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Sontacchi A., Noisternig M., Majdak P., Höldrich R.

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University of Music and Dramatic ArtsGraz, Austria

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Outline

• HRIR based Binaural Sound Reproduction Systems using Ambisonic

• Definitions

• Mathematical Model

• Results

• Outlook

Binaural Systems using Ambisonic

Binaural Reproduction Systems:

• filtering virtual source signals with HRIRs

• incorporate head tracking to improve source localisation

Problem:

• time-varying interpolation between HRIRs

Binaural Systems using Ambisonic

Why Ambisonic?

• head movement:- time-invariant HRIR filter - cheap time-variant rotation matrix

• decoding is independent from coding

• number of transmit channels is independent from number of virtual sources

Binaural Systems using Ambisonic

• encode signals depending on source position

• rotate Ambisonic depending on head position

• decode Ambisonic to virtual speaker signals

• convolve speaker signals with HRIRs

Definitions

• localisation function

• localisation error

• localisation blur

• average localisation error

• average localisation blur

localisation

errorlocalisation

blur

Mathematical Model

Intentions:

• classifying Binaural Reproduction Systems

• prediction of localisation performance

Main assumption:

• the reference HRIRs result in optimal localisation

• 2D systems only

Mathematical Model

HRIRs

Device under test

ILD

ITD

ILD

ITD

ITDA ILDA

Merger

∑

Mathematical ModelParameter

Result

0 0.51

1.5 2 2.5 3 3.5 4 4.5

x 10-4

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

Time in s

Am

plitu

de

HRIR for 0°

Interaural Time Difference (ITD)

HRIR, ϕ=0°

0 0.5 1 1.5 2 2.5

x 10 4

-60

-50

-40

-30

-20

-10

0

10

20

Frequenz in HzA

mpl

itude

in d

B

Amplitudengang

0 0.5 1 1.5 2 2.5

x 10 4

-70

-60

-50

-40

-30

-20

-10

0

10

Frequenz in Hz

Phas

e in

rad

Phasengang

0 0.5 1 1.5 2 2.5

x 104

-60

-50

-40

-30

-20

-10

0

10

20

Frequency in Hz

Am

plitu

de in

dB

Magnitude Response

0 0.5 1 1.5 2 2.5

x 10 4

-70

-60

-50

-40

-30

-20

-10

0

10

Frequency in Hz

Phas

e in

rad

Phase Response

FFT0 0.5 1 1.5 2 2.5

x 104

-4

-2

0

2

4

6

8

10x 10 -3

Frequenz in Hz

Gru

ppen

lauf

zeit

in s

Gruppenlaufzeit

0 0.5 1 1.5 2 2.5

x 104

-4

-2

0

2

4

6

8

10x 10 -3

Frequency in Hz

Gro

up D

elay

Tim

e in

s

Group Delay Time

���Φ⋅−

π2

1

Interaural Time Difference (ITD)

Calculation of the group delay time:

• impulse response (HRIR)

• zero phase filter over critical bands

• energy center of gravity per band

• group delay time per band 0 0.5 1 1.5 2 2.5

x 104

-4

-2

0

2

4

6

8

10x 10-3

Frequency [Hz]G

roup

Del

ay T

ime

[s]

Group Delay Time

Interaural Time Difference (ITD)

ITD over critical bands: difference of the group delay time between ipsi- and contralateral eardrum

left ear

Group Delay TimeITD

critical bands

azimuth angleright ear

Interaural Level Difference (ILD)

Calculation of the ILD:

• amplitude response (HRTF)

• energy-difference over critical bands between ipsi- and contralateral eardrums

left earILD

critical bands

azimuth angleright ear

energy over critical bands

Interaural Difference Angle (ITDA/ILDA)

0 50 100 150 200 250 300 350 400-5

0

5x 10-4

Azimuth Angle [°]

ITD

[s]

Search Algorithm:

Deviation

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Merging of ITDA and ILDA

• ITDA: fade out above 800 Hz

• ILDA: fully weighted

ITDA

ILDA

Res

ult

0 5 10 15 20 25

0

0.2

0.4

0.6

0.8

1

Gewichtung der ITD

Frequenzgruppe in bark

Gew

icht

ungs

fakt

or

0 5 10 15 20 25

0

0.2

0.4

0.6

0.8

1

Frequenzgruppe in bark

Gew

icht

ungs

fakt

or

Gewichtung der ILD

Results (1)

• localisation function (averaged over critical bands)

• localisation blur (standard deviation over critical bands)

