Pre-inverse ᆺ ᆺ ANC ࢩࢫࢸ࣒ࡢ ᥎ᐃ⢭ᗘᨵၿ࡟㛵ࡍࡿ◊✲

Pre-inverse ᆺ ᆺ ANC ࢩࢫࢸ࣒ࡢ ᥎ᐃ⢭ᗘᨵၿ࡟㛵ࡍࡿ◊✲

2017 ᖺ 1 ᭶

኱ᵳ࿴ᚿ

ෆ

ෆᐜ᱾ᴫ

ᮏㄽᩥࡣ㸪Pre-inverse ᆺ࢔ࢡࢸ࢕ࣈࣀ࢖ࢬࢥࣥࢺ࣮ࣟࣝ㸦ANC: Active Noise

Control㸧ࡢ᥎ᐃ⢭ᗘᨵၿᡭἲ࡟ࡘ࠸࡚ᥦ᱌㸪᳨ウࡋࡓ◊✲ᡂᯝࢆࡲ࡜ࡵࡓࡶࡢ࡛

࠶ࡿ㸬ANC ࢩࢫࢸ࣒ࡣ㦁㡢࡟ᑐࡋ㸪ྠ᣺ᖜ࡛㏫఩┦ࡢ␲ఝ㦁㡢ࢆⓎ⏕ࡉࡏࡿࡇ

࡜࡟ࡼࡾே㛫࡟࡜ࡗ࡚୙ᛌ࡛࠶ࡿ㦁㡢ࢆᡴࡕᾘࡍᢏ⾡࡛࠶ࡿ㸬ANCࢩࢫࢸ࣒࡛

ࡼࡃ౑⏝ࡉࢀ࡚࠸ࡿFiltered-x࢔ࣝࢦࣜࢬ࣒ࡣ㸰ḟ⤒㊰ࡢኚື࡟ᑐࡍࡿ㏣ᚑࡀ㐜

࠸ሙྜࡸኚືࡀ኱ࡁ࠸ሙྜࡣࢩࢫࢸ࣒ࡀⓎᩓࡋ࡚ࡋࡲ࠺ၥ㢟ࡀ࠶ࡿ㸬ࡇࡢၥ㢟

ࢆゎỴࡍࡿࡓࡵ࡟Pre-inverseᆺANCࢩࢫࢸ࣒ࡀᥦ᱌ࡉࢀ࡚࠸ࡿࡀ㸰ḟ⤒㊰ࢆ᥎ ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱࡢ᭦᪂࢔ࣝࢦࣜࢬ࣒࡛ồࡵࡿホ౯㛵ᩘࡢ໙㓄࡟እ஘ᡂศࡀ

