2025/7/5 応用音響研究会招待講演＠北海道大学

音場の局所再生およびマルチスポット再生技術の理論と実装

https://ken.ieice.org/ken/program/index.php?tgs_regid=3cb3c91e36f42a5e40c29da5382a869e2c827c708c91576ded865eb61bf845c1&tgid=IEICE-EA

Transcript

1. ࠃཱݚڀ։ൃ๏ਓɹ৘ใ௨৴ݚڀػߏ /*$5
   Ϣχόʔαϧίϛϡχέʔγϣϯݚڀॴ
   ઌਐతԻ੠຋༁ݚڀ։ൃਪਐηϯλʔ
   ઌਐతԻ੠ٕज़ݚڀࣨ
   Ԭຊ
   ୓ຏ  
   &"ݚڀձট଴ߨԋˏ๺ւಓେֶ Ի৔ͷہॴ࠶ੜ͓ΑͼϚϧνεϙοτ࠶ੜٕज़ͷ
   ཧ࿦ͱ࣮૷
2. *OUSPEVDUJPO
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3. Ԭຊ୓ຏˏ/*$5͚͍͸Μͳ
   ݚڀςʔϚɿ෺ཧɾ਺ཧϞσϧʹجͮ͘Ի৴߸ɾԻۭؒͷ૑ग़
   Իڹ৴߸ॲཧɿಛʹԻ৔ऩ࿥ɾ੍ޚ ϚΠΫϩϗϯɾεϐʔΧΞϨΠ৴߸ॲཧ
   
   ೥݄ʙ೥݄ɿ౦๺େ޻ֶ෦ػցܥ ֶ෦ݚڀɿৼಈΠϯςϯγςΟ
   
   ೥݄ʙ೥݄ɿ౦๺େֶ৘ใՊֶݚڀՊ म࢜ɾത࢜ɾϙευΫ
   
   ೥݄ʙ೥݄ɿ/*$5௒ྟ৔ײϓϩδΣΫτˏ/*$5
   
   ೥ʙݱࡏɿࣗ਎ͷՊݚඅ౳!/*$5
   Ի੠ॲཧ
   
   ೥݄ʙݱࡏɿχϡʔϥϧωοτϫʔΫΛ༻͍ͨԻ੠߹੒ɾԻ੠೾ܗੜ੒!/*$5
   झຯɿҿΈձ ೥ʙ೥͸ίϩφͷͨΊօແˠࣗ୐൩ऌঢ়ଶˠ೥෮׆ ɼδϣΪϯά
   ঺հϖʔδ
   /*$5ݚڀ৬ɾݚڀٕज़৬࠾༻αΠτɿIUUQTXXXOJDUHPKQFNQMPZNFOUSFTFBSDIFSPLBNPUPUBLVNBIUNM
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   ͚͍͸Μͳ4DJFODFQFEJBɿIUUQTLFJIBOOBMJOLKQTDJFODFQFEJBSFTFBSDIFSUBLVNBPLBNPUP *OUSPEVDUJPO
   PG
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4. 5PEBZ`T
   KPH  5P
   ࡳຈࢢ৔֎ࢢ৔঎ళ֗
5. ࠃཱݚڀ։ൃ๏ਓ৘ใ௨৴ݚڀػߏ
   ૯຿ল؅׋ͷࠃͷݚڀॴ ܦ࢈লɿ࢈૯ݚ<"*45>ɼจՊলɿࠃཱ৘ใֶݚڀॴ</**>
   খۚҪຊ෦ɿి࣓೾ɼ௨৴ɼηΩϡϦςΟɼྔࢠ*$5ɼ೔ຊඪ४࣌ੜ੒ ి೾࣌ܭɼ/51
   ͚͍͸ΜͳɿଟݴޠԻ੠຋༁ɼࣗવݴޠॲཧ ੜ੒"*
   ਆށɿະདྷ*$5
   େࡕਧాɿ೴৘ใ
   ࣛౡɿӉ஦
   ઋ୆ɿରࡂ֐*$5ˡ౦๺େֶ ग़਎େֶ ͷෑ஍಺ ˞೥݄ΑΓ݉຿ *OUSPEVDUJPO
   PG
   /*$5  খۚҪຊ෦ ͚͍͸Μͳݚڀॴ
6.  ଍ͷΘΒ͡ݚڀੜ׆೥ˠ೥͔Βͭͷ੒Ռ͕༥߹ Ԭຊ୓ຏˏ/*$5͚͍͸Μͳ
   ݚڀςʔϚɿ෺ཧɾ਺ཧϞσϧʹجͮ͘Ի৴߸ɾԻۭؒͷ૑ग़
   Իڹ৴߸ॲཧɿಛʹԻ৔ऩ࿥ɾ੍ޚ ϚΠΫϩϗϯɾεϐʔΧΞϨΠ৴߸ॲཧ
   
   ೥݄ʙ೥݄ɿ౦๺େ޻ֶ෦ػցܥ ֶ෦ݚڀɿৼಈΠϯςϯγςΟ
   
   ೥݄ʙ೥݄ɿ౦๺େֶ৘ใՊֶݚڀՊ म࢜ɾത࢜ɾϙευΫ
   
   ೥݄ʙ೥݄ɿ/*$5௒ྟ৔ײϓϩδΣΫτˏ/*$5
   
   ೥ʙݱࡏɿࣗ਎ͷՊݚඅ౳!/*$5
   Ի੠ॲཧ
   
   ೥݄ʙݱࡏɿχϡʔϥϧωοτϫʔΫΛ༻͍ͨԻ੠߹੒ɾԻ੠೾ܗੜ੒!/*$5
   झຯɿҿΈձ ೥ʙ೥͸ίϩφͷͨΊօແˠࣗ୐൩ऌঢ়ଶˠ೥෮׆ ɼδϣΪϯά
   ঺հϖʔδ
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8.  Ԭຊ୓ຏˏ/*$5͚͍͸Μͳ
   ݚڀςʔϚɿ෺ཧɾ਺ཧϞσϧʹجͮ͘Ի৴߸ɾԻۭؒͷ૑ग़
   Իڹ৴߸ॲཧɿಛʹԻ৔ऩ࿥ɾ੍ޚ ϚΠΫϩϗϯɾεϐʔΧΞϨΠ৴߸ॲཧ
   
