
subjects.
is
rarely
stimuli
near
threshold
different than threshold).
may
be
(3),
or
Furthermore,
provide
the
In
right
adaptive
presented
trials, hence providing little
opportunity for a subject to get acquainted to the task
of
and
a different shape (possibly non-monotonic).
it is not clear that stimulus-adaptive
kind
a
(perception
radically different at values
Page 4
B.
Sequential Decision and Estimation Procedures
The method presented in this study was motivated by a desire to
reduce
the
number
of
observations
at
extremal
levels
(stimulus values corresponding to performance
different
from
a
desired
performance
level)
and
trials,
is
estimates
several
at
each
of
then
from
constructed
stimulus
values
3
near
stimulus value corresponding to the desired performance
the
introduction,
it
is
not
a
priori
experimenter what stimulus values will produce
psychometric
recording
calculating a percent correct at the end of the run.
A pyschometric function
in
with
Performance estimates are usually obtained
the run, presenting a specified, fixed number of
stated
a
a particular stimulus value which is fixed throughout
selecting
responses
in
of testing requires estimation of performance level at
method
several stimulus values.
by
substantially
A typical experiment
fixed-number-of-trials (FNOT) procedure.
this
stimulus values
function.
Hence,
in
a
FNOT
a
to
5
such
and at the
level.
As
clear to the
suitably
sampled
procedure, there will
necessarily be cases where a considerable number of trials are
used
to estimate performance at extremal stimulus values.
Most extremal stimulus values correspond
chance performance.
stimulus
discern.
value
near
perfect
or
In each case, after the first 5 to 10 trials it
is usually apparent to both the subject and
the
to
the
experimenter
that
being used is either very easy or very hard to
Intuitively, in order to save time
and
preserve
subject
Page 5
vitality,
the
experimenter
the remaining trials.
continued
should stop the run without presenting
However,
the
FNOT
procedure
of all the trials in the run.
presentation
requires
the
Practically,
an experimenter often implements an arbitrary criterion (e.g., if
a
subject has 10 consecutive correct responses, then stop) in order to
terminate such runs early.
the
above
intuitive
In the following sections, we
about
notions
formalize
data
experimental
reducing
collection into a systematic, well-defined, objectively
implemented
rule.
i) Theoretical Development of Sequential Testing
A detailed description and development of
can
be
found
in
Wald
(1945,
sequential
analysis
1947) and Bernard (1946).
In this
section, we present the results for a family of sequential tests and
apply them to psychophysical procedures.
The general form of the
classical
hypothesis
test.
sequential
In
test
is
similar
to
the
a conventional, binary hypothesis
test, one typically obtains a fixed number of observations, computes
the value of a statistic and based on whether this value lies in the
acceptance or rejection region, decides to accept or reject the null
hypothesis.
The acceptance and rejection regions are delineated by
a single criterion or several criteria depending on the form of
statistic's
conditional
density
functions,
the
a
the
priori
probabilities of the two hypotheses and the conditional probablities
of error.
Page 6
The sequential tests described here involve the
operations
on
a
statistic,
same
but with three decision regions;
stop testing and accept the null hypothesis, (II) stop
reject
the
null
sort
(I)
testing
and
hypothesis, or (III) take another observation and
repeat the test (until the maximum number of observations have
taken).
Moreover,
the
value
of
the
compared to the criterion at the end of
sequential
of
testing
affords
an
statistic
each
opportunity
is
updated and
observation.
of
been
making
Hence,
an
early
decision when the null hypothesis is either clearly wrong or clearly
right.
Furthermore, unlike
constant
updated
criteria,
at
sequential
the
the
end
of
the
conventional
criteria
each
hypothesis
tests
with
in the sequential tests are also
observation.
For
the
family
of
tests considered in this paper, the criteria delineating
the three decision regions are linear functions of the
1945)
CA (m) = IA + Sm
(Wr. L )
C (m) = I
(.
+ Sm
where
C (m), C (m) = acceptance and rejection criteria
IA , IA
= acceptance and rejection intercepts
S
= slope of the decision lines
m
= number of observations
Z )
form
(Wald,
Page 7
As in classical hypothesis testing, the criteria are
of
the
conditional
probabilities
functions
and the form of the statistic's
conditional density functions.
ii) Application to Psychophysical Testing
For the application presented in this study, the decision
statistic
( the total number of correct responses ) can be considered a sum of
Bernoulli random variables
presented
in
a
run.
and
the
observations
are
the
trials
The null "hypothesis" in the psychophysical
test is that the subject's performance level (Ps ), is greater
or
equal
to
the upper value of the desired performance range (R),
about the target level of performance (P
R/2).
),
i.e.,
(Ps
>
PT
+
The alternative hypothesis is that the subject's performance
is less than or equal to the lower value of the range (P
R/2).
than
Hence,
the
<
and
and one of the three decisions is made:
; accept the null hypothesis
CA(m)
(PS
if k(m) <
C (m)
> Pr
+
R/2)
; reject the null hypothesis
(P5
if C (m) < k(m) < C (m)
R
-
total number of correct responses at the end of
the mth trial (k(m)) is compared to the values of CA(m)
if k(m) >
P
A
< P
+ R/2)
; present another trial and
repeat the test (until the
maximum number of trials
have been presented)
(IP
S
- P-
I < R/2 )
C, (m)
Page 8
The sequential test illustrated in Figure I.1 has been designed
for
a
symmetric, 21,2AFC experiment.
