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[Internoise 2023 (invited)] Multilingual sound spot synthesis systems

[Internoise 2023 (invited)] Multilingual sound spot synthesis systems

Internoise 2023
21 Aug. 2023@Makuhari Messe
03.2 Spatil Capture & Reproduction
1-5-9 (invited) 14:20-14:40

Takuma OKAMOTO

August 21, 2023
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  1. Multilingual sound spot synthesis systems
    1
    Takuma OKAMOTO

    National Institute of Information and Communications Technology, Japan
    ˏMakuhari Messe
    03.2 Spatil Capture & Reproduction

    1-5-9 (invited)

    View full-size slide

  2. Multiple sound spot synthesis technology

    Technology introduction video

    Implementations of multiple sound spot synthesis systems

    Combined with real-time multilingual speech translation system

    Demo with implemented systems

    Conclusion

    Acknowledgements
    Outline
    2

    View full-size slide

  3. 3
    Mode-matching-based sound
    fi
    eld control
    Localized sound zone control

    Sound
    fi
    eld recording and synthesis
    z = 0 [m]
    [dB]
    1.5 2 2.5
    y [m]
    -2
    -1.5
    -1
    -0.5
    0
    0.5
    1
    1.5
    2
    x [m]
    -30
    -25
    -20
    -15
    -10
    -5
    0
    [dB]
    z = 0 [m]
    X axis [m]
    -1 0 1
    Y axis [m]
    -1.5
    -1
    -0.5
    0
    0.5
    1
    1.5
    -40
    -30
    -20
    -10
    0
    Y axis [m]
    X axis [m]
    z = 0 [m]
    [dB]
    −2 −1 0 1 2
    −2
    −1.5
    −1
    −0.5
    0
    0.5
    1
    1.5
    2
    −40
    −35
    −30
    −25
    −20
    −15
    −10
    −5
    0
    z = 0 [m]
    [dB]
    -1 0 1 2 3 4
    y [m]
    -2
    -1
    0
    1
    2
    x [m]
    -40
    -35
    -30
    -25
    -20
    -15
    -10
    -5
    0
    ICASSP 2014

    JASA 2017
    ICASSP 2015

    JIHMSP 2017
    WASPAA 2015 JIHMSP 2017 IWAENC 2018 WASPAA 2019

    ICASSP 2021
    Quiet zone
    Listening
    zone
    rq
    rq
    rb
    r1
    r2
    ro
    ri
    ICASSP 2017
    Reproduced sound field and reproduction error
    Sound field represented by angular spectrum coefficients
    Sound field recorded by linear receiver (Spatial Fourier transform)
    2.5D HOA for circular secondary sources (J. Ahrens et al. 2008.)

    Analytical driving function of 2.5D synthesis
    Analytical approaches to sound field recording and reproduction
    Analytical conversion of sound field representation
    Analytical driving function of 2.5D synthesis for circular secondary sources