   ೥݄ʙ೥݄ɿ౦๺େ޻ֶ෦ػցܥ ֶ෦ݚڀɿৼಈΠϯςϯγςΟ
   
   ೥݄ʙ೥݄ɿ౦๺େֶ৘ใՊֶݚڀՊ म࢜ɾത࢜ɾϙευΫ
   
   ೥݄ʙ೥݄ɿ/*$5௒ྟ৔ײϓϩδΣΫτˏ/*$5
   
   ೥ʙݱࡏɿࣗ਎ͷՊݚඅ౳!/*$5
   Ի੠ॲཧ
   
   ೥݄ʙݱࡏɿχϡʔϥϧωοτϫʔΫΛ༻͍ͨԻ੠߹੒ɾԻ੠೾ܗੜ੒!/*$5
   झຯɿҿΈձ ೥ʙ೥͸ίϩφͷͨΊօແˠࣗ୐൩ऌঢ়ଶˠ೥෮׆ ɼδϣΪϯά
   ঺հϖʔδ
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9. ԿނϚϧνεϙοτ࠶ੜͷݚڀΛ͍ͯ͠Δͷ͔
   ࠷ॳͷ͖͔͚ͬɿՃࢉܕεϙοτ࠶ੜΛര଎࣮૷ͯ͠ײܹ
   Ի৔੍ޚٕज़Ͱͳ͍ͱ࣮ݱͰ͖ͳ͍Իۭؒͷ૑ग़
   Ԡ༻ઌ͸Ի৔࠶ݱΑΓ΋ͨ͘͞Μ͋Δ
   ࣮૷
   JT
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   Ϛϧνεϙοτ࠶ੜ͸࣮ࡍʹฉ͚͹ͦͷੌ͕͞ҰൃͰ఻ΘΔ
   ٯʹݴ͑͹ฉ͔ͳ͍ͱͦͷੌ͞͸ҰੜΘ͔Βͳ͍
   ԿނখܕԽΛ໨ࢦ͢ͷ͔
   ΑΓͨ͘͞ΜͷํʹϚϧνεϙοτ࠶ੜٕज़Λମݧ͍͖͍ͨͩͨ
   Ի৔੍ޚٕज़ͷݚڀΛීٴ͍ͨ͠ 3FTFBSDI
   NPUJWBUJPO  
   DIεϐʔΧΞϨΠ
   ˏ౦๺େ ɾɾɾ ɾɾɾ ri s(t) z (D0 r1/c) z (D0 ri/c) z (D0 rN /c) ɾɾɾ ɾɾɾ n1(t) ni(t) nN (t) ɾɾɾ ɾɾɾ r1 rN rN ri r1 Target spot <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> SNR 20 dB <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> Ճࢉܕεϙοτ࠶ੜ
10. εϐʔΧΞϨΠΛ༻͍ͨہॴ࠶ੜɾϚϧνεϙοτ࠶ੜɾϚϧνԻ৔੍ޚ
    B
    ہॴ࠶ੜɿԻѹͷΈΛ੍ޚ
    ͋ΔྖҬʹͷΈ͋ΔಛఆͷԻ͕ฉ͑͜
    ଞͷ৔ॴͰ͸ฉ͑͜ͳ͍
    C
    Ϛϧνεϙοτ࠶ੜɿԻѹͷΈΛ੍ޚɼ B ͷॏͶ߹Θͤ
    ͦΕͧΕͷྖҬʹͦΕͧΕผͷԻ͕ฉ͑͜Δ
    D
    ϚϧνԻ৔੍ޚɿԻѹ͚ͩͰͳ͘೾໘ͷ޲͖΋੍ޚ  .VMUJQMF
    TPVOE
    TQPU
    TZOUIFTJT
    UFDIOPMPHZ Bright zone (Listening area) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> Dark zone (Quiet area) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> B
    ہॴ࠶ੜ ͜Μʹͪ͸ )FMMP 㟬޷ Japanese area <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> English area <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> Chinese area <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> C
    Ϛϧνεϙοτ࠶ੜ ಧ͚͍ͨਓ͚ͩʹඞཁͳԻΛಧ͚Δٕज़
    ݚڀͷϙΠϯτɿ೗ԿʹʮԻ͕ฉ͑͜ͳ͍ྖҬʯΛܗ੒͢Δ͔ D
    ϚϧνԻ৔੍ޚ
11. ϔουηοτ
    ϝϦοτɿଞ΁ͷԻ࿙Ε͕ͳ͍ɼԻ࣭͕Α͍
    σϝϦοτɿਓ਺෼Λ༻ҙ͢Δඞཁ͕͋Δɼ઀৮ܕͰ͋ΔͨΊײછରࡦతʹݒ೦͋Γ
    ௒Ի೾εϐʔΧ
    ϝϦοτɿݸਓ͝ͱͷσόΠεෆཁɼӶ͍ࢦ޲ੑɼඇ઀৮
    σϝϦοτɿԻ࣭͕՝୊ɼ௒Ի೾ྖҬͰ͸
    E#Ҏ্ͷԻѹϨϕϧ ݈߁ඃ֐΁ͷݒ೦
    εϐʔΧΞϨΠΛ༻͍ͨہॴ࠶ੜɾϚϧνεϙοτ࠶ੜ
    ϝϦοτɿݸਓ͝ͱͷσόΠεෆཁɼӶ͍ࢦ޲ੑɼඇ઀৮ɼ݈߁ඃ֐ͳ͠ɼԻ࣭͕Α͍
    ݚڀ՝୊ɿ੍ޚਫ਼౓޲্ɼখܕԽɼ࣮༻Խ  $PNQBSJTPO
    XJUI
    PUIFS
    NFUIPET ϔουηοτ΍௒Ի೾εϐʔΧʹมΘΔ
    ৽ͨͳԻ੠ఏٕࣔज़
12. Ұൠਓ޲͚આ໌ฤ 
13.  ௚ײతͳઆ໌ ˞ݫີͰ͸͋Γ·ͤΜ
14. ݚڀಈը঺հ  IUUQTXXXOJDUHPKQQVCMJDJUZOJDU@TUBUJPO
17. ֶձ޲͚આ໌ฤ 
18. εϐʔΧΞϨΠΛ༻͍ͨԻ৔੍ޚͷ୅දྫɿԻѹϚονϯά๏
    -ݸͷεϐʔΧʹΑΔԻ৔
    ੍ޚ఺ͷԻѹޡࠩΛ࠷খԽ
    ดܗղͱͯ͠ͷۦಈ৴߸
    ہॴ࠶ੜͷ৔߹  1SFTTVSFNBUDIJOH 0
    ,JSLFCZ
    FU
    BM
    +
    "DPVTU
    4PD
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     Bright zone Dark zone Ωb Ωd × × × × × × × × × × × × × × × × × × × × × × × × × × × × : Loudspeaker × : Control point <latexit sha1_base64="GwLWEo8lZ6D1dFnsNCiMQSmVeU4=">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</latexit> psyn(r) = L l=1 dl(rl)G (r|rl) = g(r)→d <latexit sha1_base64="jCoap7Tik57y8e5IeMfC6CW79iE=">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</latexit> minimize d ||Gd → pdes ||2 + ωPM ||d||2 <latexit sha1_base64="uRKzIwgaC9FrTHR/wtDri2ZJ37E=">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</latexit> dPM = GHG + ωPMI →1 GHpdes <latexit sha1_base64="s129UKw4MSVr/dS5D/oXmQylHGg=">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</latexit> pdes = [pdes(r1), · · · , pdes(rMb ) !b , 0, · · · , 0 !d ]→ .
    1PMFUUJ
    UI
    $POW
    "&4
    
19. ϑʔϦΤม׵
    ࣌ؒྖҬˠप೾਺ྖҬ
    Ի৔ͷԁ౵ௐ࿨ల։ɿԁ౵࠲ඪܥͷۭؒϑʔϦΤม׵
    ԁप্ͷۭؒԻѹ෼෍ˠೋ࣍ݩԁ౵ௐ࿨εϖΫτϧ
    Ի৔ͷ಺૷ɾ֎૷͕Մೳ
    Ի৔੍ޚํࣜ
    Իѹ௚઀੍ޚ 1SFTTVSF
    NBUDIJOH
    ੍ޚ఺ͷԻѹΛ௚઀੍ޚ ྫɿ#P4$
    Ϟʔυ੍ޚ .PEF
    NBUDIJOH
    ԁ౵ٿ໘ௐ࿨εϖΫτϧΛ੍ޚ ߴ࣍"NCJTPOJDTɿ)0" $ZMJOESJDBM
    IBSNPOJD
    FYQBOTJPO  r <latexit sha1_base64="ucx5KlNgcR3PTGw2mrN5+6hRX8c=">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</latexit> <latexit sha1_base64="ucx5KlNgcR3PTGw2mrN5+6hRX8c=">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</latexit> <latexit sha1_base64="ucx5KlNgcR3PTGw2mrN5+6hRX8c=">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</latexit> <latexit sha1_base64="ucx5KlNgcR3PTGw2mrN5+6hRX8c=">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</latexit> <latexit sha1_base64="h4zWSmDsAtveKKjQHsTlk8YLuC4=">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</latexit> F(!) = Z 1 1 f(t)ej!tdt <latexit sha1_base64="BTAar0wVsN7ezeVHyIgOcqSegK4=">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</latexit> f(t) = 1 2⇡ Z 1 1 F(!)e j!td! <latexit sha1_base64="c8pRammyZvowRnr25nJOo0ZB52Q=">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</latexit> ˚ Am = 1 2⇡Jm(kr) Z 2⇡ 0 S(r, )e jm d <latexit sha1_base64="bTnAwbfu/aFicOiZlh1y0JZsaUg=">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</latexit> S(r, ) = 1 X m= 1 ˚ AmJm(kr)ejm
20. ॏΈ෇͖Ϟʔυ੍ޚ๏ʹجͮ࣍͘ݩԻ৔੍ޚ
    ɹݸͷεϐʔΧʹΑΔԻ৔
    ɹݸͷϩʔΧϧ੍ޚྖҬͷ࠶ݱޡࠩΛ࠷খԽ
    ղੳతॏΈߦྻ܎਺
    ॏΈ෇͖Ϟʔυ੍ޚ๏ʹΑΔۦಈ৴߸ 8FJHIUFE
    NPEFNBUDIJOH  /
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    % <latexit sha1_base64="zNgudirRmzITVdomx5TDr2a3MEw=">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</latexit> psyn(r) = L X l=1 dl(rl)G (r|rl) = g(r)>d <latexit sha1_base64="T60FFITnJRV8UGlpENVwobG0GKs=">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</latexit> minimize d J = Q X q=1 Z r2Vq g(r)>d pdes(r) 2 dr <latexit sha1_base64="U6bnXNdZ1Qv4n7xQhay0FXQb9S4=">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</latexit> '(q) n (r) = Jn(kr(q))ejn (q) <latexit sha1_base64="wqYj+AWK/v/rCSzn17J3ZzydyMg=">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</latexit> G (r | rl) ' Nq X n= 1 c(q) n,l '(q) n (r) <latexit sha1_base64="7v6zZ2a1n5OqkTd63a4WFhm0rBQ=">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</latexit> pdes(r) ' Nq X n= 1 a(q) n '(q) n (r) <latexit sha1_base64="CJfLeNdnplenQ9mjm+kufBI854w=">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</latexit> g(r)> = '(q)(r)>C(q) <latexit sha1_base64="MyZMitsZrCXS+9ECn+crQasqGGY=">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</latexit> J ' Q X q=1 Z r2Vq '(q)(r)> ⇣ C(q)d a(q) ⌘ 2 dr = Q X q=1 ⇣ C(q)d a(q) ⌘ H W (q) ⇣ C(q)d a(q) ⌘ <latexit 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sha1_base64="EbXjxpBmKJywtBAqOki5O80dCps=">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</latexit> ˆ d = Q X q=1 C(q)H W (q)C(q) + I ! 1 Q X q=1 C(q)H W (q)a(q) <latexit 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21.  .PEFNBUDIJOHCBTFE
    TPVOE
    fi FME
    DPOUSPM Ϛϧνεϙοτ࠶ੜɾۙ๣ΤϦΞ࠶ੜɾऩ࿥
    Ի৔ऩ࿥ɾ࠶ੜ 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 *$"441
    