The targeted level was P
75% correct, R = 10% with conditional error probabilities of
probability
of
rejecting
hypothesis is true) and
the
null
hypothesis
ý (the probability of
X
=
(the
given
the
null
accepting
the
null
hypothesis given the alternative hypothesis is true) equal to 0.05.
Note that the slope of the decision lines, S, is equal to 0.75,
the probability of a correct answer at the target performance level.
Furthermore, if R is decreased, the
pulled
farther
parallelness),
likely.
apart
thus
two
decision
lines
would
be
(but still maintain the same slope and their
making
an
early
termination
decision
less
Finally, by increasing the conditional error probabilities
(the testing decision is more prone to error), the lines
will
come
closer together (again with the same slope and parallelness) thereby
making an early termination decision more likely.
Page 9
Implementation of the Test
C.
The incorporation of the sequential decision rule is
simple.
extremely
Most psychophysical test keep track of the number of trials
presented and the corresponding number of correct responses.
test
is
to
If the
be implemented on a computer, it is a simple matter to
write a subroutine to inspect subject performance at the end of each
trial.
If the
automated
experiment
equipment,
is
being
number
of
without
the
use
of
a piece of graph paper (with decision regions
drawn on the graph with axes
versus
performed
of
total
number
correct
(ordinate)
trials presented (abcissa)) can be used to track
subject performance and stop the
test
when
the
subject's
"path"
enters one of the two decision regions (see Figure J-.1).
As stated in section B-ii, the "null" hypothesis is iPs - Pr) <
R/2, i.e.
subject performance is inside the desired range about the
target performance level.
no
preference
for
the
For most psychophysical tests,
type
there
is
of error made in reaching a decision
about the null hypothesis.
Hence, o( (the probability of incorrectly
deciding
R)
PS
is
outside
will
probability of incorrectly deciding P.
usually
be
equal
is inside R).
to
ý (the
Note that the
general sequential decision rule does not require these assumptions.
The author has made these assumptions
psychophysical
(which
are
valid
for
most
experiments) in order to simplify the application of
the decision rule.
Henceforth, a sequential test with-
=
.
will be
Page 10
referred to as a symmetric sequential test.
For symmetric tests, the acceptance and
the decision lines is just equal to the
response
intercepts,
In addition, the slope of
and IR , are negatives of each other.
IA
rejection
at the target performance level.
a
of
probability
correct
For example, in the test
of Figure 1.1, PT =75 percent correct which implies S = 0.75.
Thus, by specifying PT , R and
),
the
experimenter
obtains
,
S
IA
and I .
calculated from the equations below for S and Ip
c P,-
S-
and is intended as a
parameter
graphical,
Having
-IK )
figure,
Figure 4.2 is
( Wald, 1945 )
on PT- , one moves vertically
decided
The
value
of
I'A
(or
is the value of the intersection point plotted
on the ordinate for three values of
the
and
symmetric-sequential-decision-rule
until one intersects the desired R curve.
equivalently,
o.
"
-
computer.
both
R/L)
IT=
=
of
ý' (the value
directly
'
.
opposite the PT
The slope S (at the top
of
abcissa), although equal to
the target P, is provided for completeness.
To provide an illustration of this
experimenter
wants
to
experiment where PT
interval
between
70
apply
a
figure's
symmetric
use,
decision
suppose
rule
to
= 75 percent correct, R = 10 percent (i.e.
and
80 percent correct) and
Figure1J.Z, S is seen to be 0.75 and IA
2 = 0.05.
an
an
the
From
equal to approximatley 5.5.
Page 11
D.
Statistics of the Test
Thus,
values.
performance
is
a
measure
reasonable
how
a
number of observations at extremal stimulus
the
reduce
to
desire
by
motivated
was
Recall that the sequential decision rule
test's
sequential
the
of
it allocates the number of trials to the
well
desired range of stimulus values.
Figure
versus
presented
trials
average
the
.3 shows theoretical plots of
Ps ,
level,
performance
subject
number
for a
symmetric sequential test with PR = 75 percent correct, R = 10%
S=
0.15 .
and
0.10
0.05,
and
Note that for the conditional error
probabilities considered, the maximum number
trials
of
within the range of desired performance levels R.
that the farther Ps
of
always
is
In addition, note
is away form PT , the less trials are presented
at that level.
over
One way to interpret the advantages of sequential testing
FNOT
procedures
the measurement
provides
better
is
of
that for a fixed number of trials allocated to
a
psychometric
function,
sequential
testing
estimates (smaller standard deviations) of subject
performance
at
stimulus
values
threshold.
Quantitatively,
the
illustrated by a graph of the type
corresponding
to
and
amount
of
the
shown
in
Figure
near
the
advantage can be
r.4.
Figure f-.3, the same sample symmetric sequential test is used.
As
in
Page 12
Alternatively, the advantage of a sequential decision rule over
an
that
is
procedure
FNOT
fixed
for
estimate errors (standard
deviations) at stimulus values corresponding to
in
R,
test requires approximately 40 % less trial
sequential
the
levels
performance
than the FNOT procedure.
of
The early termination, besides reducing the number
a
causes
in
bias
general, for the tests
negligible,
thresholds
predicted
the
in
considered
this
In
bias
is
this
particularly within the desired range of probabilities.
evident from the graph, values of P5
is
at termination.
study,
.
versus the true P
Figure 11.5 plots the sequential estimate of P.
