Transcript Auditory Perception P1

Auditory Perception
Rob van der Willigen
http://~robvdw/cnpa04/coll1/AudPerc_2007_P6.ppt
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Today’s goal
Understanding psychophysical methodology
and its use to measure absolute threshold
and loudness of hearing
Psychoacoustics
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“Elemente der Psychophysik”: Interpretation
Physical dimensions of the stimulus influence detectability
Stimulus versus Perception
Is a Non-trivial relationship has a Probabilistic Nature
Is a highly subjective relationship
Recapitulation last weeks’ lecture
Psychoacoustics
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A function for detection: the PMF
Pb(a)
Pb(a)  F [u (a)  g (b)]
The psychometric function
provides an answer to both
the measurement of:
(1) a threshold &
(2) the aim to order and
distribute stimulus level
along a perceptual
dimension.
The sigmoid curve defined by function F is called
the Psychometric Function (PMF).
Recapitulation last weeks’ lecture
Psychoacoustics
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Signal detection theory (SDT)
Signal detection theory (SDT)
assumes that within a given
neural system there are
randomly fluctuating levels of
background activation.
Thus, in absence of a stimulus
neural activity is randomly
distributed over time.
The Probability Density Function
(PDF), P(x), determines how
often/long spontaneous neural
activity x(t) spends at a given
value x
The PDF is represented by the blue bars (in each plot)) and exists independent of
time. Combining of independent signals (x1 and x2) changes the shape of the PDF.
Recapitulation last weeks’ lecture
Psychoacoustics
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Signal detection theory (SDT)
The PDF of randomly fluctuating levels of neural activation summed over
time approximates the normal distribution (red line).
Recapitulation last weeks’ lecture
Psychoacoustics
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Testing paradigm: Yes-No Paradigm
Psychophysical procedures dispose of various testing paradigms,
of which I describe the yes-no and the forced-choice
(nAFC: n-alternative-forced-choice) paradigm.
With the yes-no mode subjects are given a series of trials, in which they
must judge the presence or absence of a stimulus at each case.
It is essentially a detection task.
The ratio between the number of
trials containing a stimulus and the
total number of trials is usually 0.5,
but can be any other value.
The rate of yes-responses for all
tested stimulus intensities is defined
as the dependent variable.
Psychoacoustics
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Pay-off Matrix: Yes-No Paradigm
ERROR
In a yes/no binary detection task there are
two states of the physical world (signal or
noise) and two types of responses (yes or
no).
A Subject can make two types of errors:
(1) say Yes when a noise alone is presented
(2) say No when a signal is presented
P(yes|signal)
P(yes|noise)
The frequencies of these two types of error
will be determined by two factors :
ERROR
Sensitivity of observer
Criteria of decision
P(no|signal)
P(no|noise)
1- P(yes|signal) = P(no|signal)
1- P(yes|noise) = P(no|noisel)
Psychoacoustics
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Signal detection theory (SDT)
Signal detection theory (SDT) formally
addresses the influence of spontaneous
neural activity (noise) and decision
criteria on the choices (responses)
made by the observer when presented
with a physical stimulus (signal).
Shown are the PDFs of neural activity
in absence of a stimulus and in the
presence of a stimulus.
Notice the rightward shift of the PDF
when a stimulus (signal) is present.
The delectability d’ is a measure of the
strength of a physical stimulus.
Recapitulation last weeks’ lecture
Psychoacoustics
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Response Criterion (bias): Yes-No Paradigm
P(yes|signal)
P(yes|noise)
P(no|signal)
P(no|noise)
Recapitulation last weeks’ lecture
Psychoacoustics
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Signal detection theory: ROC curves, bias
The ROC curve is traced out by
plotting P(yes|signal) (hits)
against P(yes|noise)
(False positive) as the criterion
changes systematically.
Pn=0.05
A systematic change in bias (criterion) can
be induced by changing the probability of
presenting the stimulus without a signal, Pn.
Note, since stimulus intensity remains the
same, d’ does not change
Pn=0.5
Pn=0.9
Psychoacoustics
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Signal detection theory: ROC curves, d’
ROC curves for various levels
of sensitivity: d’=0,1 and >1.
d’ = 0 no detection.
d’ ∞ maximal detection
highest sensitivity
Psychoacoustics
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Testing paradigm: nAFC Paradigm
A basically different testing mode from the yes – no paradigm is represented by the
forced-choice mode:
Subjects are given a variety of n alternatives, from which they have to choose the one
containing the stimulus.
The alternatives are presented with either spatial or temporal coincidence, or without
either coincidence.
The subjects know that exactly one alternative contains the stimulus, and that the
rest has a zero-stimulus.
Psychoacoustics
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Testing paradigm: nAFC Paradigm
The differences between these two methods
become obvious when the presented stimuli are
faint.
In the yes-no paradigm the proportion of yesanswers approaches zero, whereas in nAFC the
proportion of correct answers approaches the value
of equal probability for all alternatives, which is the
reciprocal value of the number of alternatives.
Likewise this means that e.g. in two-alternative
forced-choice (2AFC) tasks the threshold is located
where observers give 75% of correct responses,
since they already give 50% of correct responses
due to the 2AFC-inherent guessing.
The basic advantage of 2AFC consists of its well founded assumption that subjects will opt for the stimulus
evoking the strongest perception, regardless their tendency to say “yes” or “no”.
This is in contrast to the yes-no paradigm, where decision making in the presence of uncertainty is according
to the subject’s psychological characteristics, like e.g. prudence.
Unlike the yes-no mode, the dependent variable of nAFC is the rate of correct responses for all tested stimuli
instead of the rate of yes-responses.
Psychoacoustics
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Testing paradigm: nAFC Paradigm / yes-no