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     Quiet zone Listening zone rq rq rb r1 r2 ro ri *$"441
     Reproduced sound field and reproduction error Sound field represented by angular spectrum coefficients Sound field recorded by linear receiver (Spatial Fourier transform) 2.5D HOA for circular secondary sources (J. Ahrens et al. 2008.) Analytical driving function of 2.5D synthesis Analytical approaches to sound field recording and reproduction Analytical conversion of sound field representation Analytical driving function of 2.5D synthesis for circular secondary sources Sound field recorded by linear microphone arrays can be reproduced by circular loudspeaker arrays 2.5D higher-order Ambisonics for a sound field described by angular spectrum coefficients Takuma OKAMOTO, National Institute of Information and Communication Technology, Japan 1. Introduction 2. Analytical conversion of sound field representation 3. Proposed formulation 4. Computer simulations Reproduction error Sound field Lmic = Lsp = 64 ch, x = 0.05 m, r0 = 2.0 m, xs = [1, 5, 0]T ˜ P( k, !) = ˜ P(kx, !) = Z 1 1 P(x, 0, !)ejkxxdx = Z 1 1 P(x, 0, !)ejk cos( k)xdx ˚ D2.5D,m(r0, !) = ( j)|m| 1 ⇡r0h(2) |m| (kr0) Z ⇡ 0 ˜ P( k, !) sin( k)e jm k d k ˚ D2.5D,m(r = 0, r0, !) = 1 2⇡r0 · ˇ Pm |m| (!) jkh(2) |m| (kr0)Y m |m| (⇡/2, 0)⇤ ˇ Pm |m| (rs, !) = jkh(2) |m| (krs)Y m |m| (✓s, s)⇤ ˇ Pm |m| ( k, !) = 4⇡( j)|m|Y m |m| (⇡/2, k)⇤ Plane wave : Point source : Z k p Higher order Ambisonics (HOA) Recording stage Reproduction stage Spectrum division method (SDM) Angular spectrum Spherical harmonics expansion Flexible sound field recording and reproduction J. Ahrens et al. 2012. WFS for SHE Proposed approach Integrated with from to k = 0 ⇡ (k/2⇡) ˜ P( k, !) sin( k) *$"441
     (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 8"41""
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    4DJ
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sha1_base64="4+PPGmsftDSr+89kP3iDJgP1RIA=">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</latexit> <latexit sha1_base64="4+PPGmsftDSr+89kP3iDJgP1RIA=">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</latexit> Estimation <latexit 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sha1_base64="XRMgqSyauROpNi/jKmh6GVf/8Ng=">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</latexit> <latexit sha1_base64="XRMgqSyauROpNi/jKmh6GVf/8Ng=">AAACbXichVHLSgMxFD0d3/VVFUFQpFiqriRTBMWVIIJL21oVaykzY9TQeTGTFrT4A64FF6KgICJ+hht/wEU/QVy4UHDjwtvpgGhRb0hycnLPzUmiu6bwJWO1iNLS2tbe0dkV7e7p7euPDQyu+07ZM3jOcEzH29Q1n5vC5jkppMk3XY9rlm7yDb20VN/fqHDPF469Jg9cXrC0PVvsCkOTRG0t+1JYASzGEmyGBRFvBmoIEghj1YndYBs7cGCgDAscNiRhExp8anmoYHCJK6BKnEdIBPscR4iStkxZnDI0Yks07tEqH7I2res1/UBt0CkmdY+UcSTZI7tlr+yB3bEn9vFrrWpQo+7lgGa9oeVusf94JPv+r8qiWWL/S/WnZ4ldzAdeBXl3A6Z+C6OhrxyevmYXMsnqJLtiz+T/ktXYPd3ArrwZ12meOUOUPkD9+dzNYD01oxJOpxKLs+FXdGIUE5im957DIlawihyda+ME57iIvCjDypgy3khVIqFmCN9CmfoEnpCN5w==</latexit> Conversion <latexit 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     8"41""
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sha1_base64="tTaOHeeIUBO/tb8yoU9wi6pdx90=">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</latexit> R <latexit sha1_base64="YHzWqcuZOxs1ENpMpbK5O77InDU=">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</latexit> ri <latexit sha1_base64="IOKaDbSz36CI9XnqI1Q49P9zGZs=">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</latexit> re <latexit sha1_base64="eB3ED7x+wvZmfbFTHa6tV28iddE=">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</latexit> Cylindrical <latexit sha1_base64="UfxNXJCLQYmpUqyLXjfKQpgTS9g=">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</latexit> ba✏e <latexit sha1_base64="jbvLfRNejVRo6h1J2kuPPawKZwc=">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</latexit> Global <latexit sha1_base64="xY4EfUF+ki6JDpxHhufQcYrETgo=">AAACd3ichVHLSgMxFD0d3/XRqhvBhcXS0lXJdKHiquDGpVX7AJUyM6Y1OJ0ZZtJiLf6AP+BCEBSkip/hxh9w0U8QlwoiuPB2OiBa1BuSnJzcc3OS6I4pPMlYJ6QMDA4Nj4yOhccnJqci0emZgmfXXYPnDdu03ZKuedwUFs9LIU1eclyu1XSTF/XDte5+scFdT9jWtmw6fK+mVS1REYYmiSpHZ1xeJRCzKzFhSe5yT5ajcZZmfsT6gRqAOILYsKNt7GIfNgzUUQOHBUnYhAaP2g5UMDjE7aFFnEtI+PscJwiTtk5ZnDI0Yg9prNJqJ2AtWndrer7aoFNM6i4pY0iwR3bLXtgDu2NP7OPXWi2/RtdLk2a9p+VOOXI6t/X2r6pGs8TBl+pPzxIVrPheBXl3fKZ7C6OnbxyfvWytbiZaSXbFnsn/Jeuwe7qB1Xg1rnN88xxh+gD153P3g0ImrS6lM7lMPJsJvmIU81hEit57GVmsYwN5OvcIF2jjJvSuLChJJdVLVUKBZhbfQlE/AVBJkVc=</latexit> region of interest <latexit sha1_base64="vKF6xXSpPaEvokoE8FWKYQc+GdY=">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</latexit> Rl <latexit sha1_base64="4Dyi8hfBeATTsUj8rZHzcqFfm9w=">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</latexit> Rq <latexit sha1_base64="vKF6xXSpPaEvokoE8FWKYQc+GdY=">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</latexit> Rl <latexit sha1_base64="vKF6xXSpPaEvokoE8FWKYQc+GdY=">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</latexit> Rl <latexit sha1_base64="T1Y7Oc5TScHPEBYoSqQLnV2sDMM=">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</latexit> Interior Ambisonics <latexit sha1_base64="RBbvDr1eV60H5EkJzP33VJ153rI=">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</latexit> Exterior Ambisonics
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     Bright zone Dark zone Ωb Ωd × × × × × × × × × × × × × × × × × × × × × × × × × × × × : Loudspeaker × : Control point <latexit sha1_base64="47T/Ezzm1r3SUpou6vxJ0GvyP2Y=">AAADPXicjVHNThRBEK4ZRXFFWfVi4mXjBoOXTQ8xaEyWELxwMYHFBRIGJj29vTBhembS3bvJ0ukX8AU4cMKEEONDePDiC5jIA3ggGC+YcPFg7ewksBB/ajJdVV/VV/11d5jFkdKEHDnutesjN26O3irdHrtzd7x87/6ySjuS8SZL41SuhlTxOEp4U0c65quZ5FSEMV8Jt1/16ytdLlWUJm90L+Prgm4mUTtiVCMUlL/ywPiC6i0pTGhtpV7x25Iy41nzeqhifdURgRF1z25cLmXnqeol1k76YRq3VE+gM9Iiyz7dMD5V+r9a6xexFm6XM1TbzKOKC6WGHZIxzArKVVIjuVWuBl4RVKGwhbR8CD60IAUGHRDAIQGNcQwUFH5r4AGBDLF1MIhJjKK8zsFCCbkd7OLYQRHdxnUTs7UCTTDvz1Q5m+EuMf4SmRWYIF/Ie3JKPpMP5Jj8+uMsk8/oa+mhDwdcngXjbx8unf2TJdBr2Dpn/VWzhja8yLVGqD3Lkf4p2IDf3dk9XXrZmDBPyDtygvr3yRH5hCdIuj/ZwSJv7EEJH8C7fN1Xg+Wpmjddm158Vp2dK55iFB7BY5jE+34OszAPC9AE5sw4LUc4ifvR/eZ+d38MWl2n4DyAIXPPfgOTW+bU</latexit> eb = 1 Mb Mb m=1 psyn(rm)→psyn(rm) = dHRbd <latexit sha1_base64="IQl7XEEXJjQ/STEfu54n5s5tXcY=">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</latexit> !b <latexit sha1_base64="IQl7XEEXJjQ/STEfu54n5s5tXcY=">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</latexit> !b <latexit sha1_base64="bXEe+VZqL1++8jdLSojgLejHIx0=">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</latexit> (Rb)l,m = 1 Mb G (rm |rl)H G (r|rl) <latexit sha1_base64="IQl7XEEXJjQ/STEfu54n5s5tXcY=">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</latexit> !b <latexit sha1_base64="tO65uoAwRXqiy860RXvl6MftGI4=">AAACeHichVHLSgMxFD0dX7W+qt0IborF16akIiquim7c+WwrtKXMTGM7OC9m0kId+gP+gAsXoiAqfoYbf8BFP0FcKgjiwtvpgGhRb0hycnLPzUmi2LrmCsZaIamnt69/IDwYGRoeGR2Ljk9kXavmqDyjWrrlHCiyy3XN5BmhCZ0f2A6XDUXnOeVoo72fq3PH1SxzXzRsXjTkiqkdaqosiCpFY4Utg1fkklcwZFF1DK/cbJaiCZZkfsS7QSoACQSxbUWvUUAZFlTUYIDDhCCsQ4ZLLY8UGGziivCIcwhp/j5HExHS1iiLU4ZM7BGNFVrlA9akdbum66tVOkWn7pAyjhn2yG7ZC3tgd+yJffxay/NrtL00aFY6Wm6Xxk4m997+VRk0C1S/VH96FjjEqu9VI++2z7RvoXb09ePTl7213Rlvll2yZ/J/wVrsnm5g1l/Vqx2+e4YIfUDq53N3g+xiMrWcXN5ZSqTXg68IYwrTmKf3XkEam9hGhs5t4Bw3uA29S3FpTlropEqhQBPDt5AWPwExlZJN</latexit> !d <latexit sha1_base64="P+qn9tukBI1LlqH01QmUhBAOd4c=">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</latexit> ω = dHRbd dHRdd <latexit sha1_base64="D8TCL39MuP1s1GBckjI2WumPOFo=">AAAC83ichVFLLwRBEK4Zr7Ueu7gIl41FONj0iCyRSISLI8sisWx6ehsT88pM78aa9B9wcHVwIkRE/AoXf8DBTxBHEhcHtbOTeAXV6a7q76uvurpbd03DF4Q8KGpDY1NzS6w13tbe0ZlIdnWv+k7ZYzzPHNPx1nXqc9OweV4YwuTrrseppZt8Td+br/FrFe75hmOviKrLNy26YxvbBqMCoWLyaKSgO2bJr1rogpwsBgWLil3PCkpSbgVjmvyN16Uc/cyVPnGUMSlTM6mCzgX9gC26L+WfmmIyTTIktNTPQIuCNES26CQvoQAlcIBBGSzgYIPA2AQKPo4N0ICAi9gmBIh5GBkhz0FCHLVlzOKYQRHdw3UHdxsRauO+VtMP1QxPMXF6qEzBELknV+SZ3JFr8kjefq0VhDVqvVTR63Utd4uJw97l139VFnoBux+qP3sWsA1TYa8G9u6GSO0WrK6vHBw/L0/nhoJhckaesP9T8kBu8QZ25YVdLPHcCcTxA7Tvz/0zWB3PaNlMdmkiPTsXfUUM+mEARvC9J2EWFmAR8njui9KnpJVBtayeqGfqeT1VVSJND3wx9eYdu4fFsg==</latexit> (R→1 d Rb)dacc = ωmaxdacc <latexit sha1_base64="yRPlG3JqNmad1O8axVQWhx1PSQo=">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</latexit> ωmax ɿ࠷େݻ༗஋ɹˠ <latexit sha1_base64="fRaVZ0X+5f1q/IIex+JUH9Xb+58=">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</latexit> dacc ɿ<latexit sha1_base64="NYVUd84b0ioSmOdoN29I2KKfOK8=">AAAConichVHLLgRBFD3aa4zXYCOxEYOwMKkWQSSSCRuxMjMGiWHS3VPo6Fe6ayYZnf4BP2BhhYiIz7BhSyx8gliS2Fi409OJILiVqnvq3Htu3apSHUP3BGOPDVJjU3NLa6wt3t7R2dWd6Old8+yyq/G8Zhu2u6EqHjd0i+eFLgy+4bhcMVWDr6v7i7X4eoW7nm5bq6Lq8C1T2bX0HV1TBFHFxPxYQbWNklc1yfnZoOgXTEXsuaZfCoJtf0IOfourQTBeTCRZioU2+BPIEUgishU7cYECSrChoQwTHBYEYQMKPBqbkMHgELcFnziXkB7GOQLESVumLE4ZCrH7tO7SbjNiLdrXanqhWqNTDJouKQcxwh7YJXthN+yKPbH3X2v5YY1aL1Xyal3LnWL3YX/u7V+VSV5g71P1Z88CO5gNe9WpdydkarfQ6vrKwdFLbi474o+yU/ZM/Z+wR3ZNN7Aqr9p5hmePEacPkL8/90+wNpmSp1PTmalkeiH6ihgGMIQxeu8ZpLGEFeTp3DPc4g730rC0LGWkXD1Vaog0ffhiUuEDA32kAg==</latexit> (R→1 d Rb) ͷ࠷େݻ༗ϕΫτϧ ˠ
    ݻ༗஋෼ղͱΈͳͤΔ
23. ՄมεύϯτϨʔυΦϑϑΟϧλʔ
    ԻѹϚονϯάɿίϯτϥετΛ੍ޚͰ͖ͳ͍
    ԻڹίϯτϥετɿԻѹΛ੍ޚͰ͖ͳ͍
    ˠ྆ํͷ͍͍ͱ͜औΓΛ͍ͨ͠
    ɹΛॴ๬ԻѹɼɹΛͰ͖Δ͚ͩແԻʹ
    ௿ϥϯΫۙࣅΛಋೖͨ͠ۦಈ৴߸
    ɹɹɹ͓ΑͼɹɹɹɿԻѹϚονϯά๏ͱҰக
    ɹɹɹ͓ΑͼɹɹɹɿԻڹίϯτϥετ๏ͱҰக  7BSJBCMF
    TQBO
    USBEFP ff
    7"45 5
    -FF
    FU
    BM
    *$"441
    