As
trials,
+ R/2
greater than Pr
have positive, increasing biases while values of P 5
-
less than P.
R/2 have negative, increasing biases.
All of the above statements remain essentially true for any P
chosen, the only major difference being in the place of the maximum,
as stated earlier, the maximum
i.e.
By
R.
within
decrease
the
improvement
choosing
degree
over
to
number
different Rs and
which
sequential
of
trials
is
always
s, one can increase or
testing
provides
an
an FNOT procedure, but not the basic advantage of
the sequential decision rule.
Finally, an advantage of the sequential decision rule which
hard
to quantify is the salutary effect it has on subjects.
is
During
the course of using the sequential test in psychophysical tests, the
author
has
found
subjects
to
be
more alert during experimental
sessions and has found that they maintain a higher level of interest
compared to a FNOT procedure.
Page 13
E.
Data Analysis
The above statistical
advantages
based on an important assumption.
of
sequential
testing
are
The number correct and the number
of trials presented are retained at the end of each run and not just
the
estimated
There are two reasons for this :
correct.
percent
(1) since the number of trials presented during a run is not
the
same,
estimates of percent correct at each stimulus
different
value are based on different total number of trials,
not
always
hence,
it
is
to calculate percent correct estimates from individual
correct
runs and average those estimates to obtain a grand average, and
(2)
the variance of the estimates (due to the random nature of the total
number of trials) which are obtained at
sufficiently
large
to
negate
the
the
end
reduction
of
the
run
in variance usually
obtained by averaging percent correct estimates across runs.
at
the
are
Hence,
end of the experimental session, a subject performance at a
particular
stimulus
cumulative
number
value
is
computed
correct
to
the
from
cumulative
the
ratio
number
of
of
the
trials
presented at that stimulus value.
This is not to say that estimates of percent correct at the end
of
individual
runs are not useful.
Estimates should be calculated
and used to help the experimenter in deciding
next set of observations.
i) Computation of Percent Correct
where
to
place
the
Page 14
show
We now
sequential
an
example
experimental
of
how
from
data
hypothetical
a
session should be analyzed in order to (1)
use local estimates for placement of succeeding observations and (2)
guarantee reduction in estimate variances.
Let
K- (X-) = number of correct responses
obtained during the jth run
using stimulus vaule Xý .
Nj
(XC
)
= number of trials presented
during the jth run using
stimulus value X- .
Suppose we perform an experiment using the
decision
rule
presented
in section D.
sample,
sequential
Thus, we are interested in
the stimulus value (which for the purposes of this example, will
in
some
arbitrary units) corresponding to P. = 75 percent correct.
Let us say we
believe
initially
(either
through
assumptions regarding
encompass
be
the
choose
past
the
stimulus threshold.
Kl(0)
P(O) = ------ x 100 = 52
stimulus
experience
physical
these values could be as follows,
N1(0)
three
nature
or
of
values
through
the
which
we
reasonable
stimulus)
to
A possible result of testing at
Page 15
Kl(1)
------
P(1) =
x 100 = 64
K1(5)
P(5) = ------ x 100 = 95
N1(5)
We now choose another three
stimulus
values
on
based
these
A reasonable set to test next would be any three stimulus
results.
values in the interval (1,5).
Hence, after the seconds set, we
may
have
Kl(2)
P(2) = ------
x 100 = 70
N1(2)
Kl(3)
P(3) =
------
x 100 = 76
N1(3)
Kl(4)
P(4) =
------
x 100 = 84
N1(4)
We would continue
in
this
manner,
presenting
new
stimulus
values or possibly returning to previously presented stimulus values
until our alloted time
trials)
had
been
(or
reached.
equivalently,
At
the
the
alloted
number
of
end of the session, we would
collect the total number correct and the total number of trials
and
compute collective, percent correct estimates of subject performance
at all the stimulus values presented.
Page 16
F.
Estimation of Thresholds
By
the
plotting
Xi,
values,
we
probabilities,
obtain
a
P(Xi)
psychometric
versus
the
function with constituent
points calculated from unequal numbers of observations.
in
stimulus
stated
As
sections, we are interested in extracting that value of
earlier
the stimulus corresponding to some desired level of performance.
There exist several methods for extracting
values
(
1972
Ashton,
).
threshold
stimulus
A method which takes into account the
unequal number of observations and at
the
same
time,
provides
a
measure of the statistical goodness of the analysis is the method of
Z
Minimum Logit
As
is
( MLz).
evinced
quasi-sigmoidal
by
the
name,
this
method
a
assumes
psychometric function which can be described by the
logistic curve
A
+
N--
where N is equal to the number of alternatives
in
a
forced-choice
experimental paradigm.
In most psychophysical experiments, threshold is defined as the
stimulus
value
corresponding
to
a performance level equal to the
geometric mean between the worst possible performance and
possible
performance.
the
best
Thus, the stimulus value at threshold, X
is that value of Xi which satisfies
,
Page 17
P(T)
( 11.4 )
NJ
or
S=
( 7.5)
/
Therefore,
T
b
Ashton gives formulas for estimating
cumulative
score.
program, which took
the
calculated
psychometric
functions
These
stimulus
were
the estimate of
and
Even
in
threshold
was
psychometric
functions
deteriorated
were
generally
to
close
the
estimates.
