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[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

Takuma OKAMOTO
September 17, 2022

[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

Takuma OKAMOTO

September 17, 2022
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  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
  2. *OUSPEVDUJPO WJBQSPNPUJPOWJEFPT XJMMCFVQMPBEFEPO:PV5VCF  *NQMFNFOUBUJPOPGBDPNQBDUDJSDVMBSBSSBZPGMPVETQFBLFST .VMUJQMFTPVOETQPUTZOUIFTJTTZTUFNXJUINVMUJMJOHVBMOFVSBMUFYUUPTQFFDI 3FBMJNQMFNFOUFEEFNPTZTUFNBU"4+ "53BOE,*$, 4QBUJBM'PVSJFSUSBOTGPSNCBTFENVMUJQMFTPVOETQPUTZOUIFTJT VTJOHBDJSDVMBSBSSBZXJUINFBTVSFEJNQVMTFSFTQPOTFT

    &YQFSJNFOUT %FNPXJUIBOJNQMFNFOUFETZTUFN $PODMVTJPOT "DLOPXMFEHFNFOUT 0VUMJOF 
  3. ٕज़঺հϏσΦ  *OUSPEVDUJPO

  4.  ۙ೔:PV5VCFʹެ։༧ఆ

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

  6.  ͪ͜Β΋ۙ೔:PV5VCFʹެ։༧ఆ

  7. ͜Ε·Ͱʹߏஙͨ͠Ի੠Ϛϧνεϙοτ࠶ੜγεςϜ .PUJWBUJPO  ͜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
  8. νϟωϧখܕԁܗεϐʔΧΞϨΠͷࢼ࡞ Ͱ͖Δ͚ͩখ͘͞ˠ௚ܘΘ͔ͣDN DIΞϯϓ 3.&%JHJGBDF64#ಉࠝ ɾέʔϒϧΛؚΊͯग़ுσϞՄೳ λϒϨοτͰϚϧνεϙοτ Ի৔ ΛճసՄೳɿԬຊΒɼԻߨ࿦ɼ೥݄ *NQMFNFOUBUJPOPGBDPNQBDUBSSBZ 

    13.44 cm 2.5 cm 3.1 cm <latexit sha1_base64="PjnHn/kBdngue+nAIaVXwZWL0Ys=">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</latexit> 13.44 cm DIΞϯϓ 3.&%JHJGBDF64#ಉࠝ
  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
  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 <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
  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 <latexit sha1_base64="w77DHJ0cpBVEi7ri+sh27w+FFVo=">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</latexit> Hl(rref , m) <latexit sha1_base64="Wy59NiOwY6A1dWR0TPNly4DfzeU=">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</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=">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</latexit> rref = 0.5 m <latexit sha1_base64="LwwKhr9cp+/Jnh0BmV8PGPlW/1o=">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</latexit> 16 ⇥ 72 = 1152 ݸͷ఻ୡؔ਺Λଌఆ
  12.  3FTVMUT (a) 750 Hz (b) 1.5 kHz (c) 3

    kHz (d) 4.5 kHz (e) 6 kHz (f) 7.5 kHz <latexit sha1_base64="VfmioT/LlcjFVadPNw6mS/v2lr8=">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</latexit> rref = 0.5, S = ⇡ and = ⇡/2
  13.  ձ৔ʹ͓͚Δ࣮ػσϞ ঁੑ உੑ DI εϐʔΧ ঁੑ உੑ DI εϐʔΧ

    ೔ຊޠ ӳޠ தࠃޠ ؖࠃޠ DI εϐʔΧ ೔ຊޠ ӳޠ தࠃޠ ؖࠃޠ DI εϐʔΧ  ɿԻݯ ߹੒Ի੠ Իָ Իָ DI εϐʔΧ Իָ Իָ DI εϐʔΧ  ɿԻݯ Իָ ୯७࠶ੜ Ϛϧνεϙοτ࠶ੜ ݴޠχϡʔϥϧ߹੒Ի੠ 7PJDF5SB౥ࡌϞσϧ ϑϦʔίϯςϯπ IUUQTXXXEFMGDPN
  14. νϟωϧখܕԁܗΞϨΠΛ༻͍ͨϚϧνεϙοτ࠶ੜγεςϜͷ࣮૷ ΞϯϓɼέʔϒϧΛؚΊͯϙʔλϒϧԽˠग़ுσϞ͕Մೳ 
 ˠεϐʔΧΞϨΠͷσϞֶ͕ձձ৔ͰͰ͖ΔΑ͏ʹͳͬͨ ଟݴޠχϡʔϥϧԻ੠߹੒Λಋೖͨ͠ݴޠԻ੠ϚϧνεϙοτγεςϜͷ࣮૷ 
 ˠ຋༁͞Ε֤ͨݴޠͷԻ੠͕ͦΕͧΕҧͬͨ৔ॴͰฉ͑͜ΔԻ੠຋༁ͷ৽ͨͳ6*ΛఏҊ ࠓޙͷ՝୊ طଘํࣜͱͷൺֱ ΑΓৄࡉͳԻ৔ܭଌ͕ඞཁ

     ߴԻ࣭ԽˠখܕԽʹಛԽͨͨ͠Ί௿Ҭ )[ҎԼ ͷग़ྗ͕ෆे෼ +45"45&1τϥΠΞ΢τ֫ಘˠߴ඼࣭ԽͷͨΊͷΞϧΰϦζϜɾεϐʔΧͷ։ൃ ଟݴޠ຋༁Ҏ֎ͷల։ ຊٕज़ʹڵຯΛ࣋ͬͨํɼ͝࿈བྷ͍ͩ͘͞ 
 ˠۙ೔ٕज़঺հ)1͓Αͼٕज़঺հಈըˏ:PV5VCFެ։༧ఆ  $PODMVTJPOTBOEGVUVSFXPSL
  15. ֎෦ࢿۚ ຊݚڀͷҰ෦͸+414Պݚඅ+1,͓Αͼ+45 プ ϩ グ ϥϜϚωʔ ジ ϟʔ 1. ͷҭ੒ɾ

    ׆༂ਪਐ プ ϩ グ ϥϜ ࣮ࢪ୅දऀɿ඗ాܒଠ ͷॿ੒Λड͚ͨ΋ͷ で ͋Δ 
 ˠ+45"45&1τϥΠΞ΢τʮԻ੠৴߸ʹ࠷దͳϚϧνεϙοτ࠶ੜεϐʔΧγεςϜͷ։ 
 ɹൃʯ ୅දɿԬຊɼاۀɿ๺೔ຊԻڹɼࢧԉਓࡐɿ඗ా ֫ಘɼ೥݄ΑΓ։࢝ ಺෦࿈ܞ Ի੠Ϛϧνεϙοτ࠶ੜٕज़ͷࣾձల։͸/*$5Πϊ ベ ʔγϣϯ デザ ΠϯΠχγΞςΟ ブ ڞ૑ デザ Πϯ プ ϩ ジ ΣΫτͱͯ͠ߦΘΕɼ プ ϩ ジ ΣΫτϝϯ バ ʔͷ඗ాܒଠࢯɼਢ౻ඒ༏رࢯɼ ܂ݪສබࢯ ໊ڞ/*$5૯߹৬ ʹײँͷҙΛද͢Δ  "DLOPXMFEHFNFOUT