@ Florence, Italy, 8th May 2014.

Generation of multiple sound zones
by spatial filtering in wavenumber domainusing a linear array of loudspeakers

Takuma OKAMOTO
National Institute of Information Communications and Technology (NICT), Japan1

Presentation contents
Introduction
Acoustically bright zone or multi-zones generation using loudspeakers

PurposeConventional methods and their problems
Novel approach

Proposed method
Basic theory : Spectral division method (SDM)
Analytically-derived spatial filters in wavenumber domain
Computer simulations
Demonstrations

Concluding remarks2Introduction
Generation of acoustically bright and dark zones using anarray of loudspeakers
S2 (ω)F2 (x0 , ω)(a) generating bright and dark zones

Bright zone..
.

(b) multiple spots generation

S2 (ω)
Dark zone+Applications
S1 (ω)F1 (x0 , ω)
Personal audio system
Dark zone
Multiple-language guide system..
Virtual reality applications.

D(x0 , ω)Sound zone..
.

S2 (ω)
Sound zone

S1 (ω)(b)

Bright zone

without headphone

S1 (ω)(a)3

Previous methods and their problems
Most methods based on multiple points control

G(!)
..
.

..
.

..
.

..
.

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

Principle
Numerical calculation of the inverseof the spatial correlation matrix
Problems
Quite unstable
Iterative calculation for deciding
regularization parameter

Energy difference maximization (EDM)(M. Shin et al. in JASA, 2010.)
Principle
Numerical calculation of the eigenvectorof the spatial correlation matrix
Problem
Iterative calculation for deciding tuning factor

4

Novel approach
Problems of conventional methods

S2 (ω)F2 (x0 , ω)

Unstable
Iterative calculation

Bright zone..
.

S2 (ω)
Dark zone

3 characteristics of proposed method+Analytically derived stable filters
S1 (ω)F1 (x0 , ω)No iterative calculation
Dark zone
Implemented by using actual 64 loudspeakers..
.

NomenclatureD(x0 , ω)Sound zone..
.

S2 (ω)
Sound zone

S1 (ω)(b)

Bright zone

S1 (ω)

Sound source signal : S(!)
Driving signals of loudspeakers(a) Generating bright and dark zone
D(x0 , !) = S1 (!)F1 (x0 , !)(b) Generating multiple sound zones
MX
D(x0 , !) =Si (!)Fi (x0 , !)i=1(a)How to calculate?
5Basic theory
Spectral division method (SDM)(J. Ahrens et al. in IEEE ASLP., 2010.)

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
Z 1
P (x, !) =D(x0 , !)G3D (x x0 , !)dx0

Secondary source D(x, 0, ω)

x1

Spatial Fourier transform along with x-axisP̃ (kx , y, !) = D̃(kx , !) · G̃(kx , y, !)yP (x, yref , ω)y = yrefDriving signals of secondary sourcesP̃ (kx , yref , !)D̃(kx , !) =G̃(kx , yref , !)

Fx

1

1
D(x, !) =2⇡

Z 1

P̃ (kx , yref , !) jkx xedkx
1 G̃(kx , yref , !)Driving signals in each wavenumber domain is completely orthogonaleach other and much stable rather than multiple points control

6

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

Secondary sourceP̃ (kx , yref , !)F̃ (kx , !) =G̃(kx , yref , !)P (x, yref , !) = 1
P (x, yref , !) = 0

P (x, yb ) = ⇧✓xlb◆=P (x, yb ) = 1
Brightfor |x|  lb /2
elsewhereDark

y = yblbxb
y1,0,P (x, yb ) = 0

Dark

Modeled by
Rectangular window⇢x

FxShiftP̃ (kx ) = lb sinc✓k x lb2⇡◆x
Shift theorem introduced to shift rectangular✓◆ window along with -axis
k x lbP̃shift (kx ) = P̃ (kx ) exp(jkx xb ) = lb sincexp(jkx xb )2⇡

Spatial filters for generating bright and dark zones
lb sinc (kx lb /2⇡) exp(jkx xb )Arbitrary length : lbF̃ (kx , !) =Arbitrary position : [xb , yb ]TG̃(kx , yb , !)7

Computer simulations

PSPL (x, !) = 10log10 P̂ (x, !)2Dark zone xd
yb = 2 m

Bright to dark ratio
PBDR(!) = 10log10 P

xb P̂ (xb , !)xd P̂ (xd , !)22

Control line
K = 64 ch (EDM)

Sound pressure level

Bright zone xb

Evaluation values

lb = 1.6 m

L = 3.2 m

N = 64 ch

Speed of sound : 343.25 m/sdistance between
adjacent loudspeakers : 0.05 m
Tuning factor for EDM : 0.9999

Loudspeakers

Simulation condition

0.4 m(for calculating (19))

8Simulation results : PSPL (x)
40

1.5

40

1.5

35

35

11020
15−0.50.5

25020
15−0.51030

X axis [m]2530X axis [m]2

Y axis [m]

3−1.5

0

1[dB]

2

Y axis [m]35−1.5

0

1[dB]

3535
130

X axis [m]15−0.50.525020
15−0.510−1−112

Y axis [m]3

Proposed (500 Hz)0[dB]

30
0.5

25020
15−0.510

10−15−1.50[dB]

40

35

3020

Y axis [m]31.5102EDM (5 kHz)
40

1.5

125

15−0.5

EDM (2 kHz)40

0.5

205EDM (500 Hz)
1.5

0−15
125

10−1−1.5

0.5

10−1X axis [m]X axis [m]30X axis [m]

35

10.5

40

1.5

5−1.5
12

Y axis [m]3

Proposed (2 kHz)

0[dB]

5−1.5
12Y axis [m]3

Proposed (5 kHz)

0[dB]

9

Spatio−temporal−averaged SPL [dB]Simulation results : BDR
3530

2520EDM
Proposed

15

Spatial Nyquist Frequency
1001234
Temporal Frequency [kHz]PBDR(!) = 10log10 P

xb P̂ (xb , !)xd P̂ (xd , !)52210

DEMO 1
implemented by PureData

11

DEMO 2
implemented by actual linear array ofloudspeakers

12Concluding remarks
Acoustically bright zone or multi-zones generation using
loudspeakers
Analytically derived stable filters
No iterative calculation
Implemented by using an actual linear array of 64 loudspeakers

14Grazie mille!!
Acknowledgement
This study is partly supported by Grant-in-Aid for Young Scientists B(No. 25871208) from JSPS

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