Nj(X.)s
as
input
the
and
where
the
psychometric
considerably non-sigmoidal ( but still monotonic ),
However,
and
used in an analysis
the
cases
threshold.
functions
were
, as well as
value along with a plot of the
threshold
function.
b
formula
K (Xi)s
the
0- and
estimates
not
the
for
rapidly
as
robust
visually
the
for
as
spread
estimated
of
the
non-sigmoidal
the
threshold
APPENDIX III
Estimation of Model Parameters
For the development which follows
in
this
appendix
we
will
assume
t
1.
(1) the
2.
(2) the stimuli used in the interaural time and
intensity
o(
s and
experiments
s are Gaussian random variables
interaural
are perfectly correlated ( hence no
variability in the interaural differences
present
in
the
stimuli )
3.
(3) a symmetric, 2I-2AFC experimental paradigm.
We can represent the interaural
differences
present
in
each
= interaural difference, either intensity (zL ) or
time
interval of a given presentation by
Interval
Stimulus 1 (Sl)
Stimulus 2 (S2)
where
(
-).
A9
h8~Z
- a g/,
- '& -2
4A /
Page 2
I.
Separate Differences Assumption
For a single observation of either interaural difference alone,
we form a likelihood-ratio-test ( LRT ) as shown below
decide S2
f(
69
: S2)
&, : S2)
f(
f(
---------------f(
S)
f(
>
( III.1 )
S)----------
:Si) f(
Sl)
decide Sl
where
f( 8 ) = probability density function of
the interaural difference
@-
= interaural difference observation
in the ith interval
= decision threshold
For Sl and S2 equally likely and a minimum probability of error
constraint, we have
je
y
= 1 and hence
_d+
a8S2-- 0
1.
-( -2
C
2-
2-
a
( 111.2)
Page 3
Taking the In of both sides and collecting
like
terms,
we
get
a
decision rule of the form
decide S2
6
1=
0
/j
(
II.3 .)
decide S1
where 1 is usually refered to as a sufficient statistic.
Since 1 is a Gaussian random variable, we can characterize
performance
the
of this test by a quantity known as d ( Van Trees, 1968
) given by the expression
EE 1 : S2 ] - E[ 1 : S1 I
( 111.4 )
d=------------------------
Var[ 1 : S2
From equation 111.3 and the stimulus presentation structure, we have
EE 1 : S2 ] = A
E[E
l
S
1 = S1
3
=-
(
4
•9
2-
-
-
(-e)
A&)
12.
and
Var[ 1 : Si ] = Var[ 1 : S2 ]
=
-6),
Page 4
= Var[ 0z :S2] + VarEC
:S22
;
but since there is no stimulus difference variability,
Var[ 9 :S2] = Var[ 9/:S2]3£/=
where
6
.
or
=
Therefore,
2
A &
--------f=
( I.5 )
-d
At threshold, d ( for a single observation ) is equal to 1
hence
) = threshold interaural difference value.
t
where (•
For
observations,
we have that d
increases by a factor of
6'
Thus for 6
Vz
k'
(
2/.
=
Odr
and hence
(a&)
we have
2-7
t--
( 111.6 a )
and
Page 5
and similarly for time
Z7
( 111.6 b )
(4T7)
Fixed, Weighted Linear Sum Assumption
II.
We now assume a single, compound binaural
difference
variable
of the form
S13
: o+b
.
Assuming a single observation of the combined
a
perform
LRT
equation 111.3 .
Unlike the development in section I however,
i1 : Sli
G
=-~
,
,
and
Var[ 1 : S2
2 = Var[ 1 : S1 2
+ b
Thus,
2 A&
d
=
we
can
obtain a decision rule identical to the one in
and
EE 1 : S2 ] =
E
differences,
-----------
b
Z)
) /er
Page 6
or at threshold
0).
="iý'U
+(tr
.
For intensity discrimination experiments , ( &L9
f
+ be
) = ( ,&D ) or
(611,W.
and
4.2
+
+
For
independent observations of the compound variable, we have
, =bY2r - b
b
+ + bz
4
C0
( III.7a )
2K/Y
=
and
K7:
+bdL
f2I/
T:E-~inr)
b
( III.7b )
(LACt
Note that with the fixed, weighted
effectively
only
one
source
of
sum
assumption,
processing
note
that
the values of ~
and e
is
noise in the system.
Therfore, Equations III.7a,b imply that b must equal (
addition,
there
In
will be smaller (
even though we cannot estimate them ) under the fixed-sum assumption
than in the separate differences assumption.
Appendix IV
Predictor Equations for Correlation Discrimination
and Binaural Detection
For the development which follows in
this
appendix,
we
will
assume
s and
T
s are Gaussian random variables
1.
(1) the
2.
(2) the means of the
3.
(3) the variances of the
scaled
o4
sum
of
the
o
s and 't
s are equal to zero
sa and 't s are equal
processing
noise
variance
to
the
and
the
variance in the stimulus differences
4.
(4) a symmetric, 21-2AFC experimental paradigm
We can represent the stimulus parameters in each interval of
given presentation by
a
Page 2
Inteival
2
Stimulus 1 (Sl)
Stimulus 2 (S2)
/Z
7
T
&·
where
R = reference stimulus value
T = test stimulus value
A.
Separate Differences Assumption
As
in
Appendix
III,
for
a
single
observation
interaural difference alone, we can form a LRT of the
__,
e.
