rob van der willigen http://~robvdw/cnpa04/coll1/audperc_2007_p6.ppt auditory perception

Rob van der WilligenRob van der Willigenhttp://~robvdw/cnpa04/coll1/AudPerc_2007_P6.ppthttp://~robvdw/cnpa04/coll1/AudPerc_2007_P6.ppt

Auditory PerceptionAuditory Perception

Q ui ckTi me™ and a TI FF (LZW) decompressor are needed to see thi s pi cture. Today’s goalToday’s goal

Understanding psychophysical methodology and its use to measure absolute threshold and loudness of hearing

Q ui ckTi me™ and a TI FF (LZW) decompressor are needed to see thi s pi cture.

Psychoacoustics

“Elemente der Psychophysik”: Interpretation

Physical dimensions of the stimulus influence detectability

Is a Non-trivial relationship has a Probabilistic Nature

Is a highly subjective relationship

Stimulus versus Perception

Recapitulation last weeks’ lecture


A function for detection: the PMF

Psychoacoustics

The psychometric functionprovides an answer to both the measurement of:

(1) a threshold &

(2) the aim to order and distribute stimulus level along a perceptual dimension.

Pb(a

)

)]()([)( bgauFaPb

The sigmoid curve defined by function F is called the Psychometric Function (PMF).



Psychoacoustics

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


The PDF of randomly fluctuating levels of neural activation summed over time approximates the normal distribution (red line).



Psychoacoustics

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

Pay-off Matrix: Yes-No Paradigm

P(no|noise)

P(yes|signal)

P(no|signal)

P(yes|noise)

In a yes/no binary detection task there aretwo 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

The frequencies of these two types of error will be determined by two factors :

Sensitivity of observer

Criteria of decision

ERROR

ERROR

1- P(yes|signal) = P(no|signal)

1- P(yes|noise) = P(no|noisel)


Psychoacoustics


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.



Psychoacoustics

Response Criterion (bias): Yes-No Paradigm

P(no|noise)

P(yes|signal)

P(no|signal)

P(yes|noise)



Psychoacoustics

Signal detection theory: ROC curves, bias

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=0.9

Pn=0.5

Pn=0.05

The ROC curve is traced out by plotting P(yes|signal) (hits) against P(yes|noise)(False positive) as the criterion changes systematically.


Psychoacoustics

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

Testing paradigm: nAFC ParadigmA 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

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 yes-answers 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

Testing paradigm: nAFC Paradigm / yes-no

nP thnAFCpositive

115.0)|,(

)1(5.0

115.0lim)|/,(

nP

nthnoyespositive


Psychoacoustics

Testing paradigm: nAFC Paradigm & d’

)(1)()(0

)()1()(

xFxFxP

xFxP

c

c

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 toto the proportion of correct responses, Pc (x), when lapses, , are very small (zero) and when corrected for guessing,.

F-1 is the inverse cumulative normal distribution function

1

)()(

xPF cx

2)()(' )(1 xcPFxd


Psychoacoustics

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:

Note that P{X < b} does not necessarily equal F(b)since F(b) also includes the probability that X equals b.

The CDF can be measured bymeans of a psychophysical detection / discrimination task. To obtain the PDF, the CDF must be differentiated.


Psychoacoustics

The CDF can be measured bymeans 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.

Some Maths on the CDF


Psychoacoustics

Some Maths on the ERF


Using the inverse function F-1

follows:

ccPFz n )(fa

1fa

ccPFz s )(hit

1hit

Elimination of c:

'fafahit dzzz ns

Linear function

Psychoacoustics

Signal detection theory: sensitivity and z-score


Psychoacoustics

Testing paradigm: nAFC vs. yes-no & d’

)]|([)]|([ nyesPzsnyesPzd '

2

)]|([)]|([ nyesPzsnyesPzd

'

Yes-no

2AFC


Psychoacoustics

Testing paradigm: z-score calc with Matlab


Psychoacoustics

Testing paradigm: method of limits under 2AFC


Psychoacoustics


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


One-up / one down adaptive tracking versusTwo-down / one-up (descending stairs)


Psychoacoustics


down up

Descending stairs


Intensity (I) of a wave is the rate at which sound energy flows through a unit area (A) perpendicular to the direction of travel:

Pressure, P, is measured in watts [W=J/s]

A is measured in square meters [m2]

Psychoacoustics

Physical parameters of sound waves: Intensity

A

P

Area

PowerTimeArea

Energy

Time

Distance

Area

Force

Velocity ParticlePressureIntensity


Psychoacoustics

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.