    5
    -FF
    FU
    BM
    *&&&"$.
    5"41-
     <latexit sha1_base64="IQl7XEEXJjQ/STEfu54n5s5tXcY=">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</latexit> !b <latexit sha1_base64="tO65uoAwRXqiy860RXvl6MftGI4=">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</latexit> !d <latexit sha1_base64="Kpi4CPcJpc6jG9w9FodbQRP4Gy8=">AAADKXichVFNb9QwEJ2Er7J8dIELEheLVRECuvJWqCBOFRzguG3ZttCUlZO4rdXYiRxnpa3Xf4A/wIETSAih/gw4cOWARLlyQhyLxIUDs9lIbFsVJkpm/Oa9l7EdZonIDaW7nn/s+ImTpyZO186cPXd+sn7h4lKeFjrinShNUr0SspwnQvGOESbhK5nmTIYJXw63Hgz7yz2uc5Gqx6af8TXJNpRYFxEzCHXrH4JCxdjnxgZhmsR5X2KysXM2SDOumUm1YpJbKZSQYps7R2xAHBkMxvkPXdcGkplNLW3o3H6r6fFlNsaMeX6LIH0weGZnHLlJAlmgMTnKOT7oTEbKbr1Bm7QMcrhoVUUDqmin9bcQQAwpRFCABA4KDNYJMMjxWYUWUMgQWwOLmMZKlH0ODmqoLZDFkcEQ3cLvBq5WK1TheuiZl+oI/5Lgq1FJYIp+pu/oHv1Id+h3+vtIL1t6DGfpYw5HWp51J59fXvz1X5XEbGDzr+qfMxtYh7vlrAJnz0pkuItopO9tv9hbvLcwZa/R1/QHzv+K7tL3uAPV+xm9mecLL6GGF9A6eNyHi6WZZmu2OTt/uzF3v7qKCbgCV+E6nvcdmINH0IYORN4Nr+098Z76O/4n/4v/dUT1vUpzCfaF/+0PyPDcag==</latexit> minimize d ||Gbd → pdes,b ||2 + µ||Gdd||2 <latexit sha1_base64="OTM1tvjTy3xVtNTt3FpesYzkEbM=">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</latexit> d = UR(!R + µI)→1UH R GH b pdes,b <latexit sha1_base64="K3dgfII629DUZYGyfx/V75nUAJI=">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</latexit> UHRbU = ! UHRdU = I <latexit sha1_base64="5juXuNOruoCN3ExAbBdoQZVdDLQ=">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</latexit> µ = 1 <latexit sha1_base64="bj6l7VnVUh9yjDodQpj6zu3o35U=">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</latexit> R = L <latexit sha1_base64="5juXuNOruoCN3ExAbBdoQZVdDLQ=">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</latexit> µ = 1 <latexit sha1_base64="jqNlUw2M4nZ0suGO1pvwxYxd9ac=">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</latexit> R = 1 Bright zone Dark zone Ωb Ωd × × × × × × × × × × × × × × × × × × × × × × × × × × × × : Loudspeaker × : Control point <latexit sha1_base64="pTF/e3JxVtU/qsD7MdqSBPRKGnc=">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</latexit> Subspace rank V <latexit sha1_base64="9n/yfmAie5gb7avD5PwZ1s7H3aU=">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</latexit> µ <latexit sha1_base64="HZ4VCqR5oQMvT1rTacAz+ZAcqWA=">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</latexit> 1 <latexit sha1_base64="HZ4VCqR5oQMvT1rTacAz+ZAcqWA=">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</latexit> 1 <latexit sha1_base64="HBx8WXTptTbOtgk0zfHxUXvo6l4=">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</latexit> 0 <latexit sha1_base64="89rjgjWRVkxvwAGL4s3g6Es5nGc=">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</latexit> L <latexit sha1_base64="+F8CCUD9l7OX9ZXpDc+3/nwCbqc=">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</latexit> MVDR <latexit sha1_base64="4SCpEUi1+xKB4CtPv4YUP/R1B7M=">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</latexit> VAST-NF <latexit sha1_base64="k+lAPEnAyMEXvtm1bOr/HJbTZz8=">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</latexit> ACC-PM <latexit sha1_base64="blIOccvfi9uaZ1CiBy+GkXRvn3I=">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</latexit> ACC <latexit sha1_base64="jcc8pN0ndqMR9FGIiy/KRvHYZHc=">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</latexit> PM (Wiener) <latexit sha1_base64="HrwMcDLiKWp8AG0mhHRhSHfV/QM=">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</latexit> VS Wiener <latexit sha1_base64="W9j2BDhNDgKVeZ3woA4p6F8Oy2c=">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</latexit> VS MD
24. ৼ෯Ϛονϯά๏
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    ดܗղͱͯ͠͸ಘΒΕͳ͍ˠޯ഑๏౳Ͱղ͘
    ྫɿ"MUFSOBUJOH
    EJSFDUJPO
    NFUIPE
    PG
    NVMUJQMJFST
    "%..
    ࣌ؒྖҬͰͷϑΟϧλͷ҆ఆੑΛอূ  "NQMJUVEF
    NBUDIJOH Bright zone Dark zone Ωb Ωd × × × × × × × × × × × × × × × × × × × × × × × × × × × × : Loudspeaker × : Control point 5
    "CF
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    5"41-
     <latexit sha1_base64="lZCegu7JxJVA5gbK+y7Z1Yah708=">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</latexit> minimize d |||Gd| → |pdes |||2 + ωAM ||d||2 <latexit sha1_base64="SPSLL2P3WxFtppfNZLazpFKcIDI=">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</latexit> minimize {dk }K k=1 K k=1 |||Gd| → |pdes |||2 + ωAMD(dk) <latexit sha1_base64="+ZvNXS4JwGMarAPkxG20PpExa08=">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</latexit> D(dk) = K k=2 ||dk → dk→1 ||2 <ॏཁ>แғܕΞϨΠΛ༻͍࣮ͨ૷ɿIUUQTZPVUVCFP:XLNQ;D:
25.  4'$- 5
    0LBNPUP
    8"41""
    