ྵࡲࢀࡿࡇ࡜࡟ࡼࡾࣂ࢖࢔ࢫࢆᣢࡗࡓㄗᕪ(ࣂ࢖࢔ࢫㄗᕪ)ࡀⓎ⏕ࡋ㸪᥎ᐃ⢭ᗘࡀ

ຎ໬ࡋ࡚ࡋࡲ࠺ၥ㢟ࡀ࠶ࡿ㸬᥎ᐃ⢭ᗘࢆྥୖࡉࡏࡿࡓࡵ࡟ࡣ⏝࠸ࡿ⿵ຓ㞧㡢ࡢ 㟁ຊࢆ኱ࡁࡃࡍࡿᚲせࡀ࠶ࡾ㸪ࡇࡢ⿵ຓ㞧㡢ࡀࢩࢫࢸ࣒඲యࡢ᥎ᐃ⢭ᗘࡢຎ໬

ࢆᘬࡁ㉳ࡇࡋ࡚ࡋࡲ࠺㸬

௨ୖࡢࡼ࠺࡞ᢏ⾡ⓗ⫼ᬒࡢࡶ࡜࡟⾜ࡗࡓ◊✲ࢆࡲ࡜ࡵࡓᮏㄽᩥࡣ㸲❶ࡼࡾ࡞

ࡾ㸪ࡲࡎ㸪➨㸯❶࡛ࡣ㸪ᗎㄽ࡜ࡋ࡚ᮏ◊✲ࢆ⾜࠺࡟⮳ࡗࡓ⫼ᬒ㸪ᚑ᮶ࡢ◊✲ᴫせ㸪 ᮏ◊✲ࡢ┠ⓗ୪ࡧ࡟ྛ❶ࡢᴫせࢆ㏙࡭࡚࠸ࡿ㸬

➨㸰❶࡛ࡣ㸪Pre-inverse ᆺANCࢩࢫࢸ࣒ࡢ㦁㡢㝖ཤᛶ⬟ྥୖࢆ┠ⓗ࡜ࡋ㸪⿵

ຓ㞧㡢ࢆ⏝࠸࡞࠸ Pre-inverse ᆺ ANC ࢩࢫࢸ࣒ࢆᥦ᱌ࡍࡿ㸬Pre-inverse ᆺ ANC ࢩࢫࢸ࣒ࡣ㸰ḟ⤒㊰ࡢ㏫ఏ㐩㛵ᩘࢆ᥎ᐃࡋ㸪ࡑࡢ᥎ᐃ್ࢆ㸰ḟ⤒㊰ࡢ๓ẁ࡟ࣇ

࢕ࣝࢱ࡜ࡋ࡚㓄⨨ࡋ㸪㸰ḟ⤒㊰ࡢไᚚࢆ⾜࠺ࡶࡢ࡛࠶ࡿ㸬㸰ḟ⤒㊰ࡢఏ㐩㛵ᩘࡣ

ࢆ཯㌿ࡋ࡚ࡋࡲ࠺࡜Ⓨᩓࡋ࡚ࡋࡲ࠺ྍ⬟ᛶࡀ࠶ࡿ㸬ࡑࡇ࡛㸪㐺ᛂᣦᩘࣇ࢕ࣝࢱࢆ

⏝࠸ࡿࡇ࡜࡛㸪㸰ḟ⤒㊰ఏ㐩㛵ᩘࡢ᭱ᑠ఩┦㒊࡜᭱኱఩┦㒊ࢆศ㞳ࡋ࡚᥎ᐃࢆ

⾜࠸㸪ࡑࢀࡒࢀࡢ㏫ఏ㐩㛵ᩘࢆồࡵࡿࡇ࡜࡛Pre-inverseᆺANCࢩࢫࢸ࣒ࢆᵓᡂ ࡍࡿ㸬ィ⟬ᶵࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡗ࡚Filtered-x࢔ࣝࢦࣜࢬ࣒࡜ẚ㍑ࢆ⾜࠸ᥦ

᱌ᡭἲࡢ᭷⏝ᛶࢆ☜ㄆࡋ࡚࠸ࡿ㸬

➨㸱❶࡛ࡣ㸪⿵ຓࣇ࢕ࣝࢱ࡟ࡼࡿ㸰ḟ⤒㊰㏫ఏ㐩㛵ᩘ᥎ᐃࢆ⏝࠸ࡿPre-inverse ᆺ ANCࢩࢫࢸ࣒ࢆᥦ᱌ࡍࡿ㸬ᚑ᮶◊✲ࡉࢀ࡚ࡁࡓPre-inverse ᆺANCࡣ㸪㸰ḟ

