[asj2022a] 16チャネル小型円形スピーカアレイを用いたマルチスポット再生システムの実装

Transcript

1. νϟωϧখܕԁܗε
   ピ
   ʔΧΞϨΠΛ༻͍ͨ
   Ϛϧνε
   ポ
   οτ࠶ੜγεςϜͷ࣮૷
   
   *NQMFNFOUBUJPOPGNVMUJQMFTPVOETQPUHFOFSBUJPOTZTUFN
   VTJOHBDPNQBDUDJSDVMBSBSSBZPGMPVETQFBLFST
   
   ̋Ԭຊ୓ຏ ৘ใ௨৴ݚڀػߏ
   
   ˚େࢁ৻ೋɼ˚্໺ࠀ࢘ɼ˚Ԭ෦࢘ɼ˚୩݈ଠ࿠ ๺೔ຊԻڹגࣜձࣾ
   
   UI4FQU "4+"OOVBM.FFUJOH"VUVNO!)PLLBJEP6OJWFSTJUZPG4DJFODF
   

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2. *OUSPEVDUJPO
   WJBQSPNPUJPOWJEFPT XJMMCFVQMPBEFEPO:PV5VCF
   
   *NQMFNFOUBUJPOPGBDPNQBDUDJSDVMBSBSSBZPGMPVETQFBLFST
   .VMUJQMFTPVOETQPUTZOUIFTJTTZTUFNXJUINVMUJMJOHVBMOFVSBMUFYUUPTQFFDI
   3FBMJNQMFNFOUFEEFNPTZTUFNBU"4+ "53BOE,*$,
   4QBUJBM'PVSJFSUSBOTGPSNCBTFENVMUJQMFTPVOETQPUTZOUIFTJT
   VTJOHBDJSDVMBSBSSBZXJUINFBTVSFEJNQVMTFSFTQPOTFT
   &YQFSJNFOUT
   %FNPXJUIBOJNQMFNFOUFETZTUFN
   $PODMVTJPOT
   "DLOPXMFEHFNFOUT
   0VUMJOF
   
   

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3. ٕज़঺հϏσΦ
   
   *OUSPEVDUJPO
   

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4. 
   ۙ೔:PV5VCFʹެ։༧ఆ
   

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5. ӳޠχϡʔϥϧԻ੠߹੒ʹΑΔٕज़঺հϏσΦ
   /*$5ʹͯ։ൃதͷ࠷৽Ϟσϧ
   
   
   

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6. 
   ͪ͜Β΋ۙ೔:PV5VCFʹެ։༧ఆ
   

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7. ͜Ε·Ͱʹߏஙͨ͠Ի੠Ϛϧνεϙοτ࠶ੜγεςϜ
   .PUJWBUJPO
   
   ͜Μʹͪ͸
   )FMMP
   㟬޷
   Japanese
   area
   (null)
   (null)
   (null)
   (null)
   English
   area
   (null)
   (null)
   (null)
   (null)
   Chinese
   area
   (null)
   (null)
   (null)
   (null)
   Bright zone
   (Listening area)
   (null)
   (null)
   (null)
   (null)
   Dark zone
   (Quiet area)
   (null)
   (null)
   (null)
   (null)
   Իͷฉ͑͜Δ
   ΤϦΞ
   Իͷฉ͑͜ͳ͍
   ΤϦΞ
   ॏͶ߹Θͤ
   N
   ࣮༻ԽͷͨΊʹ͸খܕԽ͕ඞਢ
   ֶձձ৔ͰεϐʔΧΞϨΠͷσϞ͕͍ͨ͠Ի৔੍ޚΛීٴ͍ͨ͠
   

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8. νϟωϧখܕԁܗεϐʔΧΞϨΠͷࢼ࡞
   Ͱ͖Δ͚ͩখ͘͞ˠ௚ܘΘ͔ͣDN
   DIΞϯϓ 3.&%JHJGBDF64#ಉࠝ
   ɾέʔϒϧΛؚΊͯग़ுσϞՄೳ
   λϒϨοτͰϚϧνεϙοτ Ի৔
   ΛճసՄೳɿԬຊΒɼԻߨ࿦ɼ೥݄
   *NQMFNFOUBUJPOPGBDPNQBDUBSSBZ
   
   13.44 cm
   2.5 cm
   3.1 cm
   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
   13.44 cm
   DIΞϯϓ
   3.&%JHJGBDF64#ಉࠝ
   
   