    BDDFQUFE <latexit sha1_base64="zj+JvMXaCha1ijFma47xlAPcjAY=">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</latexit> Transfer function <latexit sha1_base64="5kz1h5/WHvNluSx2Os5/7KHnWAM=">AAACf3ichVG7SgNBFD1Z3/EVtRFtgsFHFW4En5VgY6nGqKASdjejDm52l51JIAbB2h+wsFJQEQv9Bxt/wMJPEEsFGwtvNguiot5hZs6cuefOmRnLd6TSRI8xo6GxqbmltS3e3tHZ1Z3o6V1VXimwRc72HC9Yt0wlHOmKnJbaEet+IMyi5Yg1a2++tr9WFoGSnruiK77YKpo7rtyWtqmZyicGshVX7wol90UhyVXdQpL1SpUCkU+kKE1hJH+CTARSiGLRS1xiEwV4sFFCEQIuNGMHJhS3DWRA8JnbQpW5gJEM9wUOEGdtibMEZ5jM7vG4w6uNiHV5XaupQrXNpzjcA1YmMUwPdEUvdE/X9ETvv9aqhjVqXio8W3Wt8PPdR/3Zt39VRZ41dj9Vf3rW2MZ06FWydz9karew6/ry/vFLdnZ5uDpCZ/TM/k/pke74Bm751T5fEssniPMHZL4/90+wOp7OTKYnlsZTc9PRV7RiEEMY4/eewhwWsIgcn3uIC9zg1ogZo0baoHqqEYs0ffgSxswHjBGUJg==</latexit> Synthesized sound pressure <latexit sha1_base64="BiTT2soFYPCgmeS9UrxwI9V4iaY=">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</latexit> Linear layer <latexit sha1_base64="BiTT2soFYPCgmeS9UrxwI9V4iaY=">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</latexit> Linear layer <latexit sha1_base64="QTliZ0QgYQD66mlpD8wFW8hLAHU=">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</latexit> In: 1 ch <latexit sha1_base64="zCeuJ3EBWmjCURYZD0IO+Y7fE0o=">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</latexit> Optimized <latexit sha1_base64="HWZmzoppJq7TJ89X9f5UNFiNW9E=">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</latexit> Driving signals <latexit sha1_base64="HZ4VCqR5oQMvT1rTacAz+ZAcqWA=">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</latexit> 1 <latexit sha1_base64="xXSTmDNaKSAoEE3bE61HIjJYOsA=">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</latexit> dL1 <latexit sha1_base64="oqiWkFB0WZpxF4D9wxVLqjhllyk=">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</latexit> G <latexit sha1_base64="zmZ0GK9nINp4zKq5O4Pw+Ab/Dww=">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</latexit> GdL1 <latexit sha1_base64="wy0E9Facmes/c7n3cj8D31A2/8s=">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</latexit> Desired sound pressure <latexit sha1_base64="v3kAzI46rTC3KHNge07OQio/Ayo=">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</latexit> pdes <latexit sha1_base64="22w3SQIel8EI5g4uMtAR9lPQChE=">AAADH3ichVHNahRBEK4ZfxLXn6zxIngZXCIRcalZZLMrCEFBPQTcJG4SyMRhpqeTDOn5YaZ3ZZ3pF/AFPHiKICK+gVcPehIvHvYRxGMELx6smV1xDSTWMF1VX9VX/XW3Gws/lYhDTT9x8tTpqekzlbPnzl+YqV6cXUujXsJ4l0UiSjZcJ+XCD3lX+lLwjTjhTuAKvu7u3Svq632epH4UPpaDmG8Fzk7ob/vMkQTZ1fdW4Mhd5ohsSdlZmSRBtmQqZdwxcsuNhJcOAnLZU/Uks2QUq/lJ9IGazLxDM25OFuOJosdTpa7nxg3DEiTWcw7tnefHjc1zOzOVXa1hHcmaTaMIzBaaFLTbrUajbZhlCbEGY+tE1TdggQcRMOhBABxCkBQLcCClbxNMQIgJ24KMsIQiv6xzUFAhbo+6OHU4hO7RukPZ5hgNKS9mpiWb0S6C/oSYBszhV3yLB/gJ3+E3/HXkrKycUWgZkHdHXB7bM88vr/78LysgL2H3L+tYzRK2oVVq9Ul7XCLFKdiI33/24mD19spcdg1f4XfSv49D/EAnCPs/2OtlvvISKvQAf27ZODpYa9TNZr25fKu2eHf8FNNwBa7CPN33AizCQ+hAF5hmaPe1R1pH39c/6p/1L6NWXRtzLsE/pg9/AxDY10s=</latexit> LL1 = |w→(GdL1 → pdes )| + ωL1 ||dL1 ||1 <latexit sha1_base64="V6YdaMlKdAz2yXm+B+0w46eOOJI=">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</latexit> Backpropagation <latexit sha1_base64="J8KaEnmscNyrh7LAVsKMjitIFF4=">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</latexit> Out: L→ ch <latexit sha1_base64="hhP4QshY1sux1nMKIpEd29YKyzo=">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</latexit> W1 <latexit sha1_base64="RnxVkkjr1n+v16ZR5W3UwdISTEM=">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</latexit> W2 <latexit sha1_base64="TaZhMuQEiivg/MtksOXI6C7SB6w=">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</latexit> In: L→ ch <latexit sha1_base64="7eJQ5HiHFhAUCckLrepx1qS/4xw=">AAACbnichVHLSsNAFD2N7/poVRBBxGJVXJVpF1q6KrhxIfiofUAtJYlTG5omIZkWavEH3IsLQVEQET/DjT/gwk8QN0IFNy68TQOiRb1hMmfO3HPnzB3F0jVHMPbkk3p6+/oHBof8wyOjY4Hg+ETGMWu2ytOqqZt2TpEdrmsGTwtN6Dxn2VyuKjrPKpW19n62zm1HM41d0bB4oSofGFpJU2VBVH6zJhKhhY2FkFouBsMswtwIdYOoB8LwYssM3mAP+zChooYqOAwIwjpkOPTlEQWDRVwBTeJsQpq7z3EEP2lrlMUpQya2Qv8DWuU91qB1u6bjqlU6RadhkzKERfbIblmLPbA79sw+fq3VdGu0vTRoVjpabhUDx9Op939VVZoFyl+qPz0LlBB3vWrk3XKZ9i3Ujr5+eNpKJXYWm0vsir2Q/0v2xO7pBkb9Tb3e5jtn8NMDRH+2uxtkYpHoSmRlOxZOxr2nGMQM5rFM/V5FEuvYQtrt2AnOceF7laakWWmukyr5PM0kvoW0/Amu24z0</latexit> Out: L ch <latexit sha1_base64="xWs+tXOASM65w5IL0dehdMqQ5Y0=">AAADYnichVFLaxRBEK7Z9RHXRzbmIuihcYnEg0tvkCiCEPQinvJwN4FMXGZ6eneb9Dzo6V3ZdNq7HvXgwZOCiPgzvPgHPOTuRTxG8KJgzeyITBa1humq/qq+qq+7/USKVFN64FSqx46fODlzqnb6zNlzs/W58500HirG2yyWsdryvZRLEfG2FlryrURxL/Ql3/R372b5zRFXqYijB3qc8J3Q60eiJ5inEerWf7rDKMA818b1Yxmk4xCdCaw1bpxw5elYRV7ITSgiEYo9bi0xLrFu6OkB86S5b28TV0S6W+Irm4GEdKwreU/vk0eL5fRVkidKaN8eLXpoXB0n2Ksk7VqCw7L5KjQBT+0UzVWiP9CF2ye/ax8H5U7KdusN2qS5kemgVQQNKGw1rr8FFwKIgcEQQuAQgcZYggcpftvQAgoJYjtgEFMYiTzPwUINuUOs4ljhIbqLax932wUa4T7rmeZshlMk/gqZBBboJ/qOHtKP9D39Qn/8tZfJe2Raxuj9CZcn3dmnFza+/5cVotcw+MP6p2YNPbiZaxWoPcmR7BRswh/tvTjcuLW+YK7Q1/Qr6n9FD+gHPEE0+sberPH1l1DDB2gdve7poLPUbC03l9euN1buFE8xAxfhMizifd+AFbgHq9AG5jDnifPMeV75XK1V56rzk9KKU3DmoWTVS78Au3fwTQ==</latexit> minimize d J = r→V w(r) g(r)↑d → pdes(r) dr Իѹฏۉઈରޡࠩ࠷খԽܕԻ৔੍ޚ
    ࠷খೋ৐๏ɿޡࠩ෼෍͕Ψ΢ε෼෍ʹै͏ͱԾఆ
    ฏۉઈରޡࠩɿޡࠩ෼෍͕ϥϓϥε෼෍ʹै͏ͱԾఆ
    ఏҊ๏ɿԻѹฏۉޡࠩΛ࠷খԽ
    ดܗղͱͯ͠͸ಘΒΕͳ͍ˠޯ഑๏౳Ͱղ͘
    ఏҊ๏ɿ1Z5PSDIΛ༻͍ͨޡࠩٯ఻ൖͰղ͘ ͚ͩ
26. ࣍ݩϞʔυ੍ޚʹجͮ͘ہॴ࠶ੜ
    Ի͕ฉ͑͜ΔΤϦΞͷԻѹΛɼฉ͑͜ͳ͍ΤϦΞͷԻѹΛ
    ແݶԁ౵όοϑϧܕԁܗΞϨΠɿۦಈ৴߸Λղੳతʹࢉग़Մೳ
    ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ5
    0LBNPUP
    8"41""
    