⤒㊰ࡢఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱࡢ᭦᪂࢔ࣝࢦࣜࢬ࣒࡛ồࡵࡿホ౯㛵ᩘ

ࡢ໙㓄࡟እ஘ᡂศࡀྵࡲࢀࡿࡇ࡜࡟ࡼࡾࣂ࢖࢔ࢫࢆᣢࡗࡓㄗᕪࡀⓎ⏕ࡋ㸪᥎ᐃ

⢭ᗘࡀຎ໬ࡋ࡚ࡋࡲ࠺ၥ㢟ࡀ࠶ࡿ 㸬እ஘࡟ࣟࣂࢫࢺ࡞࢔ࣝࢦࣜࢬ࣒࡜ࡋ࡚

SSCF(Square Sum of Correlation Function)㐺ᛂ࢔ࣝࢦࣜࢬ࣒ࡀᥦ᱌ࡉࢀ࡚࠸ࡿ㸬 SSCF 㐺ᛂ࢔ࣝࢦࣜࢬ࣒ࡣ㦁㡢※࡜㸰ḟ⤒㊰ࢆ᥎ᐃࡍࡿࡓࡵ࡟௜ຍࡍࡿ⿵ຓ㞧 㡢࡜ㄗᕪಙྕࡢ┦஫┦㛵㛵ᩘࢆホ౯㛵ᩘ࡜ࡍࡿࡇ࡜࡟ࡼࡾ㸪እ஘ࡢᙳ㡪ࢆᢚ࠼

ࡓ㸰ḟ⤒㊰᥎ᐃࢆྍ⬟࡜ࡍࡿ㸬ࡋ࠿ࡋ㸪┿ࡢ┦஫┦㛵㛵ᩘࢆィ⟬ࡍࡿࡓࡵ࡟ࡣ㛗

᫬㛫 ᐃࡀᚲせ࡛࠶ࡾ㸪ᐇ⏝ୖࣂ࢖࢔ࢫㄗᕪࢆ᏶඲࡟ᢚᅽࡍࡿࡇ࡜ࡀ࡛ࡁࡎእ

஘ࡢᙳ㡪ࢆཷࡅ࡚ࡋࡲ࠺㸬ࡑࡇ࡛㸪ࡇࡢၥ㢟ࢆゎỴࡍࡿࡓࡵ࡟⿵ຓࣇ࢕ࣝࢱ࡟ࡼ

ࡿ㸰ḟ⤒㊰㏫ఏ㐩㛵ᩘ᥎ᐃࢆ⏝࠸ࡿPre-inverseᆺANCࢩࢫࢸ࣒ࢆᥦ᱌ࡍࡿ㸬ᮏ ᡭἲࡣ㸰ḟ⤒㊰࡟ᑐࡋ࡚⿵ຓࣇ࢕ࣝࢱࢆ୪ิ࡟㓄⨨ࡋࢩࢫࢸ࣒ྠᐃࢆ⾜࠸㸪⿵

ຓࣇ࢕ࣝࢱ࡟ᑐࡋ㸪⦪⥆࡟㸰ḟ⤒㊰ࡢ㏫ఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿࣇ࢕ࣝࢱࢆ㓄⨨ࡍ