2
9 7L
~
Z
,
S
T'
2-"•
r
P.-
where
7- = (1/K)E de' +
= (1/K)l
2&R
•e
]
r
= stimulus interaural difference
Si
of
either
Page 3
variance for the reference value
97 = stimulus interaural difference
variance for the test value
where the subscript I denotes internal.
Taking the In of both sides and collecting terms, we get a
rule of the form
decide S2
A
1P -
O( Iv.1 )
a,
decide S1
Alternatively, we can express this rule as
decide .S2
9
S1.
decide S1
Dividing each of the
". by
.i/7SZ
601.0r
71 6
S
I
8,we get
(
decision
Page 4
Thus, our test is now equivalent to
L
• ,
=
where F(1,1) is an F-distributed random variable with
degree of freedom.. For
T
1
independent observations, we have
S,
_
We can characterize the performance in such a test by
directly
Since the test is
the probability of a correct decision.
computing
=
symmetric ( Sl is equally as likely as S2 ) we have
P(correct) = "[C PV)
+
y
>
(
)<
1
-
Furthermore, from the reciprocity rules of the F-distribution
P(correct) = P
)]
2
>•'(•s
For P(correct) = 0.75 ( threshold level of performance
),
we
have
that
, Rv
t
where F
variable
(Y ;/
such
equal to 0.25 .
) = the
that
.r
value
the
of
an
cumulative
F(
,V )
distributed
random
is evaluated at this value is
Therefore, at threshold, we must have the following
relationship hold for the ratio of the variances
Page 5
r
HF
VK
oZAz
t
!/K E
Fu-(Yý
'ý)
*7
or
4
ez,
z82:8ter
Sr.
( IV.3)
4
For reference stimuli values with no stimulus interaural
variability
/
e
= O,
equation iV.3 reduces to
F
-
(Y V)
( IV.4 )
From Appendix III, we have
z
(A
r:
)
thus,
1(y 0..
2-&
or
'I
(ac)7
i) Intensity Alone
For 9 = O
alone, we get
( IV.5 )
difference
Page 6
00
2114.
ii)
f: (Y,-
,
Time Alone
For B =t
e'T
alone, we get
Cc,
CA C),
where C
2.6
=
usec/rad, a conversion factor
from
time in usecs.
iii) Weighted Linear Sum
For
=
o
, we have
+
and hence, at threshold
<
Cpoc
2
Cr
iv) Optimal Combination Rule
2/C)F UY,) --,
phase
to
Page 7
For a single observation of
interaural
both
differences,
have
*1DC
z
g
,
Cr
e
--
e
-2.
-·r~
decide S2
P,22a
-
TI&11
1
-2.
-2.'Z
-It
2.47'
2-
decide S1
Taking the log of both sides and.collecting terms we have,
(Z
7.
.
~1
7-
1 zlr~>
r~
or
(
c (
- Z
4
dr 4-
(
pc
where
2
6 00(P
2.
2.
&
c4T
TIT
Te 7
Z,
'
(1011z.
7.
5
we
Page 8
B.
Sum of Interaural Differences (SID)
For a composite interaural difference of the form
(1&o)
=4
the calculations of performance up to a critical variance ratio
identical to the calculations of section I.
Hence, we can begin our
analysis at equation IV.3 or
d'2.xr_=
e ST2.
4-
( Iv.6 )
4-
bP
where
z
-
(docA,
ar
8
T 7
and from appendix III,
Therefore, combining the above equation with equation IV.6,
z
-7
or
Zlc~
Y
.Finally,
.Finally,
r
are
Page 9
40
_
_
(a2r-A
tI
FOOTNOTES
it
(1) Although both A(t) and ( (t) are bandlimited' functions,
not clear that the interaural intensity difference (
and the interaural phase difference ( tLe)Clearly,
bandlimited.
since
phase
the
i
)
-Zol~
) are necessarily
f4LLi)
difference
a linear
is
operation on the right and left phase terms, it is bandlimited.
interaural
log
intensity
transformation
to
communications)
is
The
difference is not as easy to analyze, but the
has
private
(Braida,
observed
been
not significantly alter the spectral properties
of bandlimnited speech waveforms.
to
(2) In order for the average of the phase terms
Gaussian,
average.
one
must
be
careful
to
a
defining what is meant by the
in
When phase estimates are averaged, their distributions are
convolved.
For
non-circular
functions, this succesive averaging,
and concomitantly the successive convolving
produces
converge
estimate 'average distributions
of
the
distributions,
which approach that of a
as
the
phase,
However, for a
circular
succesive
averaging
not necessarily result in an increasingly
may
function
such
Gaussian.
Gaussian average estimate distribution.
the
This is
primarily
due
to
fact that succesive circular convolutions do not converge under
certain conditions.
Such a
condition
uniformly distributed between -7
occurs
when
the
phase
is
and '7 ( e.g, corresponding to
= 0 ). Regardless of the number of phase sample estimates averaged,
the
resulting average estimate distribution will still be a uniform
distribution.
Table 3.1
Presentation Levels Of Noise Waveforms
( dB SPL, total noise power )
Noise Center Frequency
.250
High-Frequency
Loss Listeners
500
1000
2000
4000
50
60
75
90
Flat Loss
Listener
90
90
90
90
90
MS Listener
50
50
50
50
30
Table 7.1
Noise
Center Frequency
250
.y
.Jy
14.0
500
6.3
1000.