    Sound field recorded by linear microphone arrays can be reproduced by
    circular loudspeaker arrays
    2.5D higher-order Ambisonics
    for a sound field described by angular spectrum coefficients
    Takuma OKAMOTO, National Institute of Information and Communication Technology, Japan
    1. Introduction
    2. Analytical conversion of sound field representation
    3. Proposed formulation
    4. Computer simulations
    Reproduction error
    Sound field
    Lmic = Lsp = 64 ch, x = 0.05 m, r0 = 2.0 m, xs = [1, 5, 0]T
    ˜
    P( k, !) = ˜
    P(kx, !) =
    Z 1
    1
    P(x, 0, !)ejkxxdx =
    Z 1
    1
    P(x, 0, !)ejk cos( k)xdx
    ˚
    D2.5D,m(r0, !) =
    ( j)|m| 1
    ⇡r0h(2)
    |m|
    (kr0)
    Z ⇡
    0
    ˜
    P( k, !) sin( k)e jm k d k
    ˚
    D2.5D,m(r = 0, r0, !) =
    1
    2⇡r0
    ·
    ˇ
    Pm
    |m|
    (!)
    jkh(2)
    |m|
    (kr0)Y m
    |m|
    (⇡/2, 0)⇤
    ˇ
    Pm
    |m|
    (rs, !) = jkh(2)
    |m|
    (krs)Y m
    |m|
    (✓s, s)⇤
    ˇ
    Pm
    |m|
    ( k, !) = 4⇡( j)|m|Y m
    |m|
    (⇡/2, k)⇤
    Plane wave :
    Point source :
    Z k p
    Higher order Ambisonics (HOA)
    Recording stage Reproduction stage
    Spectrum division method (SDM)
    Angular spectrum
    Spherical harmonics expansion
    Flexible sound field recording and reproduction
    J. Ahrens et al. 2012.
    WFS for SHE
    Proposed approach
    Integrated with
    from to
    k = 0 ⇡
    (k/2⇡) ˜
    P( k, !) sin( k)
    ICASSP 2016
    (a) (c) (d)
    (b)
    ˇ
    Sm
    n
    Data-based synthesis
    Model-based synthesis
    ˜
    Sm(kx) ˜
    S(R, , kx)
    D(x0)
    R
    y0
    x x x
    y y y
    z z z
    Appropriate rotation
    ˜
    S(ysyn, 0, kx)
    ysyn
    WASPAA 2017 Appl. Sci. 2018
    A0
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    A 1
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
    A1
    1
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    AAACbHichVG7SgNBFD1Z3/EVH4UQBDEkWMmsCAariI2lr5hIjGF3HXXIvtidBGLwB2wtLNRCQUT8DBt/wMJPEMFGwcbCm82CaFDvMDNnztxz58yM7prCl4w9RpS29o7Oru6eaG9f/8BgbGh4w3cqnsGzhmM6Xl7XfG4Km2elkCbPux7XLN3kOb282NjPVbnnC8delzWXFy1tzxa7wtAkUZsLpbp6uE29FEuwaRbERCtQQ5BAGMtO7Bpb2IEDAxVY4LAhCZvQ4FMrQAWDS1wRdeI8QiLY5zhElLQVyuKUoRFbpnGPVoWQtWndqOkHaoNOMal7pJxAkj2wG/bK7tkte2Ifv9aqBzUaXmo0600td0uDR2Nr7/+qLJol9r9Uf3qW2EU68CrIuxswjVsYTX314OR1bX41WU+xS/ZM/i/YI7ujG9jVN+Nqha+eIkofoP587lawMTOtEl6ZTWTS4Vd0I45JTNF7zyGDJSwjS+daOMYZziMvyqgSV8abqUok1IzgWyipT9uajRY=
    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
    A 2
    2
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
    A0
    2
    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
    A2
    2
    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
    A 3
    3
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    A1
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    A3
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    ···
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    ···
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    sha1_base64="LkI1ID8vpBUegAiZ3D3P4NOAYks=">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
    · · ·
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
    · · ·
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    · · ·
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    (a) recording S(r, /2, )
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
    (c) 2.5D synthesis with D(r0)
    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