ࡿ㸬ࡇࢀ࡟ࡼࡾ㸰ḟ⤒㊰ࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱࡢ᭦᪂࢔ࣝࢦࣜࢬ࣒࡛ồࡵࡿ

ホ౯㛵ᩘࡢ໙㓄࡟እ஘࡟ࡼࡿಙྕᡂศࢆྵࡲ࡞࠸ᅇ㊰ᵓᡂ࡜࡞ࡿࡓࡵ㸪ࣂ࢖࢔

ࢫㄗᕪࡀ⌮ㄽୖⓎ⏕ࡋ࡞࠸㸬ࡇࢀ࡟ࡼࡾ㸰ḟ⤒㊰ࡢ᥎ᐃ࡟౑⏝ࡍࡿ⿵ຓ㞧㡢ࡢ

ㄽ

ㄽᩥ┠ḟ

➨㸯❶ ᗎㄽ ··· 1

1.1 ᮏ◊✲ࡢ⫼ᬒ··· 1

1.2 ◊✲┠ⓗ࡜◊✲ᴫせ ··· 4

➨㸰❶ ⿵ຓ㞧㡢ࢆ⏝࠸࡞࠸ Pre-inverse ᆺ ANC ࢩࢫࢸ࣒

7

2.1 ㅖゝ ··· 7

2.2 ᇶᮏཎ⌮ ··· 9

2.2.1 㸰ḟ⤒㊰ࡢ᥎ᐃ ··· 11

2.2.2 㸯ḟ⤒㊰ࡢ᥎ᐃ ··· 20

2.2.3 㸯ḟ⤒㊰࡜㸰ḟ⤒㊰ྠ᫬᥎ᐃ᫬ࡢၥ㢟Ⅼ ··· 22

2.3 ィ⟬ᶵࢩ࣑࣮ࣗࣞࢩࣙࣥ ··· 23

2.4 ⤖ゝ ··· 29

➨㸱❶ ⿵ຓࣇ࢕ࣝࢱ࡟ࡼࡿ㸰ḟ⤒㊰㏫ఏ㐩㛵ᩘ᥎ᐃࢆ⏝࠸ࡿ Pre-inverse ᆺ ANC ࢩࢫࢸ࣒ 31

3.2 SSCFࢆ⏝࠸ࡓPre-inverseᆺANCࢩࢫࢸ࣒··· 33

3.3 ⿵ຓࣇ࢕ࣝࢱ࡟ࡼࡿ㸰ḟ⤒㊰㏫ఏ㐩㛵ᩘ᥎ᐃࢆ⏝࠸ࡿ Pre-inverseᆺANCࢩࢫࢸ࣒ ··· 39

3.4 ィ⟬ᶵࢩ࣑࣮ࣗࣞࢩࣙࣥ ··· 44

3.4.1 ࢩ࣑࣮ࣗࣞࢩࣙࣥ᮲௳ ··· 44

3.4.2.1 ࢱࢵࣉᩘࡢ᳨ウ ··· 48

3.4.2.2 㐜ᘏᩘz^Mࡢ᳨ウ ··· 49

3.4.3 㸰ḟ⤒㊰ࡢ᥎ᐃ⢭ᗘࡢẚ㍑ ··· 50

3.4.4 㦁㡢పῶᛶ⬟ ··· 52

3.4.5 ₇⟬㔞ࡢẚ㍑ ··· 54

3.5 ᐇ⿦ᐇ㦂 ··· 55

3.5.1 ᐇ⿦᮲௳ ··· 55

3.5.2 ᐇ⿦⤖ᯝ ··· 58

3.6 ⤖ゝ ··· 60

➨ ➨㸲❶ ⤖ㄽ 61

ㅰ㎡ 65

ཧ⪃ᩥ⊩ 67

◊✲ᴗ⦼ 71

ᅗ

ᅗ┠ḟ

ᅗ 2. 1 ⿵ຓ㞧㡢ࢆ⏝࠸࡞࠸Pre-inverseᆺANCࢩࢫࢸ࣒ᵓᡂᅗ ··· 10

ᅗ 2. 2 ⿵ຓ㞧㡢ࢆ⏝࠸࡞࠸Pre-inverseᆺANCࢩࢫࢸ࣒ࡢ㸰ḟ⤒㊰ᵓᡂᅗ 11 ᅗ 2. 3 Hˆ_SMc (z)ᵓᡂᅗ ··· 13

ᅗ 2. 4 Hˆ_SAc (z)ᵓᡂᅗ ··· 14

ᅗ 2. 5 Hˆ_SMc (z)࡜Hˆ_SAc (z)ࡢ᥎ᐃ᫬ࡢಙྕࡢὶࢀ ··· 15

ᅗ 2. 6 s(m)^⟬ฟᅇ㊰ ··· 18

ᅗ 2. 7 s(m)^㸪v(m)^㸪v(mV)^ࡢ㛵ಀ ··· 18

ᅗ 2. 8 㸰ḟ⤒㊰཰᮰᫬ࡢࣈࣟࢵࢡᅗ ··· 21

ᅗ 2. 9 Filtered-x࢔ࣝࢦࣜࢬ࣒ ··· 25

ᅗ 2. 10 ࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝ ··· 28

ᅗ 3. 1 Pre-inverse ᆺANCࡢᵓᡂᅗ ··· 34