4.3
2000
2.0
4000
1.5
FIGURE CAPTIONS
Figure 2.1 Interaural time jnds as a function of
frequency
for
Hawkins, (
normal
listeners.
)3 McFadden
and
)
(
Pasanen,
the
Klump
(+)
noise
and
center
Eady,
Henning,
(A
)
and
(o )
the
nqise
Bernstein and Trahiotis.
Figure 2.2 Interaural intensity jnds as
center
frequency
a
for normal listeners.
and Leshowitz and (0--)
function
of
( A ) Hawkins, (V
) Zurek
Durlach and Colburn.
Figure 2.3 NOSO and NOS"Y detection thresholds as a function of
noise
center
Webster, (3
frequency
for
) Bourbon, (
normal
listeners.
) Wightman and (O
Figure 2.4 Block-box description of
a
the
( V ) Hirsch and
) Zurek.
general
model
of
binaural
interaction ( from Colburn and Durlach, 1978 ).
Figure 3.1 Audiogram of subject FG, a high-frequency loss listener.
Figure 3.2 Audiogram of subject DH, a high-frequency loss listener.
Figure 3.3 Audiogram of subject VF, a flat-loss listener.
Figure 3.4 Audiogram of subject CS, an MS patient.
Figure 3.5 Representative
psychometric
normal subjects in the NOSTr
function
for
detection task at Z000 Hz.
one
of
the
Page 2
Figure 3.6 Representative
psychometric
function
for
one
of
the
impaired listeners in the NOS7r detection task at 4000 Hz.
Figure 4.1 Average interaural time jnds for normal
-ancillary experiment' of
subjects
in
an
this study (V--7 ), along with results of
Figure 2.1.
Figure 4.2 Average interaural intensity jnds for normal subjects
an
ancillary
in
experiment of this study (V-V), along with results of
Figure 2.2.
Figure 4.3 Average interaural correlation jnds for
in
normal
subjects
an ancillary experiment of this study (v-•), along with a result
from Gabriel and Colburn ( 1981).
Figure 4.4 Average NOSO and NOSTr detection
subjects
thresholds
for
normal
in an ancillary experiment of this study (-r ), along with
results of Figure 2.3.
Figure 4.5 Interaural time jnds for subject FG as a function of
the
noise center frequency.
Figure 4.6 Interaural time jnds for subject DH as a function of
the
noise center frequency.
Figure 4.7 Interaural time jnds for subject VF as a function of
the
noise center frequency.
Figure 4.8 Interaural time jnds for subject CS as a function of
noise center frequency.
the
Page 3
Figure 4.9 Interaural intensity jnds for subject FG as a function of
the noise center frequency.
Figure 4.10 Interaural intensity jnds for subject DH as
a
function
a
function
a
function
of the noise center frequency.
Figure 4.11 Interaural intensity jnds for subject VF as
of the noise center frequency.
Figure 4.12 Interaural intensity jnds for subject CS as
of the noise center frequency.
Figure 4.13 Interaural correlation jnds for subject FG as a function
of the noise center frequency.
Figure 4.14 Interaural correlation jnds for subject DH as a function
of the noise center frequency.
Figure 4.15 Interaural correlation jnds for subject VF as a function
of the noise center frequency.
Figure 4.16 Interaural correlation jnds for subject CS as a function
of the noise center frequency.
Figure 4.17 NOSO (4--A) and NOS1T (V--V)
detection
thresholds
for
subject FG as a function of the noise center frequency.
Figure 4.18 NOSO (4-- ) and NOSrTY (V--V) detection
thresholds
subject DH as a function of the noise center frequency.
for
Page 4
Figure 4.19 NOSO (4--6) and NOS7r ('--V) detection
thresholds
for
subject VF as a function of the noise center frequency.
Figure 4.20 NOSO (d--d) and NOS7r (V--V)
detection
thresholds
for
subject CS as a function of the noise center frequency.
Figure 4.21 Binaural Time Audiograms for subjects FG ( V
), VF ( +
),
and CS ( O
), DH (6
).
Figure 4.22 Binaural Intensity Audiograms for subjects FG (V
(
), VF ( 4
),
and CS (
), DH
).
Figure 4.23 Binaural Correlation Audiograms for subjects FG ( V
DH ( A
),
VF (
+
),
and CS ( O
),
).
Figure 4.24 Scatter plot of interaural time jnds
versus
interaural
versus
interaural
intensity jnds.
Figure 4.25 Scatter plot of interaural time jnds
correlation jnds.
Figure 4.26 Scatter
plot
of
interaural
time
jnds
versus
NOSTf
jnds
versus
versus
NOSqf
thresholds.
Figure
4.27
Scatter
plot
of
interaural
intensity
interaural correlation jnds.
Figure 4.28 Scatter plot of interaural intensity jnds
thresholds.
Page 5
Figure 4.29 Scatter plot of interaural correlation jnds versus NOS
thresholds.
Figure 4.30 Scatter plot of
interaural
time
jnds
hearing
versus
loss.
Figure 4.31 Scatter plot of interaural intensity jnds versus hearing
loss.
plot
Figure 4.32 Scatter
of
interaural
correlation
jnds
versus
hearing loss.
Figure 4.33 Scatter plot of NOS7r detection threshold versus hearing
loss.
Figure 5.1 Block-box description of the general
model
of
binaural
interaction used in this study.