ΘΘ⋅⋅⋅

+

ΘΘ⋅⋅⋅=Θ

∑∑

∑∑

=

=

24

1

24

1

),()()(

1

2

1

),()()(

1

2

1)(

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[ ]∑∑ ∑ ==Θ−ΘΘ⋅⋅⋅=Θ

24

1

2)(),()()(

1

2

1)(

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Results (2)

• average localisation blur(averaged over the azimuth angle)

• average localisation erroraveraged over azimuth angle referring to the MAA

[ ]∑=

Θ−Θ=�

�

��

1

2)(1

∑°

=Θ ΘΘ⋅=

360

0 )(

)(1

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Analysis

Variations of design parameters:

• reference HRIRs

• length of HRIR

• ambisonic order

• weighting of ambisonic channels

• number of virtual speaker

HRIR Type (1)

10 20 30 40

30

60

90

120

150

180

0

Kemar-HRIR (#12)Proprietary-HRIR (#9)

filter length = 128 samples

loca

lisat

ion

blur

[°]

azimuth angle [°]

-20

-15

-10

-5

0

5

10

15

20

Kemar-HRIR (#12)Propr.-HRIR (#9)

azimuth angle [°]

loca

lisat

ion

erro

r [°

]filter length = 128 samples

HRIR Type (2)

256

128

96

64

48 3

3.5

4

4.5

5

5.5

6

6.5

filter length [samples]

loca

lisat

ion

blur

[mul

tiple

s of

MA

A]

3rd ord. KEMAR, 5°3rd ord. KEMAR, 15°3rd ord. Propr., 15°4th ord. KEMAR, 5°4th ord. Propr., 15°

256

128

96

64

48 6

7

8

9

10

11

12

13

14

15

16

filter length [samples]

loca

lisat

ion

erro

r [°

]

3rd ord. KEMAR, 5° (#0)3rd ord. KEMAR, 15° (#12)3rd ord. AKG, 15° (#9)4th ord. KEMAR, 5° (#18)4th ord. AKG, 15° (#23)

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Ambisonic Order (1)

-30

-20

-10

0

10

20

4th ord. (#18)3rd ord. (#100)2nd ord. (#100)

loca

lisat

ion

erro

r [°

]

azimuth angle [°]

30

10 20 30 40 50

30

60

90

120

150

180

0

2nd ord. (#100)3rd ord. (#0)4th ord. (#18)

azimuth angle [°]

loca

lisat

ion

blur

[°]

filter length = 128 samples

Ambisonic Order (2)

256

128

96

64

48 3

3.5

4

4.5

5

5.5

6

6.5

filter length [samples]

loca

lisat

ion

blur

[mul

tiple

s M

AA

]

4th ord. (#18)3rd ord. (#0)2nd ord. (#100)

256

128

96

64

48 8

9

10

11

12

13

14

15

16

17

18

filter length [samples]

loca

lisat

ion

erro

r [°

]

4th ord. (#18)3rd ord. (#0)2nd ord. (#100)

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Ambisonic Weighting (1)

-15

-10

-5

0

5

10

15

3rd ord., Kaiser window (#24)4th ord., fully weighted (#18)4th. ord. Kaiser window (#22)

azimuth angle [°]

loca

lisat

ion

erro

r [°

]

filter length = 128 samples

10 20 30 40

30

60

90

120

150180

0

Kaiser window, 3rd order (#24)Fully weighted, 4th order (#18)Kaiser window, 4th order (#22)

length of filter = 128 samples

lo

calis

atio

n bl

ur [°

]

azimuth angle [°]

Ambisonic Weighting (2)

256

128

96

64

48 3

3.5

4

4.5

5

5.5

6

6.5

length of filter [samples]

3rd ord., weighting: 0.4 (#3)3rd ord., fully weighted (#0)3rd ord., Kaiser window (#24)4th ord., fully weighted (#18)4th ord., Kaiser window (#22)

loca

lisat

ion

blur

[mul

tiple

s of

MA

A]

256

128

96

64

48 7

8

9

10

11

12

13

14

15

16

17

filter length [samples]

3rd ord., weighting: 0.4 (#3)3rd ord., fully weighted (#0)3rd ord., Kaiser window (#24)4th ord., fully weighted (#18)4th ord., Kaiser window (#22)

loca

lisat

ion

erro

r [°

]

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Conclusion

• prediction of localisation is possible

• results correspond with ambisonic theory- ambisonic not less than 3rd order for correct localisation

- weighting of channels using Kaiser-window yields better localisation

- filter length up to 128 samples

• model was evaluated using listening tests

Outlook

• incorporate IGD (���������������������) as a cue for high frequency localisation

• classification regarding coloration and externity

• extend the model for 3D applications• warping tables to predict and minimise the

localisation errors for further implemen-tations

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University of Music and Dramatic Arts

Graz, Austria

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