    AAACvXichVHLbtNAFL11eZTwaCgbJDYWaVG6icZVEYgNleiCZR+kjRRHkT25TUYdz1ieSdJg+Qf4ARasQEII8Q9s2PADLLrvpqrKpkhsWHDtWEJQAdfyzLln7rlzZiaMpTCWscMZZ/bCxUuX565Url67fmO+enNhx+hhwrHJtdRJKwwMSqGwaYWV2IoTDKJQ4m64/yRf3x1hYoRWz+wkxk4U9JXYEzywRHWrLV/hmOsoClQv9UORtb1O6kehPqBMy14U2IG7WPMWs6ziWzywaZ0vuyuN++uumSg7QCOMOxZUlK3X8wZuknVTli13qzXWYEW454FXghqUsaGr78CHHmjgMIQIEBRYwhICMPS1wQMGMXEdSIlLCIliHSGDCmmHVIVUERC7T2OfsnbJKsrznqZQc9pF0p+Q0oUl9oW9Z2fsM/vAjtmPv/ZKix65lwnN4VSLcXf+xe3t7/9VRTRbGPxS/dOzhT14WHgV5D0umPwUfKofPX95tv1oaym9x96wE/L/mh2yT3QCNfrG327i1iuo0AN4f173ebCz0vAIb67W1lbLp5iDO3AX6nTfD2ANnsIGNGnfj3AEp/DVeeygIx01LXVmSs0t+C2c8U/19Kuf
    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
    Estimation
    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
    AAACbXichVHLSgMxFD0d3/VVFUFQpFiqriRTBMWVIIJL21oVaykzY9TQeTGTFrT4A64FF6KgICJ+hht/wEU/QVy4UHDjwtvpgGhRb0hycnLPzUmiu6bwJWO1iNLS2tbe0dkV7e7p7euPDQyu+07ZM3jOcEzH29Q1n5vC5jkppMk3XY9rlm7yDb20VN/fqHDPF469Jg9cXrC0PVvsCkOTRG0t+1JYASzGEmyGBRFvBmoIEghj1YndYBs7cGCgDAscNiRhExp8anmoYHCJK6BKnEdIBPscR4iStkxZnDI0Yks07tEqH7I2res1/UBt0CkmdY+UcSTZI7tlr+yB3bEn9vFrrWpQo+7lgGa9oeVusf94JPv+r8qiWWL/S/WnZ4ldzAdeBXl3A6Z+C6OhrxyevmYXMsnqJLtiz+T/ktXYPd3ArrwZ12meOUOUPkD9+dzNYD01oxJOpxKLs+FXdGIUE5im957DIlawihyda+ME57iIvCjDypgy3khVIqFmCN9CmfoEnpCN5w==
    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
    Conversion
    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
    (b) Am
    n
    for n + |m| even
    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
    ···
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    · · ·
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    · · ·
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
    ˇ
    A0
    0
    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
    ˇ
    A 1
    1
    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
    ˇ
    A1
    1
    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
    AAACdnichVHLSsNAFD2N7/qquhEEKZaqK7kRQXFVceNSq1XBR0nGUUPTJCRppYb+gD/gQlwoaBE/w40/4MJPEJcVdOHC2zQgKuodZubMmXvunJnRHdPwfKLHmNLS2tbe0dkV7+7p7etPDAyue3bJFTInbNN2N3XNk6ZhyZxv+KbcdFypFXVTbuiFxcb+Rlm6nmFba37FkTtF7cAy9g2h+UzlEwPb4lCKQrBQzQdqdZd7PpGiKQoj+ROoEUghimU7UcM29mBDoIQiJCz4jE1o8LhtQQXBYW4HAXMuIyPcl6giztoSZ0nO0Jgt8HjAq62ItXjdqOmFasGnmNxdViaRpge6oTrd0y090fuvtYKwRsNLhWe9qZVOvv9kePX1X1WRZx+Hn6o/PfvYx1zo1WDvTsg0biGa+vLxaX11PpsOxumSntn/BT3SHd/AKr+IqxWZPUOcP0D9/tw/wfr0lMp4ZSaVmYu+ohMjGMMkv/csMljCMnJ87hHOcY1a7E0ZVdLKRDNViUWaIXwJhT4AW2KQ6Q==
    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
    ˇ
    A0
    2
    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
    ˇ
    A 2
    2
    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
    AAACd3ichVHLSsNAFD2N7/qqdSO4UCwtbiyTIiiuKm5c1taqoLUk41hD0yQkabGG/oA/4EIQFKSKn+HGH3DRTxCXCiK48DYNiBb1DjNz5sw9d87MqJauOS5jrZDU09vXPzA4FB4eGR0bj0xEtxyzanOR56Zu2juq4ghdM0Te1Vxd7Fi2UCqqLrbV8lp7f7smbEczjU23bolCRSkZ2qHGFZeoYiS6x48EL3urjaKXaux7C6lGMRJjSebHbDeQAxBDEBkz0sQeDmCCo4oKBAy4hHUocKjtQgaDRVwBHnE2Ic3fF2ggTNoqZQnKUIgt01ii1W7AGrRu13R8NadTdOo2KWcRZ4/slr2wB3bHntjHr7U8v0bbS51mtaMVVnH8dCr39q+qQrOLoy/Vn55dHGLZ96qRd8tn2rfgHX3t5Owlt5KNewl2xZ7J/yVrsXu6gVF75dcbInuOMH2A/PO5u8FWKikT3liMpZeDrxjENOYwT++9hDTWkUGezj3GBZq4Cb1LM1JCmu+kSqFAM4lvIcmf5VaRIg==
    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
    ˇ
    A2
    2