    ࣮ଌͨ͠఻ୡؔ਺ɹɹɹɹɹΛ༻͍ͨ৔߹
    ఻ୡؔ਺ɹɹɹɹɹΛଌఆ
    ۦಈ৴߸ɿ
    ہॴ࠶ੜϑΟϧλɿ  %
    FYUFSJPS
    NPEFNBUDIJOH 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 <latexit sha1_base64="WeZsnZwk5UGw+Dx58344ySFZpfU=">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</latexit> 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 <latexit sha1_base64="w77DHJ0cpBVEi7ri+sh27w+FFVo=">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</latexit> Hl(rref , m) <latexit sha1_base64="ENxoC8BAov895nidMWiG1Mvap1E=">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</latexit> ˆ d = C(r ref )HC(r ref ) + I 1 C(r ref )Ha(r ref ) <latexit sha1_base64="pudrKLQmB8dnxmsYuHL5YGr2ceg=">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</latexit> C(rref ) = 2 6 4 c N,1(rref ) · · · c N,L(rref ) . . . ... . . . cN,1(rref ) . . . cN,L(rref ) 3 7 5 <latexit sha1_base64="u25XTEhOVbL/8OuvkFUjAmPUrGs=">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</latexit> an,rect( , S) = sinc ✓ n 2⇡ ◆ e jn s <latexit sha1_base64="DB31CbEgzeBbvhJ6gGtkWpP5wRY=">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</latexit> an,hann( , S) = ⇢ sinc ✓ 1 2 + n 2⇡ ◆ + sinc ✓ 1 2 n 2⇡ ◆ 2 e jn s ۣܗ૭ )BOO૭ <latexit sha1_base64="w77DHJ0cpBVEi7ri+sh27w+FFVo=">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</latexit> Hl(rref , m)
27. ࣮૷ͨ͠νϟωϧ௚ઢΞϨΠΛ༻͍ͨํࣜ
    ैདྷٕज़Λ্ճΔ੍ޚੑೳΛ࣮ݱ  &YQFSJNFOUBM
    SFTVMUT
    PG
    MJOFBS
    BSSBZ 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) 5
    0LBNPUP
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28. νϟωϧԁܗΞϨΠΛ༻͍ͨํࣜ
    ैདྷٕज़Λ্ճΔ੍ޚੑೳΛ࣮ݱ  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 ଟ఺੍ޚ -4 ϏʔϜϑΥʔϛϯά ఏҊ๏ 
    )[ͷ݁Ռ 4JNVMBUJPO
    SFTVMUT
    PG
    DJSDVMBS
    BSSBZ 5
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    8"41""
    
29. ۭؒϑʔϦΤม׵Λ༻͍ͨہॴ࠶ੜʹ͓͚Δ૭ؔ਺ͷτϨʔυΦϑ
    ۣܗ૭ɿ࠶ੜྖҬͷԻѹ͸େ͖͍͕ແԻྖҬͷ࿙Ε͸ଟ͍
    )BOO૭ɿ࠶ੜྖҬͷԻѹ͸େ͖͘ͳ͍͕ແԻྖҬͷ࿙Ε͸গͳ͍
    
    
    