010log10)(

I

ISILdB

Psychoacoustics

Physical parameters of sound waves: Decibel scale

Sound Intensity Level:Intensity threshold of hearing I0 = 10-12 W/m2

010

2

010 log20log10)(

P

P

P

PSPLdB

Sound Pressure Level:Pressure threshold of hearing P0 = 2 x 10-5 N/m2 = 20 Pa

Energy ratio

Pressure ratio


Psychoacoustics

Physical parameters of sound waves: RMS values

Intensity (I) – Pressure (po) Relationship:

is mass density or air 1.204 kg/m3 at 20o Celsius.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.

pn

I

rms II np

21

2

20

20

2

1p

z

pI

22

22

pII p


Psychoacoustics



0 dB = Threshold Of Hearing (TOH)10 dB = 10 times more intense than TOH20 dB = 100 times more intense than TOH30 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 isabout 3 dB

Psychoacoustics



Sound Intensity level of super imposed sources:

where L1, L2, …, Ln are SIL in dB

)10...1010log(10][ 10101021 NLLL

dBSIL

Psychoacoustics



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.

For white noise, l and SIL are related by the equations given above where Δf represents bandwidth of the sound.

Psychoacoustics

Physical parameters of sound waves: Noise Density

])[/(log10 10 dBHzfSILl

010log10][

I

IdBSIL


Psychoacoustics

THE BELL DECODER


The Intensity Density Level of three types of NOISES:

Psychoacoustics

Physical parameters of sound waves: Power Spectrum Density

WHITHE NOISE BROWN (RED) NOISE GRAY NOISE

Inte

nsi

ty d

ensi

ty level

[dB

]

Log Frequency [Hz]


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

Physical parameters of sound waves: Power Spectrum Density


Psychoacoustics

Auditory sensitivity: Absolute thresholds

MAF – Minimum Audible Field thresholdssound 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 thresholdsSPL at listener’s tympanic membranesound 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


Differences in the two measures are due to some binaural advantage, outer-ear filtering (mid frequencies), and physiological noise (low frequencies).


Psychoacoustics

Auditory sensitivity: Hearing range (MAF)


Psychoacoustics

Auditory sensitivity: upper limit


Psychoacoustics


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.

AudiogramsAudiograms measure thresholds in dB HL, and are plotted “upside-down”. Measurements usually made at octave frequencies from 250 Hz to 8000 Hz.

Threshold microstructureIndividuals show peaks and dips as large as 10 dB over very small frequency differences (probably due to OHCs and “cochlear amplifier”).


Psychoacoustics

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

Auditory sensitivity: Audiometric curve (hearing loss)


Psychoacoustics

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

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 effective long duration stimulus for the ear.

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.

LLLL ItIIItII 1)(


Psychoacoustics

Perceived Loudness: Equal-loudness Contours

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).

The pressure/ intensity in sound wave is not solely responsible for its loudness – frequency is also important.


Psychoacoustics

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

Perceived Loudness: Equal-loudness Contours

The pressure/ intensity in sound wave is not solely responsible for its loudness – frequency is also important.


Psychoacoustics

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

Perceived Loudness: sound level meters

The shapes of equal-loudness contours have been used to design sound level meters (audiometer)

At low sound levels, low-frequency components contribute little to the total loudness of a complex sound.

Thus an A weighting is used to reduces the contribution of low-frequencies


Loudness Scaling: Magnitude of perceptual change

Psychoacoustics

Fechner assumed that a JND for a faint background produces the same difference in sensation as does the JND for a loud stimulus.

As it turned out, this assump-tion is not valid, as shown by Stevens (1957) he simply asked subject to asses supra-threshold stimuli.

I

11dI

dII kdS

Measure of loudness: sensation intensity (S) in JND units

constantI/I


Louness Scaling: Stevens’ Power law

Psychoacoustics

Another function relating Loudness S in sones to stimulus intensity in I:

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.

maIS

=0.3


Loudness Scaling: sone vs. phon

Psychoacoustics

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. 4 sones are twice as loud again, viz. 60 phons.

6.00 )( ppkL

p is the base pressure of a sinusoidal stimulus, po is its absolute threshold.


Psychoacoustics

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

rob van der willigen http://~robvdw/cnpa04/coll1/audperc_2007_p6.ppt auditory perception

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