    AAACdnichVHLSsNAFD2N7/po1Y0giFiqrsqNCIorxY1LX1XBR0nGaRuaJiFJKxr6A/6AC3GhoCJ+hht/wIWfIC4VdOHC2zQgWtQ7zMyZM/fcOTOjO6bh+USPMaWlta29o7Mr3t3T25dI9g9seHbFFTIrbNN2t3TNk6Zhyaxv+KbcclyplXVTbuqlxfr+ZlW6nmFb6/6hI3fLWsEy8obQfKZyyf4dUZSiFCzUcsFUbY97LpmiDIUx2gzUCKQQxbKdvMYO9mFDoIIyJCz4jE1o8LhtQwXBYW4XAXMuIyPcl6ghztoKZ0nO0Jgt8Vjg1XbEWryu1/RCteBTTO4uK0eRpge6oRe6p1t6oo9fawVhjbqXQ571hlY6ucTx0Nrbv6oyzz6KX6o/PfvIYzb0arB3J2TqtxANffXo5GVtbjUdjNMFPbP/c3qkO76BVX0Vlyty9RRx/gD153M3g42pjMp4ZTo1Pxt9RSeGMYZJfu8ZzGMJy8jyuQc4wxWuY+/KiJJWJhqpSizSDOJbKPQJX2iQ6w==
    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
    ˇ
    A 3
    3
    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
    ˇ
    A 1
    3
    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
    AAACd3ichVHLSsNAFD2N7/porRvBhWJp6cYyUcHiSnHjsj6qgo+SjNM2NE1CkhZr6A/4Ay4EQUGq+Blu/AEXfoK4VBDBhbdpQLSod5iZM2fuuXNmRrV0zXEZewxJXd09vX39A+HBoeGRSHQ0tuWYVZuLHDd1095RFUfomiFyrubqYseyhVJRdbGtllda+9s1YTuaaWy6dUvsV5SioRU0rrhE5aOxPV4SvOwtN/LeXOPAm5Eb+WicpZkfU51ADkAcQWTNaBN7OIQJjioqEDDgEtahwKG2CxkMFnH78IizCWn+vkADYdJWKUtQhkJsmcYirXYD1qB1q6bjqzmdolO3STmFBHtgN+yF3bNb9sQ+fq3l+TVaXuo0q22tsPKRk/GNt39VFZpdlL5Uf3p2UUDG96qRd8tnWrfgbX3t+PRlY3E94SXZJXsm/xfskd3RDYzaK79aE+tnCNMHyD+fuxNszaZlwmvz8aVM8BX9mMA0UvTeC1jCKrLI0blHOEcT16F3aVJKSql2qhQKNGP4FpL8CeVbkSI=
    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
    ˇ
    A1
    3
    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
    AAACdnichVHLSsNAFD2N7/qquhEEEUvVldyooLhS3Lj01SpoLck41tA0CUla0dAf8AdciAsFFfEz3PgDLvwEcVlBFy68TQOiRb3DzJw5c8+dMzO6YxqeT/QUU5qaW1rb2jvinV3dPb2Jvv6MZ5dcIdPCNm13S9c8aRqWTPuGb8otx5VaUTflpl5Yqu1vlqXrGba14R85MlvU8paxbwjNZyqX6NsRB1IUgsVKLpiu7AZqJZdI0iSFMdII1AgkEcWKnbjBDvZgQ6CEIiQs+IxNaPC4bUMFwWEui4A5l5ER7ktUEGdtibMkZ2jMFnjM82o7Yi1e12p6oVrwKSZ3l5UjSNEj3VKVHuiOnunj11pBWKPm5Yhnva6VTq73ZHD97V9VkWcfB1+qPz372Mdc6NVg707I1G4h6vry8Wl1fX4tFYzRJb2w/wt6onu+gVV+FVercu0Mcf4A9edzN4LM1KTKeHUmuTAXfUU7hjCKCX7vWSxgGStI87mHOMc1bmLvyrCSUsbrqUos0gzgWyj0CV9skOs=
    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
    ˇ
    A3
    3
    AAACdnichVHLSsNAFD2Nr1ofrboRBCmWqiu5VUFxpbhx6asq+CjJOLahaRKStFJDf8AfcCEuFFTEz3DjD7joJ4hLBV248DYNiIp6h5k5c+aeO2dmNNvQXY+oHlFaWtvaO6Kdsa7unt54oq9/w7XKjpBZYRmWs6WprjR0U2Y93TPklu1ItaQZclMrLjb2NyvScXXLXPeqttwtqXlTP9CF6jGVS/TtiIIURX+hlvOnanvcc4kUTVAQyZ8gE4IUwli2EtfYwT4sCJRRgoQJj7EBFS63bWRAsJnbhc+cw0gP9iVqiLG2zFmSM1RmizzmebUdsiavGzXdQC34FIO7w8ok0vRAN/RM93RLj/T+ay0/qNHwUuVZa2qlnYsfD669/qsq8eyh8Kn607OHA8wGXnX2bgdM4xaiqa8cnTyvza2m/VG6oCf2f051uuMbmJUXcbkiV08R4w/IfH/un2BjciLDeGU6NT8bfkUUQxjBOL/3DOaxhGVk+dxDnOEK15E3ZVhJK2PNVCUSagbwJRT6AGNukO0=
    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
    ICASSP 2019
    WASPAA 2021
    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
    Zone 1
    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
    Zone Q
    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
    Zone q
    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
    R
    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
    ri
    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
    re
    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
    Cylindrical
    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
    ba✏e
    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
    Global
    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
    region of interest
    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
    Rl
    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
    Rq
    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
    Rl
    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
    Rl
    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
    Interior Ambisonics 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
    Exterior Ambisonics