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9. νϟωϧখܕԁܗεϐʔΧΞϨΠΛ༻͍ͨݴޠԻ੠Ϛϧνεϙοτ࠶
   ੜγεςϜ
   ຋༁͞Ε֤ͨݴޠͷԻ੠͕ͦΕͧΕҧͬͨ৔ॴͰฉ͑͜ΔԻ੠຋༁ͷ৽ͨͳ6*ͱ࣮ͯ͠૷
   ϦΞϧσϞలࣔ
   ۚ
   ɿ͜Ε͔Β΍Γ·͢ˠݚमһ೔ాͷॳൃද
   ͱඃΓ·ͨ͠ɽɽ
   ໦
   ۚ
   ɿ͚͍͸Μͳ3%ϑΣΞˏ"53
   ໦
   ۚ
   ɿژ౎εϚʔτγςΟΤΩεϙˏ,*$, "53͔ΒLN౦ͷͱ͜Ζ
   
   
   "OOPVODFNFOU
   )FMMP
   χϡʔϥϧݴޠࣝผ
   
   χϡʔϥϧԻ੠ೝࣝ
   χϡʔϥϧ
   ػց຋༁
   Ϛϧνεϙοτ
   ࠶ੜϑΟϧλ
   ଟݴޠ
   χϡʔϥϧ
   Ի੠߹੒
   )FMMP
   ͜Μʹͪ͸
   㟬޷
   উ֞ೞࣁਃ
   B
   DIԁܗεϐʔΧ C
   ݴޠσϞγεςϜ
   
   ೔ຊޠ
   ӳޠ
   தࠃޠ ؖࠃޠ
   DI
   εϐʔΧ
   DN
   ࠓճͷσϞ
   

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10. ࣍ݩϞʔυ੍ޚʹجͮ͘ہॴ࠶ੜ
    Ի͕ฉ͑͜ΔΤϦΞͷԻѹΛɼฉ͑͜ͳ͍ΤϦΞͷԻѹΛ
    ແݶԁ౵όοϑϧܕԁܗΞϨΠɿۦಈ৴߸Λղੳతʹࢉग़Մೳ
    

    ɹɹɹɹɹɹɹɹɹɹɹɹɹɹɹ50LBNPUP 8"41""
    ࠓճͷ࣮૷ɿ༗ݶԁ౵όοϑϧ֤εϐʔΧͷݸମࠩ
    ఻ୡؔ਺ɹɹɹɹɹΛଌఆ
    ۦಈ৴߸ɿ
    ہॴ࠶ੜϑΟϧλɿ
    
    %FSJWJOHESJWJOHTJHOBMTPGMPVETQFBLFST
    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
    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
    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
    ۣܗ૭
    )BOO૭
    

    View Slide

11. ΠϯύϧεԠ౴ͷଌఆ
    εϐʔΧ਺ɿ
    ੍ޚ఺਺ɿɹɹɹɹ ›ִؒ
    
    ج४ڑ཭ɿ
    αϯϓϦϯάप೾਺ɿL)[
    ଌఆ৴߸ɿٯ࣌ؒҾ͖৳͹͠ύϧε 541
    ৴߸αϯϓϧɼճಉظՃࢉ
    ఻ୡؔ਺ɾہॴ࠶ੜϑΟϧλͷࢉग़
    ఻ୡؔ਺
    541৴߸৞ΈࠐΈˠΠϯύϧεԠ౴ˠαϯϓϧ੾Γग़͠ˠ཭ࢄϑʔϦΤม׵
    

    ˠෳૉप೾਺εϖΫτϧ Ϗϯ
    ɿ
    ہॴ࠶ੜϑΟϧλɿ
    ۦಈ৴߸ɿɹˠ཭ࢄٯϑʔϦΤม׵ˠ࣮෦੒෼ˠ'*3ϑΟϧλ αϯϓϧ
    
    
    &YQFSJNFOUT
    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
    Hl(rref , m)
    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
    ˆ
    d
    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
    L = 16
    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
    M = 72
    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
    rref = 0.5 m
    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
    16 ⇥ 72 = 1152 ݸͷ఻ୡؔ਺Λଌఆ
    

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12. 
    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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
    rref = 0.5, S = ⇡ and = ⇡/2
    

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13. 
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14. νϟωϧখܕԁܗΞϨΠΛ༻͍ͨϚϧνεϙοτ࠶ੜγεςϜͷ࣮૷
    ΞϯϓɼέʔϒϧΛؚΊͯϙʔλϒϧԽˠग़ுσϞ͕Մೳ
    

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    ˠ຋༁͞Ε֤ͨݴޠͷԻ੠͕ͦΕͧΕҧͬͨ৔ॴͰฉ͑͜ΔԻ੠຋༁ͷ৽ͨͳ6*ΛఏҊ
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    ͷग़ྗ͕ෆे෼
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    ଟݴޠ຋༁Ҏ֎ͷల։
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15. ֎෦ࢿۚ
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    ֫ಘɼ೥݄ΑΓ։࢝
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