1


P ( positive, nAFC | th)  0.5  1      
n


1


P ( positive, yes / no | th)  lim 0.5  1      
n 
n


 0.5  (1     )
Psychoacoustics
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Testing paradigm: nAFC Paradigm & d’
Pc ( x)    (1     ) F ( x)
  0  Pc ( x)  F ( x)   1  F ( x)
If the stimulus is not detected then one
guesses with rate ,  or (1/n).
For 2AFC tasks, the signal detection
measure d-prime, d’, can be related to
to the proportion of correct responses,
Pc (x), when lapses, , are very small
(zero) and when corrected for guessing,
.
Pc ( x)  
F ( x) 
1 
d ' ( x)  F 1 ( Pc ( x)) 2
F-1 is the inverse cumulative normal
distribution function
Psychoacoustics
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Some Maths on the CDF
All probability questions about X can be answered
in terms of the CDF F(x).
For example:
The probability that X is strictly smaller than b is:
The CDF can be measured by
means of a psychophysical
detection / discrimination
task. To obtain the PDF, the
CDF must be differentiated.
Note that P{X < b} does not necessarily equal F(b)
since F(b) also includes the probability that X equals b.
Psychoacoustics
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Some Maths on the CDF
The CDF can be measured by
means of a psychophysical detection /
discrimination task.
The CDF can be described
mathematically by use of the ERROR
FUNCTION: erf
The inverse CDF F’(x) can be obtained
by the equations as given below.
Psychoacoustics
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Some Maths on the ERF
Psychoacoustics
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Signal detection theory: sensitivity and z-score
Using the inverse function F-1 follows:
z hit  F 1 Phit (c)  
s  c

n  c
zfa  F Pfa (c)  

Elimination of c:
1
s  n
z hit  zfa 
 zfa  d '

