Generation of multiple sound zones by spatial filtering in ... · Numerical calculation of the...
Transcript of Generation of multiple sound zones by spatial filtering in ... · Numerical calculation of the...
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!!