Figure 5.2 The separate-interaural-differences assumption ( a )
and
the Sum of Interaural Differences ( SID ) assumption ( b ).
Figure 6.1 Probability density distribution of interaural
differences for
= 0.995.
Figure 6.2 Probability density distribution of interaural
differences for
intensity
= 0.8.
Figure 6.3 Probability density distribution of interaural
differences for
intensity
e=
0.0
intensity
Page 6
Figure 6.4 Probability
differences for
of' interaural
phase
density
distribution
of
interaural
phase
distribution
of
interaural
phase
= 0.8
Figure 6.6 Probability
differences for
distribution
= 0.995
Figure 6.5 Probability
differences for
density
density
= 0.0
Figure 6.7 Probability density distribution of interaural
intensity
differences for 10log(S/N) = -26.0 dB.
Figure 6.8 Probability density distribution of interaural
intensity
differences for 10log(S/N) = -22.0 dB.
Figure 6.9 Probability density distribution of interaural
intensity
differences for 101og(S/N) = 0.0 dB.
Figure 6.10 Probability density
distribution
of
interaural
phase
of
interaural
phase
of
interaural
phase
differences for 10log(S/N) = -26.0 dB.
Figure 6.11 Probability density
distribution
differences for 10log(S/N) = -22.0 dB.
Figure 6.12 Probability density
distribution
differences for 10log(S/N) = 0.0 dB.
Figure 6.13 Plot of interaural intensity variance as a
the waveform correlation.
function
of
Page 7
Figure 6.14 Plot of interaural phase variance as a function
of
the
waveform correlation.
Figure 6.15 Plot of interaural intensity variance as a
function
of
function
of
signal-to-noise ratio in an NOSWr paradigm.
Figure 6.16 Plot of interaural
phase
variance
as
a
signal-to-noise ration in an NOSTr paradigm.
Figure 7.1 Probability density distribution of
intensity
obtained
differences for
by
numerical
= 0*995.
simulation,
averaged
interaural
Solid curve is distribution
dashed
curve
is
Gaussian
distribution with the same mean and variance.
Figure 7.2 Probability density distribution of
intensity
obtained
differences
by
numerical
= 0.8.
for
simulation,
averaged
interaural
Solid curve is distribution'
dashed
curve
is
Gaussian
distribution with the same mean and variance.
Figure 7.3 Probability density distribution of
phase
differences
obtained
by
for
numerical
=
0.995.
simulation,
averaged
interaural
Solid curve is distribution
dashed
curve
is
Gaussian
distribution with the same mean and variance.
Figure 7.4 Probability density distribution of
phase
differences
obtained
by
for
numerical
=
0.8.
simulation,
Solid
dashed
distribution with the same mean and variance.
averaged
interaural
curve is distribution
curve
is
Gaussian
Page 8
Figure 7.5 Probability density distribution of
intensity
differences
distribution obtained
for
by
10log(S/N)
numerical
averaged
= -26.0 dB.
simulation,
interaural
Solid curve is
dashed
curve
is
Gaussian distribution with the same mean and variance.
Figure 7.6 Probability density distribution of
intensity
differences
distribution obtained
for
by
10log(S/N)
averaged
= -22.0 dB..
numerical 'simulation,
interaural
Solid curve is
dashed
curve
is
Gaussian distribution with the same mean and variance.
Figure 7.7 Probability density distribution of
phase
differences
for
distribution obtained
10log(S/N)
by
=
numerical
-26.0
averaged
dB.
simulation,
interaural
curve is
Solid
dashed
curve
is
Gaussian distribution with the same mean and variance.
Figure 7.8 Probability density distribution of
phase
differences
for
distribution obtained
10log(S/N)
by
=
numerical
-22.0
averaged
dB.
simulation,
interaural
Solid
dashed
curve is
curve
is
Gaussian distribution with the same mean and variance.
Figure 8.1 Correlation predictions of the optimal combination
and
a
linear
combination
rule
( L)
(7
)
along with observed, normal
performance (V--P).
Figure 8.2 NOSTY detection
combination
(V
)
and
threshold
predictions
of
a -linear combination rule (A
observed, normal performance (v--V).
the
optimal
) along with
Page 9
Figure 8.3 Correlation jnd predictions of the SID rule
Ks
for
using
equal
time and intensity averaging (&-----A ), along with observed
correlation jnds (V---V ) for normal listeners.
Figure 8.4 Correlation jnd prediction of time alone rule (---along with observed correlation jnds (7---J
)
) for normal listeners.
Figure 8.5 Correlation jnd predictions using intensity alonie (--~)
) along with observed correlation jnds for normal listeners(V--7)
Figure 8.6 NOSI'T
A--•
), along
detection threshold predictions. using
with
observed
thresholds
(7--V )
the
SID
for
normal
(
listeners.
Figure 8.7 NOST't detection threshold predictions usning time alone (
d--A ) along
with
observed
thresholds
(V---V)
for
normal
listeners.
Figure 8.8 NOS7r'detection thresholds using intensity alone (A---
)
along with observed thresholds (V--7 ) for normal listeners.
Figure 8.9 Variance threshold values as a function of
noise
center
versus
noise
frequency for four values of K.
Figure 8.10 Correlation predictions using time
center
frequency for K = 10 (
alone
), K = 20 ( A ), K = 40 (3 ) and K
= 80 ( o).