Linear function
Psychoacoustics
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Testing paradigm: nAFC vs. yes-no & d’
'
d  z[ P( yes | sn)]  z[ P( yes | n)]
Yes-no
z[ P( yes | sn)]  z[ P( yes | n)]
d 
2
2AFC
'
Psychoacoustics
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Testing paradigm: z-score calc with Matlab
Psychoacoustics
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Testing paradigm: method of limits under 2AFC
Psychoacoustics
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Testing paradigm: method of limits under 2AFC
Alternative to determining d’ from the
psychometric curve is the method of limits
One-up / one down adaptive
tracking.
Correct response creates an
decrease in stimulus level whereas
a incorrect response creates a
increase in stimulus level.
Averaging over a 5 or more
reversals (i.e., change in the
correctness of the response)
approximates the threshold.
Psychoacoustics
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Testing paradigm: method of limits under 2AFC
One-up / one down adaptive tracking versus
Two-down / one-up (descending stairs)
Psychoacoustics
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Testing paradigm: method of limits under 2AFC
Descending stairs
down
up
Psychoacoustics
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Physical parameters of sound waves: Intensity
Intensity (I) of a wave is the rate at which sound energy flows
through a unit area (A) perpendicular to the direction of travel:
Intensity  Pressure  Particle Velocity
Force Distance
Energy


Area
Time
Area  Time
Power P


Area
A

Pressure, P, is measured in watts [W=J/s]
A is measured in square meters [m2]
Psychoacoustics
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Physical parameters of sound waves: Intensity
Intensity (and pressure) follows the inverse
square law for free field propagation.
At a distance 2r from the source, the area
enclosing the source is 4 times as large as the
area at a distance r.
Yet the power radiated remains the same
irrespective of the distance; consequently the
intensity, the power per area, must decrease.
Psychoacoustics
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Physical parameters of sound waves: Decibel scale
Energy ratio
Intensity threshold of
hearing I0 = 10-12 W/m2
 I 
dB ( SIL )  10 log 10 

 I0 
Sound Pressure Level:
Pressure ratio
Sound Intensity Level:
Pressure threshold of
hearing
P0 = 2 x 10-5 N/m2 = 20 Pa
2
P
P
dB( SPL)  10 log 10    20 log 10  
 P0 
 P0 
Psychoacoustics
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Physical parameters of sound waves: RMS values
Intensity (I) – Pressure (po) Relationship:
p02
1
I

 p02
r n 2  z
r is mass density or air 1.204 kg/m3 at 20o Celsius.
n is speed or air, 343.2 m/s, p0 zero-peak pressure amplitude.
z is acoustic impedance or air 413.2 kg/(s·m2) or 413.2 N·s/m3.
2
I 2p
 Ip 
  
 2 2
2
I rms 
Ip
n
n

1
2
Ip
Psychoacoustics
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Physical parameters of sound waves: Decibel scale
Psychoacoustics
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Physical parameters of sound waves: Decibel scale
0 dB = Threshold Of Hearing (TOH)
10 dB = 10 times more intense than TOH
20 dB = 100 times more intense than TOH
30 dB = 1000 times more intense than TOH
An increase in 10 dB means that the intensity of the sound
increases by a factor of 10
If a sound is 10x times more intense than another, then it has a
sound level that is 10*x more decibels than the less intense sound
An increase of 6 dB represents a doubling of the sound pressure
An increase of about 10 dB is required before the sound subjectively
appears to be twice as loud.
The smallest change of the pressure level we can hear is
about 3 dB
Psychoacoustics
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Physical parameters of sound waves: Decibel scale
Sound Intensity level of super imposed sources:
SIL[dB]  10 log( 10
L1
10
 10
L2
10
 ...  10
where L1, L2, …, Ln are SIL in dB
LN
10
)
Psychoacoustics
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Physical parameters of sound waves: Noise Density
When dealing with noises, it is advantageous to use density instead of
sound intensity e.g., the sound intensity within a bandwidth of 1 Hz.
The logarithmic correlate of the density of sound intensity is called sound
intensity density level, usually shortened to density level, l.
l  SIL  10 log 10 (f / Hz )[ dB]
 I 
SIL[ dB ]  10 log 10 