    View full-size slide

  4. Interior sound
    fi
    eld reproduction
    4QIFSJDBMBSSBZˏ5PIPLV6OJW Surrounding arrays@Tohoku Univ
    4VSSPVOEJOHBSSBZ!5PIPLV6OJW 4QIFSJDBMBSSBZ!/*$5
    -JOFBSBSSBZTˏ/*$5 -JOFBSBSSBZTˏ/*$5
    Loudspeaker systems cannot be typically carried out 4
    Exterior sound
    fi
    eld reproduction
    Previous implemented systems
    Linear sound
    fi
    eld reproduction

    View full-size slide

  5. 4QIFSJDBMBSSBZˏ5PIPLV6OJW Surrounding arrays@Tohoku Univ
    4VSSPVOEJOHBSSBZ!5PIPLV6OJW
    5
    Previous implemented systems
    Developed with co-chairs of this session

    Dr. Sakamoto and Dr. Trevino

    @Tohoku Univ.

    View full-size slide

  6. Principle

    Sound pressure for audible area: 1, that for inaudible area: 0 -> Spatial rectangular window

    Fourier transform of rectangular window -> analytically derived as Sinc function

    Properties

    Considering wave equation

    Stable driving signals by omitting evanescent components
    6
    Mode-matching-based localized sound
    fi
    eld control
    y
    x
    z
    r0
    rref
    Φ
    φs
    P(rref , φ, 0, ω) = 1
    P(rref , φ, 0, ω) = 0
    Bright zone Circular loudspeaker array
    Reference circle
    Dark Zone
    x
    Linear sound source
    lb
    xb
    Bright
    Dark
    shift
    Dark
    Window function
    y
    y = yb
    P(x, yb) = 0
    T. Okamoto et al. J. Accost. Am. 2017

    T. Okamoto WASPAA 2015

    View full-size slide

  7. Using a linear array of 64 loudspeakers

    Outperforms conventional methods
    7
    Experimental results using linear array
    DS CM LS SFT (rect.) SFT (Hann)
    z = 0 [m]
    [dB]
    1.5 2 2.5
    y [m]
    -2
    -1.5
    -1
    -0.5
    0
    0.5
    1
    1.5
    2
    x [m]
    -30
    -25
    -20
    -15
    -10
    -5
    0
    z = 0 [m]
    [dB]
    1.5 2 2.5
    y [m]
    -2
    -1.5
    -1
    -0.5
    0
    0.5
    1
    1.5
    2
    x [m]
    -30
    -25
    -20
    -15
    -10
    -5
    0
    z = 0 [m]
    [dB]
    1.5 2 2.5
    y [m]
    -2
    -1.5
    -1
    -0.5
    0
    0.5
    1
    1.5
    2
    x [m]
    -30
    -25
    -20
    -15
    -10
    -5
    0
    z = 0 [m]
    [dB]
    1.5 2 2.5
    y [m]
    -2
    -1.5
    -1
    -0.5
    0
    0.5
    1
    1.5
    2
    x [m]
    -30
    -25
    -20
    -15
    -10
    -5
    0
    z = 0 [m]
    [dB]
    1.5 2 2.5
    y [m]
    -2
    -1.5
    -1
    -0.5
    0
    0.5
    1
    1.5
    2
    x [m]
    -30
    -25
    -20
    -15
    -10
    -5
    0
    0 1 2 3 4 5
    Temporal frequency [kHz]
    0
    5
    10
    15
    20
    25
    30
    35
    40
    Bright to dark ratio [dB]
    DS CM LS SFT (rect.) SFT (Hann)
    T. Okamoto et al. J. Accost. Am. 2017

