Alaphangmagassag (virtual pitch)

Terhardt (1972-74): megkulombozendo

“virtual pitch” es

“spectral pitch” dimenziok

Virtual pitch: valoszinuleg (=biztos) idoelemzesbol

adodik

Spectral pitch: hangkepelemzes

Ket eszleles: hangmagassag es hangszin

Alaphangmagassag erzekelese:idobe telik? (peldak)

“Virtual pitch” hatara kb 1 kHz

Dominans frekvenciaterulet (<1500 Hz) es felhangrendszamok (2-6) (Ritsma, 1962)

Autokorrelacio reszlegesen megmagyarazza

(Matlab peldak)

E Λ

Szurt zajnak autokorrelacioja alacsony, feher zajnak nulla

Feloldott es feloldatlan komponensek:

Harmonikus felhangok linearisan (Hz) kovetik egymast,

Mig a ful tonotopiai rendszere Greenwood egyenletet koveti

BM_mm = (16,7) log10 ((0,006046) freq + 1)(Greenwood egyenlőség)

Basilar membrane (=alaphàrtya?)

Theorem

(a b)2 a2 b2 2ab

proof obvious but no room to give it here...

Time-domain processing

•output of cochlea temporally structuredoutput of cochlea temporally structured•neural circuitry specialized for timeneural circuitry specialized for time

Licklider

Licklider

from cochleafrom cochlea

Licklider

Auditory Tuning Curve

02.5

57.5

0.1

0.34

0.77

1.5

2.8

0.5

kHz

lag (ms)

period --> pitchperiod --> pitch

similar model, based on similar model, based on binaural interactionbinaural interaction

Licklider, Jeffress: excitatory interactionLicklider, Jeffress: excitatory interaction

delayed s(t-T)

direct s(t)

fast synapses

Jeffress

Harmonic cancellation: inhibitory interactionHarmonic cancellation: inhibitory interaction

delayed s(t-T)

direct s(t)

I

E

de Cheveigné

02.5

57.5

0.1

0.34

0.77

1.5

2.8

0.5

kHz

lag (ms)

period --> pitchperiod --> pitch

medial superior olive (MSO)medial superior olive (MSO)

AVCN

cochlée

MSO

LSO

MNTB

DCN

PVCN

corps trapézoide

cochlée

AVCN

DCN

PVCN

bushy“bushy”

“bu

shy”

Lateral superior olive (LSO)Lateral superior olive (LSO)

AVCN

cochlée

MSO

LSO

MNTB

DCN

PVCN

corps trapézoide

cochlée

AVCN

DCN

PVCN

bushy“bushy”

“bu

shy”

Principle of MSOPrinciple of MSO

"coincidence counter" neuron"coincidence counter" neuron

Activated if impulses areActivated if impulses aresimultaneoussimultaneous at input at input

Model by Jeffress (1948)Model by Jeffress (1948)

Right earRight ear

Left earLeft ear Delay lineDelay line

Principle of LSOPrinciple of LSO

"anti-coincidence counter" neuron"anti-coincidence counter" neuron

activated activated except ifexcept if impulses impulsesare simultaneous at inputare simultaneous at input

MNTB

Durlach

model similar to Jeffress’s, based on model similar to Jeffress’s, based on binaural interactionbinaural interaction(Equalization-Cancellation)(Equalization-Cancellation)

2 types of model

•Correlation (auto- & cross-)Correlation (auto- & cross-)

(excitatory interaction)(excitatory interaction)•CancellationCancellation

(inhibitory interaction)(inhibitory interaction)

2 types of model

•Correlation (auto- & cross-)Correlation (auto- & cross-)

(excitatory interaction)(excitatory interaction)•CancellationCancellation

(inhibitory interaction)(inhibitory interaction)

Basic ingredients

xt

running autocorrelationrunning autocorrelation

Basic ingredients

xtL

running autocorrelationrunning autocorrelation

Basic ingredients

xtR

running autocorrelationrunning autocorrelation

Basic ingredients

xt xt

running autocorrelationrunning autocorrelation

Basic ingredients

x j x jjt1

tW

running autocorrelationrunning autocorrelation

Basic ingredients

rt () x jx jjt1

tW

running autocorrelationrunning autocorrelation

Basic ingredients

running autocorrelationrunning autocorrelation

rtL( ) x j

L x jL

jt1

tW

leftleft

Basic ingredients

running autocorrelationrunning autocorrelation

leftleft

rightright

rtL( ) x j

L x jL

jt1

tW

rtR( ) x j

Rx jR

jt1

tW

Basic ingredients

rtL( ) x j

L x jL

jt1

tW

running autocorrelationrunning autocorrelation

rtR( ) x j

Rx jR

jt1

tW

leftleft

rightright

running crosscorrelationrunning crosscorrelation

ct () x jLx j

R

jt1

tW

Structure

auto- and crosscorrelation

network

sound or filtered sound

LR

linear combination

control and

interpretationpitch, etc..

11 22 33fast signal processingfast signal processing

1. Licklider model of pitch

rt () x jx jjt1

tW

delayed x(t-)

direct x(t)

EE

EE

1. Licklider model of pitch

•Module 1: calculate autocorrelation & Module 1: calculate autocorrelation &

crosscorrelation for all t, crosscorrelation for all t, , , •Module 2: select autocorrelation withModule 2: select autocorrelation with

parameter parameter •Module 3: vary Module 3: vary while monitoring output while monitoring output

of 2 for a maximumof 2 for a maximum

2. Jeffress model of localization

•Module 2: select crosscorrelation withModule 2: select crosscorrelation with

parameter parameter •Module 3: vary Module 3: vary while monitoring output while monitoring output

of 2 for a maximumof 2 for a maximum

4. Cancellation model of pitch

dt ( ) (x j x jjt1

tW

)2

I

E

delayed x(t-)

direct x(t)

4. Cancellation model of pitch

dt ( ) (x j x jjt1

tW

)2

[x j2 x

j

2 2x j x jjt1

tW

]

4. Cancellation model of pitch

dt ( ) rt(0) rt (0) 2rt ( )

autocorrelation termsautocorrelation terms

•Module 2: linear combination of Module 2: linear combination of

autocorrelation terms (parameter autocorrelation terms (parameter •Module 3: vary Module 3: vary while monitoring output while monitoring output

of 2 for a minimumof 2 for a minimum

4. Cancellation model of pitch

5. Equalization-Cancellation (Durlach)

xtL x t

R

5. Equalization-Cancellation (Durlach)

dt ( ) (x jL x j

R )2

jt1

tW

5. Equalization-Cancellation (Durlach)

dt ( )rtL(0) rt

R (0) 2ct()

autocorrelation & autocorrelation & crosscorrelation termscrosscorrelation terms

6. Cancellation model of concurrent vowel

identification

delay tuned to perioddelay tuned to periodof interfering vowelof interfering vowel

delay

autocorrelation

templatetemplatematchingmatching

6. Cancellation model of concurrent vowel

identification

delay

zt xt xtT

rt

z () ztztjt1

tW

6. Cancellation model of concurrent vowel

identification

rt

z () (xt xtT)(x tjt1

tW

x tT )

6. Cancellation model of concurrent vowel

identification

rt

z () rt ( ) rtT ( T) rtT( ) rt ( T)

autocorrelation termsautocorrelation terms

•Module 2: linear combination ofModule 2: linear combination of

autocorrelation terms (parameters autocorrelation terms (parameters , , •Module 3: set T to cancel interfering vowel,Module 3: set T to cancel interfering vowel,

vary vary , compare output of 2 to template, compare output of 2 to template

6. Cancellation model of concurrent vowel

identification