ᅗ 3. 2 Hˆ_Sc(z)᥎ᐃ᫬ࡢಙྕࡢὶࢀ ··· 36

ᅗ 3. 3 ⿵ຓࣇ࢕ࣝࢱ࡟ࡼࡿ㸰ḟ⤒㊰㏫ఏ㐩㛵ᩘ᥎ᐃࢆ⏝࠸ࡿ Pre-inverseᆺANCࢩࢫࢸ࣒ ··· 39

ᅗ 3. 4 Hˆ_S(z)᥎ᐃ᫬ࡢಙྕࡢὶࢀ ··· 41

ᅗ 3. 5 Hˆ_Sc(z)᥎ᐃ᫬ࡢಙྕࡢὶࢀ ··· 41

ᅗ 3. 6 ࢲࢡࢺࣔࢹࣝ ··· 44

ᅗ 3. 7 㸯ḟ⤒㊰ࡢ࢖ࣥࣃࣝࢫᛂ⟅ ··· 45

ᅗ 3. 9 ࢱࢵࣉᩘࡢ᳨ウ ··· 48

ᅗ 3.10 㐜ᘏᩘࡢ᳨ウ ··· 49

ᅗ 3.11 㸰ḟ⤒㊰᥎ᐃ⢭ᗘẚ㍑ᵓᡂᅗ ··· 50

ᅗ 3.12 㸰ḟ⤒㊰᥎ᐃ⢭ᗘẚ㍑(ANR=0dB) ··· 51

ᅗ 3.13 㸰ḟ⤒㊰᥎ᐃ⢭ᗘẚ㍑(ANR=-20dB) ··· 51

ᅗ 3.14 ࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝ(ANR=0dB) ··· 53

ᅗ 3.15 ࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝ(ANR=-20dB) ··· 53

ᅗ 3.16 ᐇ⿦ࢩࢫࢸ࣒ᵓᡂ ··· 55

ᅗ 3.17 ᐇ㦂㢼ᬒ ··· 56

ᅗ 3.18 ᾘ㡢ຠᯝ ··· 59

ᅗ 3.19 ᾘ㡢ຠᯝ㸦ࣃ࣮࣡ࢫ࣌ࢡࢺࣝ㸧 ··· 59

⾲┠ḟ

⾲ 2.1 G^*(z)^࡜H_P(z)ࡢタᐃ್ ··· 24

⾲ 2.2 ࢩ࣑࣮ࣗࣞࢩࣙࣥタᐃ್ ··· 26

⾲ 3.1 ࢩ࣑࣮ࣗࣞࢩࣙࣥᐇ㦂タᐃ್ ··· 46

⾲ 3.2 㸯ࢧࣥࣉࣝ࠶ࡓࡾࡢ₇⟬ᅇᩘ ··· 54

⾲ 3.3 ᐇ⿦ࢩࢫࢸ࣒࡛౑⏝ࡋࡓᶵჾ ··· 57

⾲ 3.4 ᐇ⿦ᐇ㦂タᐃ್ ··· 57

୺せグྕ

➨㸰❶

グྕ ព࿡࣭ᐃ⩏

) (n g

) (n p

) (n y

) (n f

) (n d

) ec(n

) (n q

) (n g_Cc

) (z H_P

) (z H_S

) (z H_SM

) (z H_SA

) ˆ (z H_SMc

㦁㡢

㸯ḟ⤒㊰㏻㐣ᚋࡢ㦁㡢 ほ ಙྕ

ไᚚಙྕ

㸰ḟ⤒㊰㏻㐣ᚋࡢไᚚಙྕ

ㄗᕪಙྕ

᭱኱఩┦㒊㏫ࣇ࢕ࣝࢱ㏻㐣ᚋࡢಙྕ

㸰ḟ⤒㊰ࡢධຊಙྕ

㸯ḟ⤒㊰ఏ㐩㛵ᩘ

㸰ḟ⤒㊰ఏ㐩㛵ᩘ

㸰ḟ⤒㊰ఏ㐩㛵ᩘࡢ᭱ᑠ఩┦㒊 㸰ḟ⤒㊰ఏ㐩㛵ᩘࡢ᭱኱఩┦㒊

㸰ḟ⤒㊰᭱ᑠ఩┦㒊㏫ఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿᣦᩘᆺ㐺ᛂ

ࣇ࢕ࣝࢱ

r

> @

E ) ˆ (z H_SAc

M ) (n w_j

E ) (z Q

V ) (n b_q

) ˆ (

, z

H_Oc_SA ) [(m

) (z S

si

) (m s

) (m v

) (z H_T

) ˆ (z H_Cc

F ) (n p_i

*

pi

)

