Generation of multiple sound zonesby spatial filtering in wavenumber domain

using a linear array of loudspeakers

1

@ Florence, Italy, 8th May 2014.

Takuma OKAMOTO

National Institute of Information Communications and Technology (NICT), Japan

IntroductionAcoustically bright zone or multi-zones generation using loudspeakers

PurposeConventional methods and their problemsNovel approach

Proposed methodBasic theory : Spectral division method (SDM)Analytically-derived spatial filters in wavenumber domainComputer simulationsDemonstrations

Concluding remarks

Presentation contents

2

Generation of acoustically bright and dark zones using an array of loudspeakers

(a) generating bright and dark zones

(b) multiple spots generation

ApplicationsPersonal audio systemMultiple-language guide systemVirtual reality applications without headphone

Introduction

3

...

...

Dark zone

...

Dark zone

(a)

(b)

S1(ω)F1(x0,ω)

S2(ω)F2(x0,ω)

D(x0,ω)

Bright zoneS2(ω)

S1(ω)Bright zone

Sound zoneS2(ω)

S1(ω)Sound zone

+

Most methods based on multiple points controlPrinciple

Numerical calculation of the inverseof the spatial correlation matrix

ProblemsQuite unstableIterative calculation for decidingregularization parameter

Energy difference maximization (EDM)Principle

Numerical calculation of the eigenvectorof the spatial correlation matrix

ProblemIterative calculation for deciding tuning factor

Previous methods and their problems

4

...

Control points

loudspeakers

......

...

G(!)

(e.g. J.-W. Choi et al. in JASA, 2002.)

(M. Shin et al. in JASA, 2010.)

Problems of conventional methodsUnstableIterative calculation

3 characteristics of proposed methodAnalytically derived stable filtersNo iterative calculationImplemented by using actual 64 loudspeakers

NomenclatureSound source signal : Driving signals of loudspeakers

(a) Generating bright and dark zone

(b) Generating multiple sound zones

Novel approach

5

...

...

Dark zone

...

Dark zone

(a)

(b)

S1(ω)F1(x0,ω)

S2(ω)F2(x0,ω)

D(x0,ω)

Bright zoneS2(ω)

S1(ω)Bright zone

Sound zoneS2(ω)

S1(ω)Sound zone

+

S(!)

D(x0,!) = S1(!)F1(x0,!)

D(x0,!) =MX

i=1

Si(!)Fi(x0,!)

How to calculate?

Spectral division method (SDM)Sound field reproduction using planer or linear arrays of loudspeakers

Driving signals of secondary sources are analytically derived

Acoustical single layer potential in a plane

Spatial Fourier transform along with -axis

Driving signals of secondary sources

Driving signals in each wavenumber domain is completely orthogonal each other and much stable rather than multiple points control

Basic theory

6

(J. Ahrens et al. in IEEE ASLP., 2010.)

P (x,!) =

Z 1

�1D(x0,!)G3D(x� x0,!)dx0

P̃ (kx

, y,!) = D̃(kx

,!) · G̃(kx

, y,!)

D̃(kx

,!) =P̃ (k

x

, yref ,!)

G̃(kx

, yref ,!)F�1

x

y = yref

x

y

Secondary sourceD(x, 0,ω)

P (x, yref ,ω)

x

D(x,!) =1

2⇡

Z 1

�1

P̃ (kx

, yref ,!)

G̃(kx

, yref ,!)e

�jk

x

x

dk

x

Analytically derived spatial filters in wavenumber domain Spatial filters in wavenumber domain

Shift theorem introduced to shift rectangular window along with -axis

Spatial filters for generating bright and dark zones

Proposed method

7

x

y

y = yb

Secondary source

Bright

DarkDark

P (x, yb) = 1

P (x, yb) = 0

lbxb

Shift

F̃ (kx

,!) =P̃ (k

x

, yref ,!)

G̃(kx

, yref ,!)

P (x, yref ,!) = 1P (x, yref ,!) = 0

�Modeled byRectangular window

P (x, yb) = ⇧

✓x

lb

◆=

⇢1, for |x| lb/2

0, elsewhere

P̃ (kx

) = lb sinc

✓kx

lb2⇡

◆F

x

˜

F (k

x

,!) =

lb sinc (k

x

lb/2⇡) exp(jkxxb)

˜

G(k

x

, yb,!)

˜

Pshift(kx) =˜

P (k

x

) exp(jk

x

x

b

) = lb sinc

✓k

x

lb

2⇡

◆exp(jk

x

x

b

)

x

Arbitrary length : Arbitrary position : [xb, yb]

Tlb

Simulation conditionSpeed of sound : 343.25 m/sdistance betweenadjacent loudspeakers : 0.05 mTuning factor for EDM : 0.9999

Evaluation valuesSound pressure level

Bright to dark ratio

Computer simulations

8

2 myb =L=3.2 m

N=64 ch

Loudspeakers

Control line

0.4 m

Bright zone

xbDark zone

xd

l b=1.6 m 64 ch (EDM)

K=

(for calculating (19))BDR(!) = 10log10

Pxb

��� ˆP (xb,!)���2

Pxd

��� ˆP (xd,!)���2

PSPL(x,!) = 10log10

��� ˆP (x,!)���2

Simulation results :

9

Y axis [m]

X ax

is [m

]

[dB]1 2 3−1.5

−1

−0.5

0

0.5

1

1.5

0

5

10

15

20

25

30

35

40

Y axis [m]

X ax

is [m

]

[dB]1 2 3−1.5

−1

−0.5

0

0.5

1

1.5

0

5

10

15

20

25

30

35

40

Y axis [m]X

axis

[m]

[dB]1 2 3−1.5

−1

−0.5

0

0.5

1

1.5

0

5

10

15

20

25

30

35

40

Y axis [m]

X ax

is [m

]

[dB]1 2 3−1.5

−1

−0.5

0

0.5

1

1.5

0

5

10

15

20

25

30

35

40

Y axis [m]

X ax

is [m

]

[dB]1 2 3−1.5

−1

−0.5

0

0.5

1

1.5

0

5

10

15

20

25

30

35

40

EDM (500 Hz) EDM (2 kHz) EDM (5 kHz)

Proposed (500 Hz) Proposed (2 kHz) Proposed (5 kHz)

PSPL(x)

Y axis [m]X

axis

[m]

[dB]1 2 3−1.5

−1

−0.5

0

0.5

1

1.5

0

5

10

15

20

25

30

35

40

Simulation results : BDR

10

0 1 2 3 4 510

15

20

25

30

35

Spatial Nyquist Frequency

Temporal Frequency [kHz]

Spat

io−t

empo

ral−

aver

aged

SPL

[dB]

EDMProposed

BDR(!) = 10log10

Pxb

��� ˆP (xb,!)���2

Pxd

��� ˆP (xd,!)���2

11

DEMO 1implemented by PureData

12

DEMO 2implemented by actual linear array of

loudspeakers

Acoustically bright zone or multi-zones generation using loudspeakersAnalytically derived stable filtersNo iterative calculationImplemented by using an actual linear array of 64 loudspeakers

Concluding remarks

14

AcknowledgementThis study is partly supported by Grant-in-Aid for Young Scientists B(No. 25871208) from JSPS

15

Grazie mille!!