Figure 8.11 Correlation predictions
noise
using
center frequency for K = 10 (7
and K = 80 ( O).
intensity
), K = 20 (A
alone
versus
), K = 40 (t
)
Page 10
Figure 8.12 NOST threshold
noise
predictions
center frequency for ý = 10 (V
using
time
), K = 20 (h
alone
versus
), K = 40 (D
)
and K = 80 ( a ).
Figure 8.13 NOS7r threshold predictions using intensity alone versus
noise
center frequency for K = 10 ( 7), K = 20 ( s ),
and K = 80 (
K = 40 ( 2 )
).
Figure 8.14 Modified SID rule model with different averaging lengths
(Ks) for interaural time and intensity estimates.
Figure 8.15 Correlation jnd predictions using the
SID
rule
(A-A.)
along with observed correlation jnds for normal listeners (V--7).
Figure 8.16 NOS7T detection threshold predictions using the SID rule
(4-4) along with observed thresholds for normal listeners (v--i).
Figure 8.17 Correlation jnd prediction of the SID
rule
( 4 ---
)
along with observed correlation jnds (P._• ) for subject FG.
Figure 8.18 Correlation jnd prediction using time alone
----
(
)
along with observed correlation jnds (7--- ) for subject FG.
Figure 8.19 Correlation jnd predictions using
differences
alone
(6----d
interaural
intensity
) along with observed correlation jnds (
\i7--V) for subject FG.
Figure 8.20 Correlation jnd prediction of the SID
along with observed correlation jnds (_---~7)
rule
(,--
for subject DH.
)
Page 11
Figure 8.21 Correlation jnd prediction using time alone
)
( L---
along with observed correlation jnds (V--V )' for subject DH.
Figure 8.22 Correlation jnd predictions using
differences
V---"
alone
(---A)
interaural
intensity
along with observed correlation jnds (
) for subject DH.
Figure 8.23 Correlation jnd prediction of the SID
rule
(----
)
along with observed correlation jnds (7---7 ) for subject VF.
Figure 8.24 Correlation jnd prediction using time al6ne
(~L-A
)
along with observed correlation jnds (C----V) for subject VF.
Figure 8.25 Correlation jnd predictions using
differences
alone
interaural
intensity
( ----- ) along with observed correlation jnds (
V--- ) for subject VF.
Figure 8.26
Correlation
jnd
predictions
observed correlation jnds (---7
(4----
) along
with
) for subject CS.
Figure 8.27 NOS?,' threshold predictions of the SID rule
)
(A----
along with the observed NOST- thresholds (~---7) for subject FG.
Figure
8.28
NOSTr
threshold
differences alone (6----
predictions
using
interaural
time
) along with the observed NOSTr thresholds
for subject FG(k----')o
Figure 8.29 NOS'Ti threshold predictions using
differences alone (&-A
for subject FGC 7--V),
interaural
intensity
) along with the observed NOSf thresholds
Page 12
Figure 8.30 NOS7( threshold predictions of the SID rule
along with the observed NOSTq
Figure
8.31
NOSTT
threshold
differences alone (A--A
for subject DH( •---
).
thresholds (7--V) for subject DH.
predictions
using
interaural
time
) along with the observed NOS7rf thresholds
)
Figure 8.32 NOS7i' threshold predictions using
differences alone (A-----
(A---
interaural
intensity
) along with the observed NOS'V1 thresholds
for subject DHLI ----V
Figure 8.33 NOS7- threshold predictions of the SID rule
along with the observed NOST' thresholds (C-
)
(--A
-V) for subject VF.
Figure 8.34 NOSTi threshold predictions of the SID rule
(-
A )
along with the observed NOSIT thresholds (---
• ) for subject CS.
Figure 8.35 Plot of relative usefulness (
dB
intensity
in
) of
interaural
differences to interaural time differences in correlation
discrimination (V--V ) and NOSIf'detection (----A)
versus
center
frequency of the noise for normal listeners.
Figure 8.36 Plot of relative usefulness (
intensity
in
dB
)
of
interaural
differences to interaural time differences in correlation
discrimination (V---V) and NOS7f detection (A----)
versus
center
frequency of the noise for subject FG.
Figure 8.37 Plot of relative usefulness (
intensity
in
dB
) of
interaural
differences to interaural time differences in correlation
discrimination (V----9)
and NOSTr detection (----)
frequency of the noise for subject DH.
versus
center
Page 13
Figure A-II.1 Sample performance tracks for Ps = 1.00, 0.75 and
(
•
-- )
along
with
the
decision
lines (----- -)
0.5
of the test
discussed in the text.
Figure A-II.2 Plot of the decision line intercepts ( Ia and Ir ) for
R
=
5, 10, and 15%, and
6 = 0.05, 0.10 and 0.15 as a function of
PT.
Figure A-II.3 Plot of the expected value and standard deviations
the
number
of
of trials for the sequential test described in the text
versus Ps.
Figure A-II.4 Plot of the ratio between the
FNOT-estimate
standard
deviation and the sequential-estimate standard deviation versus Ps.
Figure A-II.5 Plot of the sequentially estimated Ps versus
for the test described in the text.
true
Ps
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7.1
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7.2
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8.3
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8.4
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8.5
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8.7
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8.8
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8.12
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8.13
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8.16
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8.21
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8.23
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8.26
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8.29
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8.30
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8.31
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8.32
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8.34
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