 I0 
For white noise, l and SIL are related by the equations given above
where Δf represents bandwidth of the sound.
Psychoacoustics
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THE BELL DECODER
Psychoacoustics
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Physical parameters of sound waves: Power Spectrum Density
The Intensity Density Level of three types of NOISES:
Intensity density level [dB]
WHITHE NOISE
BROWN (RED) NOISE
Log Frequency [Hz]
GRAY NOISE
Psychoacoustics
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Physical parameters of sound waves: Power Spectrum Density
Power Spectral Density (PSD) is the
frequency response of a random or
periodic signal.
PSD shows the strength of the
variations per unit frequency as a
function of frequency.
The PSD is the average of the Fourier
transform magnitude squared, over a
large time interval.
It tells us how the average intensity is
distributed as a function of frequency.
Plot shows de PSD of white Noise
Psychoacoustics
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Auditory sensitivity: Absolute thresholds
MAF – Minimum Audible Field thresholds
sound pressure level for pure tone at absolute
threshold in a free field tested in a room,
using loudspeakers, listening binaurally,
1 meter from source SPL calibrated using
microphone, with listener not present.
MAP – Minimum Audible Pressure thresholds
SPL at listener’s tympanic membrane
sound presented over headphones (monaural)
SPL estimated from the sound level in a test coupler
attached to earphone.
Differences in the two measures are due to some binaural
advantage, outer-ear filtering (mid frequencies), and
physiological noise (low frequencies).
Psychoacoustics
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Auditory sensitivity: Absolute thresholds
Differences in the two measures are due to some binaural
advantage, outer-ear filtering (mid frequencies), and
physiological noise (low frequencies).
Psychoacoustics
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Auditory sensitivity: Hearing range (MAF)
Psychoacoustics
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Auditory sensitivity: upper limit
Psychoacoustics
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Auditory sensitivity: Absolute thresholds
Hearing Level (dB HL)
Threshold of hearing, relative to the average of the normal
population.
For example, the average threshold at 1 kHz is about 4 dB SPL. Therefore,
someone with a threshold at 1 kHz of 24 dB SPL has a hearing level of 20
dB HL.
Audiograms
Audiograms measure thresholds in dB HL, and are plotted “upsidedown”. Measurements usually made at octave frequencies from 250
Hz to 8000 Hz.
Threshold microstructure
Individuals show peaks and dips as large as 10 dB over very small
frequency differences (probably due to OHCs and “cochlear
amplifier”).
Psychoacoustics
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Auditory sensitivity: Audiometric curve (audiogram)
Plot A shows the threshold of hearing
or audibility curve for a patient with a
hearing loss (curve b) and a normal
curve (curve a).
Notice that the patient's threshold is
higher for every frequency above 128
Hz.
The normal audibility curve is usually
converted to a straight line at 0 dB
loss, and the patient's values are
plotted as deviations from the normal
values.
The result is a hearing loss curve b, as
shown in plot B.
Psychoacoustics
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Auditory sensitivity: Audiometric curve (hearing loss)
Psychoacoustics
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Auditory sensitivity: Audiometric curve (hearing loss)
The circles in the audiogram indicate the hearing
loss as measured by air conduction, whereas the
squares indicate the hearing loss as measured by
bone conduction.
Typically, in neural hearing loss (A), both
measures show the same pattern of loss.
Surgery is not indicated for this form of hearing
loss because the neural tissue probably cannot be
repaired, but some improvement in hearing is
possible with a hearing aid, depending upon the
nature of the damage.
The audiogram of a person with pure conduction
hearing loss (B). Here, bone conduction is near
normal, i.e., near 0 dB loss, but air conduction is
impaired.
Notice that the air audiogram is nearly flat with
conduction hearing loss (B), but there is a
differential loss, depending upon frequency, in
nerve hearing loss (A).
Psychoacoustics
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Absolute thresholds: temporal integration
Audiometric thresholds and international
threshold standards are measured using
long-duration tones (> 500 ms).
Detectability of tones with a fixed level
decreases with decreasing duration, below
about 300 ms.
IL is the minimum intensity which is an
( I  I L )  t  I Lt  I  t  I L  1  I L
t
effective long duration stimulus for the ear. t
represents the integration time of the
auditory system.
Thus, the auditory system does not simply
integrate stimulus time (Intensity x duration)
It may also vary with frequency.
Psychoacoustics
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Perceived Loudness: Equal-loudness Contours
The pressure/ intensity in sound wave is not solely responsible
for its loudness – frequency is also important.
1 kHz is used as a reference.
By definition, a 1-kHz tone at a
level of 40 dB SPL has a
loudness level of 40 phons.
Any sound having the same
loudness (no matter what its SPL)
also has a loudness level of 40
phons.
Equal-loudness contours are
produced using loudness
matching experiments
(method of adjustment or method
of constant stimuli).
Psychoacoustics
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SPL is not a measure of Perceived Loudness
Defined as the attribute of auditory sensation in terms of which sounds
can be ordered on a scale extending from quiet to loud.
Two sounds with the same sound pressure level may not have the
same (perceived)loudness
A difference of 6 dB between two sounds does not equal a 2x increase
in loudness
Loudness of a broad-band sound is usually greater than that of a
narrow-band sound with the same (physical) power (energy content)
Psychoacoustics
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Perceived Loudness: Equal-loudness Contours
The pressure/ intensity in sound wave is not solely responsible
for its loudness – frequency is also important.
Psychoacoustics
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Perceived Loudness: phone
A unit of LOUDNESS LEVEL (L)of a given sound or noise.
Derived from indirect loudness measurements (like Fletcher and Munson
experiment)
If SPL at reference frequency of 1kHz is X dB – the corresponding equal
loudness contour is X phon line.
Phon units can’t be added, subtracted,
divided or multiplied.
60 phons is not 3 times louder than 20 phons!
The sensitivity to different frequencies is more
pronounced at lower sound levels than at higher.
For example: a 50 Hz tone must be 15 dB higher
than a 1 kHz tone at a level of 70 dB
Psychoacoustics
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Perceived Loudness: sound level meters
The shapes of equal-loudness
contours have been used to
design sound level meters
(audiometer)
At low sound levels, lowfrequency components
contribute little to the total
loudness of a complex sound.
Thus an A weighting is used to
reduces the contribution of lowfrequencies
Psychoacoustics
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Loudness Scaling: Magnitude of perceptual change
I  dI 
dS 1 1