    
    ˠτϨʔυΦϑ
    Կނ
    ˠεϐʔΧͷνϟωϧ਺͸༗ݶͷͨΊ
    ɹۭؒप೾਺Λ్தͰଧͪ੾Γ
    ɹˠ)BOO૭ͷํ͕௿͍࣍਺ʹूத  3FDUBOHVMBS
    XJOEPX
    74
    )BOO
    XJOEPX 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 )BOO૭ -40 -30 -20 -10 0 10 20 30 40 kx 0 5 10 15 20 25 30 35 40 45 | ˜ F(kx, k)| SFT (rect.) SFT (Hann) ۣܗ૭ <latexit sha1_base64="aeXuHw7IdF49dKAuKduMFJAlHPc=">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</latexit> (a) Acoustic contrast <latexit sha1_base64="VzVlDTGOv+OkmZbh/3DqDzB84Ss=">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</latexit> (b) Bright zone output power 5
    0LBNPUP
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30. ࣮૷
    JT
    BMM
    XF
    OFFE 
31. ౸དྷԻ৔ܕΞϯϏιχΫε ೾໘߹੒๏ɼεϖΫτϧআࢉ๏ DIٿܗϚΠΫϩϗϯΞϨΠˏ౦๺େ DIแғܕεϐʔΧΞϨΠˏ౦๺େ DIแғܕϚΠΫϩϗϯΞϨΠˏ౦๺େ DIٿܗεϐʔΧΞϨΠˏ/*$5 DIೋ௚ઢϚΠΫϩϗϯΞϨΠˏ/*$5 DIೋ௚ઢεϐʔΧΞϨΠˏ/*$5  ์ࣹԻ৔ܕΞϯϏιχΫε ɹ1SFWJPVT
    TZTUFNT Ի৔ऩ࿥ɾ࠶ݱ͕໨తɼ࣋ͪӡͼ͸ࠔ೉
32. νϟωϧ௚ઢεϐʔΧΞϨΠΛ༻͍ͨϚϧνεϙοτ࠶ੜ 1SFWJPVT
    JNQMFNFOUFE
    TZTUFN  ͜Μʹͪ͸ )FMMP 㟬޷ Japanese area <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> English area <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> Chinese area <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> Bright zone (Listening area) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> Dark zone (Quiet area) <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> <latexit sha1_base64="(null)">(null)</latexit> Իͷฉ͑͜Δ
    ΤϦΞ Իͷฉ͑͜ͳ͍
    ΤϦΞ ॏͶ߹Θͤ 
    N ࣮༻ԽͷͨΊʹ͸খܕԽ͕ඞਢ ֶձձ৔ͰεϐʔΧΞϨΠͷσϞ͕͍ͨ͠Ի৔੍ޚΛීٴ͍ͨ͠ 5
    0LBNPUP
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33. νϟωϧখܕԁܗεϐʔΧΞϨΠͷ࣮૷ɿԬຊΒɼԻߨ࿦ɼ೥݄
    Ͱ͖Δ͚ͩখ͘͞
    ˠ
    ௚ܘΘ͔ͣ
    DN
    
    DIΞϯϓ 3.&
    %JHJGBDF
    64#ಉࠝ ɾέʔϒϧΛؚΊͯग़ுσϞՄೳ
    λϒϨοτͰϚϧνεϙοτ Ի৔ ΛճసՄೳɿԬຊΒɼԻߨ࿦ɼ೥݄  13.44 cm 2.5 cm 3.1 cm <latexit sha1_base64="PjnHn/kBdngue+nAIaVXwZWL0Ys=">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</latexit> 13.44 cm 
    DIΞϯϓ ϙʔλϒϧσϞγεςϜͷ࣮૷ !๺ւಓՊֶେֶ
34. ΠϯύϧεԠ౴ͷଌఆ
    εϐʔΧ਺ɿ
    ੍ޚ఺਺ɿɹɹɹɹ ›ִؒ
    ج४ڑ཭ɿ
    αϯϓϦϯάप೾਺ɿ
    L)[
    ଌఆ৴߸ɿٯ࣌ؒҾ͖৳͹͠ύϧε 541 ৴߸αϯϓϧɼճಉظՃࢉ
    ఻ୡؔ਺ɾہॴ࠶ੜϑΟϧλͷࢉग़
    ఻ୡؔ਺
    541৴߸৞ΈࠐΈˠΠϯύϧεԠ౴ˠαϯϓϧ੾Γग़͠ˠ཭ࢄϑʔϦΤม׵
    ˠෳૉεϖΫτϧ Ϗϯ ɿ
    ہॴ࠶ੜϑΟϧλɿ
    ۦಈ৴߸ɿɹˠ཭ࢄٯϑʔϦΤม׵ˠ࣮෦੒෼ˠ'*3ϑΟϧλ αϯϓϧ  &YQFSJNFOUT <latexit sha1_base64="w77DHJ0cpBVEi7ri+sh27w+FFVo=">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</latexit> Hl(rref , m) <latexit sha1_base64="Wy59NiOwY6A1dWR0TPNly4DfzeU=">AAACeXichVHLSsNAFD2Nr1pf9bEQ3KilUlyUiRYVV6Ibl221KlgpSTrVYF4k00Ib+gP+gAs3Koion+HGH3DhJ4hLBRe68DYNiIp6Q+aeOXPPnTMzqmPonmDsISJ1dHZ190R7Y339A4ND8eGRLc+uuhovaLZhuzuq4nFDt3hB6MLgO47LFVM1+LZ6uNZa365x19Nta1PUHb5nKvuWXtE1RRBVio8VDxThF1XbKHt1k5JfbjZL8QRLsyAmfwI5BAmEkbXjlyiiDBsaqjDBYUEQNqDAo28XMhgc4vbgE+cS0oN1jiZipK1SFacKhdhDGvdpthuyFs1bPb1ArdEuBv0uKSeRZPfsij2zO3bDHtn7r738oEfLS52y2tZypzR0NL7x+q/KpCxw8Kn607NABUuBV528OwHTOoXW1tcax88by/mkP8PO2RP5P2MP7JZOYNVetIscz58gRg8gf7/un2BrLi0vpDO5TGJlNXyKKCYwjRTd9yJWsI4sCrRvA6e4wnXkTZqSUtJsu1SKhJpRfAlp/gOnp5L4</latexit> ˆ d <latexit sha1_base64="A0OTGdr61YlJJWC4tpaIKJmaseE=">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</latexit> L = 16 <latexit sha1_base64="aEqWhLmRxVF3vue7qlVYc7sHri8=">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</latexit> M = 72 <latexit sha1_base64="gm1xumkjgE7MKbb0npGc7QF+r/o=">AAAChXichVG7SiRBFD22zx1foyYLJoODYuJwZ5lVEURxE0Nfo4IjQ3dbo439orpmUJtODfwBAyOFRURT/QETf8DATxBDBRMD7/Q0LKvseouqOnXqnlunqgzftgJF9NCkNbe0trV3fEt1dnX39Kb7+lcDrypNUTQ925Prhh4I23JFUVnKFuu+FLpj2GLN2P1V31+rCRlYnrui9n2x6ejbrlWxTF0xVU5nZDksObrakU4oRSWKpin3MyxlopISeyp0onI6SzmKI/MZ5BOQRRILXvocJWzBg4kqHAi4UIxt6Ai4bSAPgs/cJkLmJCMr3heIkGJtlbMEZ+jM7vK4zauNhHV5Xa8ZxGqTT7G5S1ZmMEz3dEHPdEeX9Ehv/6wVxjXqXvZ5Nhpa4Zd7j74vv36pcnhW2Pmj+q9nhQomY68We/djpn4Ls6GvHRw/L08tDYcjdEZP7P+UHuiWb+DWXszfi2LpBCn+gPzH5/4MVn/k8uO5wmIhOzuXfEUHBjGEUX7vCcxiHgso8rmHuMI1brR2bUwraOONVK0p0Qzgr9Bm3gEWvpae</latexit> rref = 0.5 m <latexit sha1_base64="LwwKhr9cp+/Jnh0BmV8PGPlW/1o=">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</latexit> 16 ⇥ 72 = 1152 ݸͷ఻ୡؔ਺Λଌఆ
35.  3FTVMUT (a) 750 Hz (b) 1.5 kHz (c) 3 kHz (d) 4.5 kHz (e) 6 kHz (f) 7.5 kHz
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sha1_base64="1M00/pveEBR7jSORblLG9avKnK4=">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</latexit> 134.4 mm <latexit sha1_base64="3lORwKhTSRY6lGHhdMC1aJ3Pt5Q=">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</latexit> (a) Previous <latexit sha1_base64="kVry3qE5FmxkRBsyJQPLK2TpxOU=">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</latexit> 32 mm <latexit sha1_base64="3mnCzfZuRum8KzhRNQJdPCKAsRk=">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</latexit> 178.6 mm <latexit sha1_base64="P31xv0mGp9rcotdxObgPas9/pIE=">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</latexit> (b) Improved <latexit sha1_base64="IdPmBurCXRyDw5Ey+qyq0M24MtA=">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</latexit> 25 mm <latexit sha1_base64="1M00/pveEBR7jSORblLG9avKnK4=">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</latexit> 134.4 mm <latexit sha1_base64="3lORwKhTSRY6lGHhdMC1aJ3Pt5Q=">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</latexit> (a) Previous <latexit sha1_base64="kVry3qE5FmxkRBsyJQPLK2TpxOU=">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</latexit> 32 mm <latexit sha1_base64="3mnCzfZuRum8KzhRNQJdPCKAsRk=">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</latexit> 178.6 mm <latexit sha1_base64="P31xv0mGp9rcotdxObgPas9/pIE=">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</latexit> (b) Improved 
47.  ೥݄೔೔ɿ/*$5Φʔϓϯϋ΢ε Ի੠຋༁ಉ࣌௨༁ͱԻ੠Ϛϧνεϙοτ࠶ੜγεςϜͷ༥߹Λలࣔ 概要 AI AI 円形のマルチスポットスピーカーの周りに⾔語が異なる4名のデモンスト レータが座り、それぞれの⾔語で会議を⾏います。発⾔内容は他の3⾔語に 同時通訳されて同時にスピーカーから出⼒されますが、各⾔語の⾳声が混ざ り合うこと無くエリア毎に1つの⾔語が聞こえます。 ・連続発話を同時通訳することができます ・多⾔語（20⾔語）に対応しています ・各エリア毎に1つの⾔語が聞こえるので、 イヤホンを付けずに多⾔語会議ができます ・講演の多⾔語同時通訳 ・多⾔語会議やビジネス分野での利⽤ ・博物館や美術館での⾔語別ガイダンス ・TV放送や動画への翻訳字幕付与 同時通訳システムの実現を⽬指し、今後以下の研究開 発を進めます。 ・⽂脈処理による⾼精度化 ・要約処理によるリアルタイム性の向上 ・⾳声マルチスポット再⽣の⾼精度化および成果展開 02 特徴 ユースケース 今後の展開 円形マルチスポットスピーカー ⾳声認識 ⾳声合成 マルチスポット スピーカー こんにちは 你好 안녕하세요 マルチスポット処理の有無による違い （上からみた4つの⾳の出⼒イメージ） ＜システム構成の概要＞ ⽔平⽅向に90度毎に別々の4種類の⾳ を出すことができます。その際に隣の ⾳を打ち消すことで⾳が混ざらずに各 ⾳をそれぞれの領域でクリアに再⽣す ることができます。 翻訳単位 判定 ⾳声合成 ⾳声合成 ※⽇本語が⼊⼒された場合に稼働するモジュールとデータの流れを表しています。 Hello 多⾔語会議システムのデモンストレーション 〜多⾔語同時通訳技術とマルチスポットスピーカーの活⽤例〜 スピーカー ない時 ある時 総務省「グローバルコミュニケーション計画2025 」より スピーカー 機械翻訳 機械翻訳 機械翻訳
48. ಉ࣌௨༁γεςϜ Ի੠Ϛϧνεϙοτ࠶ੜ ಉ࣌௨༁ͱͷ༥߹ /*$5খۚҪΦʔϓϯϋ΢ε 
    ೔ຊ࿩ऀ͕ൃ࿩ ӳޠ࿩ऀ தࠃޠ࿩ऀ    ༻͍ͨΤϦΞ࠶ੜ  
    ஞ࣍Ի੠ೝࣝ
    ˣ
    ஞ࣍ػց຋༁
    ˣ
    ஞ࣍Ի੠߹੒ ఏҊ๏Λ༻͍ͨΤϦΞ࠶ੜ  $POpEFOUJBM ؖࠃޠ࿩ऀ 
    ϚϧνεϙοτεϐʔΧͰ
    ֤ݴޠͷ຋༁߹੒Ի੠͕
    ֤ݴޠͷ࿩ऀͷΈʹϚϧνεϙοτ࠶ੜ͞ΕΔ উ֞ೞࣁਃ 㟬޷ ؖࠃޠͷΈ͕ฉ͑͜Δ
    ΤϦΞ தࠃޠͷΈ͕ฉ͑͜Δ
    ΤϦΞ ӳޠͷΈ͕
    ฉ͑͜Δ
    ΤϦΞ ͜Μʹͪ͸ ೔ຊޠ࿩ऀ )FMMP 
50. ग़ுɿ೔ຊԻڹֶձˏ໊޻େ σϞൃද σϞ ͚͍͸Μͳ3%ϑΣΞ ಺ཡϓϨε ୅ٳ ௨ৗग़ۈ ͚͍͸Μͳ3%ϑΣΞ *('
     ४උ ͚͍͸Μͳ3%ϑΣΞ σϞలࣔ σϞలࣔ ΠϯλʔωοτΨόφϯεϑΥʔϥϜ *(' ˏژ౎ࠃࡍձؗ !͚͍͸Μͳϓϥβ σϞలࣔ σϞలࣔ σϞలࣔ σϞలࣔ σϞలࣔ ୅ٳ ࢠڙͷӡಈձ $&"5&$
    ˏນுϝοη ४උ σϞలࣔ σϞలࣔ σϞలࣔ σϞలࣔ 8"41""
    ˏ.PIPOL
    .PVOUBJO
    IPVTF χϡʔϤʔΫͷࢁԞ σϞൃද ୅ٳ ୅ٳ 
51. ΤϦΞ෼ׂ਺͓Αͼݴޠ਺ͷ֦ு  ݴޠϚϧνεϙοτ࠶ੜ ݴޠϚϧνεϙοτ࠶ੜ ֦ு ैདྷ ৽ܕ
52. $&"5&$
    ˏນுϝοη  8FC্Ͱ͸ׂѪ
53. 8"41""
    !/:
    64"  8FC্Ͱ͸ׂѪ
54. ೥݄೔ ೔
    