    View full-size slide

  8. Using a circular array of 32 loudspeakers

    Outperforms conventional methods
    8
    0 1 2 3 4 5
    Temporal Frequency [kHz]
    0
    5
    10
    15
    20
    25
    BDR [dB]
    Spatial Nyquist Frequency
    LS method (open)
    LS method (baffled)
    Beamforming (open)
    Beamforming (baffled)
    Proposed (open)
    Proposed (baffled)
    z = 0 [m]
    [dB]
    -1 0 1
    X axis [m]
    -1.5
    -1
    -0.5
    0
    0.5
    1
    1.5
    Y axis [m]
    -40
    -30
    -20
    -10
    0
    z = 0 [m]
    [dB]
    -1 0 1
    X axis [m]
    -1.5
    -1
    -0.5
    0
    0.5
    1
    1.5
    Y axis [m]
    -40
    -30
    -20
    -10
    0
    z = 0 [m]
    [dB]
    -1 0 1
    X axis [m]
    -1.5
    -1
    -0.5
    0
    0.5
    1
    1.5
    Y axis [m]
    -40
    -30
    -20
    -10
    0
    Pressure matching

    (LS)
    Beamforming Proposed
    Results for 3000 Hz
    Simulation results using circular array
    T. Okamoto WASPAA 2015

    View full-size slide

  9. Multiple sound spot synthesis system with a linear array of 64
    loudspeakers
    Previous implemented system
    9
    ͜Μʹͪ͸
    )FMMP
    㟬޷
    Japanese
    area
    (null)
    (null)
    (null)
    (null)
    English
    area
    (null)
    (null)
    (null)
    (null)
    Chinese
    area
    (null)
    (null)
    (null)
    (null)
    Dark zone
    (Quiet area)
    (null)
    (null)
    (null)
    (null)
    Իͷฉ͑͜ͳ͍
    ΤϦΞ
    ॏͶ߹Θͤ
    3.2 m
    Making as small as possible for actual implementations
    We would like to promote sound
    fi
    eld control technology
    T. Okamoto ICASSP 2014

    View full-size slide

  10. Technology introduction video using neural text-to-speech

    https://youtu.be/In8AfVcoTC4
    10
    Technology introduction video

    View full-size slide

  11. 1SPUPUZQJOHBDPNQBDUDJSDVMBSBSSBZ
    "TTNBMMBTQPTTJCMFXJUIBEJBNFUFSPGNN
    1PSUBCMFEFNPTZTUFNXJUIBTJOHMFTVJUDBTF
    $POUSPMMBCMFXJUIBUBCMF
    Implementation of a compact array
    12
    13.44 cm
    2.5 cm
    3.1 cm
    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
    13.44 cm
    Ampli
    fi
    er

    (Including RME Digiface USB)

    View full-size slide

  12. Demo system presentations
    Results with NICT collaborators

    2022.6: Prototyping a small circular array

    2022.10: Technology introduction HP and video release

    Conferences

    2022.9: ASJ@Hokkaido University of Science -> Demo in oral session

    2023.3: SPEASIP invited talk@Okinawa -> Demo in oral session

    2023.3: ASJ@Online -> Demo in online session

    2023.6: ICASSP 2023@Rhodes, Greece -> Show & Tell Demo session

    Demonstrations

    2022.10: Keihanna R&D Fair@ATR & Kyoto Smartcity Expo@KICK

    2023.12: Demonstration experiment@Miraikan

    From 2023.4: Permanent demo system@NICT Central, Tokyo

    2023.4: The G7 Digital and Tech Ministers’ Meeting@Takasaki

    2023.6: Combined with real-time multilingual speech translation@NICT Openhouse
    13

    View full-size slide

  13. Linear array with small drivers for circular array

    About 1.7 m
    14
    Linear array of 64 loudspeakers

    View full-size slide

  14. 10 to 18 December 2022

    Circular array of 16 loudspeakers@Geo-Cosmos

    Linear array of 64 loudspeakers@Nobel Q
    15
    Demonstration experiment@Miraikan