k
dI
I
I/I  constant
Fechner assumed that a JND
for a faint background
produces the same difference
in sensation as does the JND
for a loud stimulus.
Measure of loudness: sensation
intensity (S) in JND units
As it turned out, this assumption is not valid, as shown by
Stevens (1957) he simply
asked subject to asses suprathreshold stimuli.
Psychoacoustics
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Louness Scaling: Stevens’ Power law
Another function relating
Loudness S in sones to stimulus
intensity in I:
S  aI
=0.3
m
The exponent m describes
whether sensation is an expansive
or compressive function of
stimulus intensity.
The coefficient a simply adjusts for
the size of the unit of
measurement for stimulus intensity
threshold above the
1-unit stimulus.
Psychoacoustics
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Loudness Scaling: sone vs. phon
SONE: a unit to describe the comparative
loudness between two or more sounds.
One SONE has been fixed at 40 phons at any
frequency (40 phon curve).
2 sones describes sound two times LOUDER
than 1 sone sound.
A difference of 10 phons is sufficient to
produce the impression of doubling loudness,
so 2 sones are 50 phons.
L  k ( p  p0 )
4 sones are twice as loud again, viz. 60 phons.
0.6
p is the base pressure of a sinusoidal stimulus, po is its absolute threshold.
Psychoacoustics
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™ and a TI FF ( LZW) decom pr essor ar e needed t o seet his pict ur e.
Predicting Loudness
Currently, predictors of loudness are only successfully for sound stimuli
extending over many seconds.
Note that the dBA scale does not include bandwidth influences on
loudness(etc.).
It is better than the dB SPL scale, but far away from human perception