    
    Ի੠Ϛϧνεϙοτ࠶ੜٕज़ɹ57஍্೾ʹͯ์ૹ 
55.  ೥݄ʰ͚͍͸ΜͳສതʱΩοΫΦϑΠϕϯτ ଞ͸8FC্Ͱ͸ׂѪ
56. Ի੠Ϛϧνεϙοτ࠶ੜεϐʔΧͷݚڀ։ൃ  
    DN 
    DN 
    DN ೥ ೥ 
    DN 
    DN +45OFXT
    ೥݄߸ܝࡌ
    Πϊϕݟͯา͖ɿୈճ
    ෳ਺ͷΤϦΞʹҟͳΔݴޠΛಧ͚Δ
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57. /*$5খۚҪຊ෦
      ৗઃσϞలࣔ లࣔࣨ)1
58.  ೥݄େࡕւ༡࣮ؗূ࣮ݧ Ի੠ೝࣝ ͜Μʹͪ͸ ଟݴޠ
    ػց຋༁ )FMMP 㟬޷ উ֞ೞࣁਃ ଟݴޠ
    Ի੠߹੒ ଟݴޠಉ࣌௨༁ٕज़ ͜Μʹͪ͸ Ի੠
    Ϛϧνεϙοτ
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59.  /*$5Φʔϓϯϋ΢ε
60. ͞ΒͳΔখܕԽ΁޲͚ͯ
    Ξϯϓɿ8ˠ8
    έʔϒϧɿ൥ࡶˠεϐʔΧΞϨΠʹ௚෇͚  5PXBSET
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    TZTUFN 1/60
61. ϦϡοΫαοΫͭͰ࣋ͪӡͼՄೳͳίϯύΫτσϞγεςϜ
    ϊʔτ1$୆Ͱಉ࣌௨༁ ೔ˠӳதؖ ΋ΦϯϓϨϛε࣮૷  $PNQBDU
    EFNP
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62. 1VSF%BUBʹ࣮ͯ૷  *NQMFNFOUFE
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63. ࣮͸σϞ͸ࡢ೔͔Β࢝·͍ͬͯͨ  %FNP
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64.  ࣮૷͔ͨ͠Βͦ͜ɾɾɾ
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65. έʔϒϧ΋શͯࣗ࡞ ࣮૷ͷཪଆ ௚ઢΞϨΠͷ࣏۩͸
    N௒͑Ͱ഑ୡͯ͠΋Β͑ͣɽɽ ະདྷؗ·Ͱ࣋ࢀ
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66. Ի৔ͷہॴ࠶ੜ͓ΑͼϚϧνεϙοτ࠶ੜٕज़
    ओྲྀͳہॴ࠶ੜํࣜΛ঺հ
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     ೔ ɿ*OUFSTQFFDI
    
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     ۚ ɿԻڹֶձϙελʔηογϣϯˏ౦๺޻ۀେֶ
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    &YQFSJFODFˏେࡕؔ੢ສത
     ౔ ɿ͚͍͸Μͳ3%ϑΣΞˏ͚͍͸Μͳϓϥβ  $PODMVTJPO
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68. Ԭຊ ୓ຏ (Takuma OKAMOTO)ˏNICT e-mail: HP: https://www.okamotocamera.com Twitter: @okamotocamerea Thank you for your !! 
69. DELL XPS 13 9340 Laptop Intel Ultra 7 155H 1.40 GHz 64 GB memory Windows 11 Pro USB cable RME Digiface USB Audio interface Two Optical cables Circular array of 16 loudspeakers for multiple sound spot synthesis and speech-to-speech translation Portable stand AC adopter 16-channel small amplifier Wireless microphone Alvoxcon UM-420 for speech recognition "DUVBM
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