    View full-size slide

  15. 16
    Circular array system@Geo-Cosmos

    View full-size slide

  16. 17
    Linear array system@Nobel Q

    View full-size slide

  17. Weekdays: 9:30-17:00
    18
    Permanent demo system@NICT Central, Tokyo

    View full-size slide

  18. 19
    DemoˏG7 Gunma, Apr. 2023

    View full-size slide

  19. T. Okamoto, K. Ueno, T. Okabe, K. Tani, Y. Yoshikata, M. Sudo, M.
    Kuwahara, and K. Hikita, 

    "Portable multilingual sound spot synthesis system with a compact
    circular array of 16 loudspeakers,"

    ICASSP 2023 Show & Tell Demo Session, June 2023.
    20
    ICASSP 2023 Show & Tell Demo

    View full-size slide

  20. 21
    DemoˏICASSP 2023, Rhodes, Greece

    View full-size slide

  21. Improving sound quality and output power
    22
    Development of new loudspeaker array
    134.4 mm
    Previous

    - Too small

    - Low sound quality

    - Low output power
    Improved

    - Still portable

    - High sound quality

    - High output power
    184 mm

    View full-size slide

  22. 23
    /*$5openhouse +VOF
    Combined with real-time multilingual speech translation system
    Machine
    transration
    Speech
    synthesis
    Multiple
    sound spot
    synthesis .
    .
    .
    Language identification
    &
    Speech recognition
    Machine Speech
    synthesis
    Multiple
    sound spot
    synthesis .
    .
    .
    Text input
    (b) as user interface for real-time speech translation
    translation
    (a) with text input

    View full-size slide

  23. Real-time speech translation with

    multiple sound spot synthesis
    24
    Explanation of demo system
    +BQBOFTFTQFBLFSVUUFST
    English

    speaker
    Chinese

    speaker



    ༻͍ͨΤϦΞ࠶ੜ

    2.

    Automatic

    speech recognition



    Machine translation



    Speech synthesis

    Sequentially
    ఏҊ๏Λ༻͍ͨΤϦΞ࠶ੜ

    $POpEFOUJBM
    Korean

    speaker
    &BDIUSBOTMBUFETZOUIFUJDWPJDFJT
    TZOUIFTJ[FEGPSFBDIMBOHVBHFBSFB
    CZNVMUJQMFTPVOETQPUTZOUIFTJT
    উ֞ೞࣁਃ
    㟬޷
    Only Korean audible area
    Only Chinese audible area
    Only

    English

    audible

    area
    ͜Μʹͪ͸
    Japanese

    speaker
    )FMMP

    View full-size slide

  24. Multiple sound spot synthesis with an improved array of 16 loudspeakers

    Four-language (English, Japanese, Chinese, and Korean) for four-spot synthesis

    Two types of music sounds for two spot synthesis
    26
    Today’s demo@Makuhari Messe

    View full-size slide

  25. 27
    Implementation is really all we need
    Conclusion

    View full-size slide

  26. Demos for multiple sound spot synthesis

    2023.10.6-7: Keihanna R&D Fair 2023@Keihanna plaza

    2023.10.8-12: Internet Governance Forum 2023@Kyoto International Conference Center

    2023.10.17-20: CEATEC 2023@Makuhari Messe

    2023:10.22-25: WASPAA 2023 Demonstrations@Mohonk Mountain House, New Paltz, NY,
    USA

    T. Okamoto, K. Ueno, T. Okabe, K. Tani, Y. Yoshikata, M. Sudo, M. Kuwahara, and K.
    Hikita, “Improving portable multiple sound spot synthesis system with a ba
    ff
    l
    ed circular
    array of 16 loudspeakers”

    Voice conversion

    2023.8.22 13:30-15:30: Interspeech 2023ˏDublin, Ireland

    T. Okamoto, T. Toda and H. Kawai, “E2E-S2S-VC: End-to-end sequence-to-sequence
    voice conversion”

    -> I must move to Haneda airport quickly after the session for presenting my poster at
    Dublin tomorrow 28
    Next presentations

    View full-size slide

  27. Funding

    This research was partly supported by JSPS KAKENHI Grant Numbers JP18K11387 and
    JP23K11177, and JST A-STEP Tryout Grant Number JPMJTM22D8

    External collaboration

    The development of the prototypes of the compact circular array of 16 loudspeakers and
    linear array of 64 loudspeakers was supported by JST Program Manager (PM) Development
    and Promotion Program (PI: Keita Hikita), and were developed in collaboration with
    Kitanihon Onkyo Co. Ltd

    The demonstration test of multiple sound spot synthesis systems using the compact
    circular array and linear array was conducted at Miraikan in Tokyo, Japan

    Internal collaboration

    we would like to thank Keita Hikita, Miyuki Sudo, and Manae Kuwahara for their support of
    NICT Innovation Design Initiative (IDI), Project of Co-Creation Design (PoCC) for the social
    deployment of multiple sound spot synthesis technology
    29
    Acknowledgements

    View full-size slide

  28. Thank you for your !!
    Takuma OKAMOTOˏNICT

    e-mail:


    HP: https://www.okamotocamera.com


    Twitter: @okamotocamerea
    30

    View full-size slide

  29. 2.5D Mode-matching-based method

    Sound pressure for audible area: 1, that for inaudible area: 0

    ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹT. Okamoto, WASPAA 2015

    For actual implemented circular array

    Measuring transfer function

    Driving signal:

    Filter:
    31
    Deriving driving signals of loudspeakers
    y
    x
    z
    r0
    rref
    Φ
    φs
    P(rref , φ, 0, ω) = 1
    P(rref , φ, 0, ω) = 0
    Bright zone Circular loudspeaker array
    Reference circle
    Dark Zone
    AAADSHichVFNa9RAGH6T+lHjR1e9CF6C20oLdZmUUkUoFL3Ug9APty1stiGZne2OzUzSSXbtOswf8A948KQgIv4ML+LdQ8+exItQoQgefJNd/Kq275CZ93nmfZ68MxOlMc9yQvYse+TEyVOnR884Z8+dvzBWuXhpLUu6irI6TeJEbURhxmIuWT3necw2UsVCEcVsPdq+W+yv95jKeCIf5P2UNUW4JXmb0zBHKqh89CV7RBMhQtnSfsRNw2tqX0TJLqIkbokw77jjVW/cGIcGWk7HZlIFWIG8ElqxtjFT835bhVR7Rs/4KTc+l3mgidkcwMVA/0M07fhph0+xTX3joSxS0ypm18+4YDvuT8f7BqmuCLSY99AR4VF+WGZ+8yygcYNKldRIGe7hxBsmVRjGUlJ5BT60IAEKXRDAQEKOeQwhZDga4AGBFLkmaOQUZrzcZ2DAQW0XqxhWhMhu47yFqDFkJeLCMyvVFP8S46dQ6cIE+UBek33yjrwhn8j3/3rp0qPopY9rNNCyNBh7cmX14FiVwDWHzi/VkT3n0IZbZa8ce09LpjgFHeh7j5/ur95emdDXyQvyGft/TvbIWzyB7H2lL5fZyjNw8AG8v6/7cLI2U/PmarPLs9WFO8OnGIWrcA0m8b5vwgIswhLUgVr3rMTatfr2e/uLfWB/G5Ta1lBzGf6IEfsHGaHjmg==
    cn,l(rref ) =
    1
    2⇡
    Z 2⇡
    0
    Hl(rref , )e
    jn
    d '
    1
    M
    M
    X
    m=1
    Hl(rref , m)e
    jn m
    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
    Hl(rref , m)
    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
    ˆ
    d = C(r
    ref
    )HC(r
    ref
    ) + I 1 C(r
    ref
    )Ha(r
    ref
    )
    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
    C(rref ) =
    2
    6
    4
    c N,1(rref ) · · · c N,L(rref )
    .
    .
    .
    ...
    .
    .
    .
    cN,1(rref ) . . . cN,L(rref )
    3
    7
    5
    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
    an,rect( , S) = sinc

    n
    2⇡

    e jn s
    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
    an,hann( , S) =

    sinc

    1
    2
    +
    n
    2⇡

    + sinc

    1
    2
    n
    2⇡

    2
    e jn s
    Rectangular window
    Hann window

    View full-size slide

  30. 32
    Results
    (a) 750 Hz (b) 1.5 kHz (c) 3 kHz
    (d) 4.5 kHz (e) 6 kHz (f) 7.5 kHz

    View full-size slide