*(z G

*

gi

*

ai

L EV(l)

࣐ࢡ࣮ࣟࣜࣥᒎ㛤㏆ఝ㡯ᩘ

㞟ྜᖹᆒ

㸰ḟ⤒㊰᭱኱఩┦㒊ఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱ )

ˆ (z

H_SAc ࡢࢱࢵࣉᩘ

) ˆ (z

H_SAc ࡢࢱࢵࣉಀᩘ

) ˆ (z

H_SAc ᭦᪂࢔ࣝࢦࣜࢬ࣒ࡢࢫࢸࢵࣉࢧ࢖ࢬ

᭱኱఩┦㒊㏫ࣇ࢕ࣝࢱ )

(z

Q ࡢࢱࢵࣉᩘ

) (z

Q ࡢࢱࢵࣉಀᩘ

᥎ᐃᚋࡢHˆ_SAc (z)ఏ㐩㛵ᩘ

) (z

Q ⟬ฟࡍࡿࡓࡵࡢኚ᥮ࣇ࢕ࣝࢱ )

(z

S ࡢࢱࢵࣉಀᩘ

) (z

S ^ࡢ㏫zኚ᥮

) (z¹

S ࡢ㏫zኚ᥮

㏫ࣇ࢕ࣝࢱ࡜㸰ḟ⤒㊰ࡢྜᡂఏ㐩㛵ᩘ

㸯ḟ⤒㊰ఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱ )

ˆ (z

H_Cc ࡢࢱࢵࣉᩘ

) ˆ (z

H_Cc ࡢࢱࢵࣉಀᩘ

) (z

H_P ࡢࢱࢵࣉಀᩘ

) (z

H_SM ࢆᵓᡂࡍࡿࢺࣛࣥࢫࣂ࣮ࢧࣝᆺࣇ࢕ࣝࢱ )

*(z

G ࡢࢱࢵࣉಀᩘ

) (z

H_SA ࡢࢱࢵࣉಀᩘ

ࣈࣟࢵࢡ㛗 ホ౯㛵ᩘ

➨㸱❶

グྕ ព࿡࣭ᐃ⩏

) (z H_P

) (z H_S

) ˆ (z H_C

) ˆ (z H_Sc

) (n g

) (n p

) (n y

) (n w

) (n f

) (n d

) (n ec

NC

) ˆ (

, n

h_Ci PC

PSc )

~(n w

)

~( n f

M x P P

㸯ḟ⤒㊰ఏ㐩㛵ᩘ

㸰ḟ⤒㊰ఏ㐩㛵ᩘ

㸯ḟ⤒㊰ఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱ 㸰ḟ⤒㊰㏫ఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱ 㦁㡢

㸯ḟ⤒㊰㏻㐣ᚋࡢ㦁㡢 ほ ಙྕ

⿵ຓ㞧㡢 ไᚚಙྕ

㸰ḟ⤒㊰㏻㐣ᚋࡢไᚚಙྕ

ㄗᕪಙྕ

) ˆ (z

H_C ࡢࢱࢵࣉᩘ

) ˆ (z

H_C ࡢࢱࢵࣉಀᩘ

) ˆ (z

H_Sc ᭦᪂࢔ࣝࢦࣜࢬ࣒ࡢࢫࢸࢵࣉࢧ࢖ࢬ )

ˆ (z

H_C ᭦᪂࢔ࣝࢦࣜࢬ࣒ࡢࢫࢸࢵࣉࢧ࢖ࢬ 㸰ḟ⤒㊰㏻㐣ᚋࡢw(n)

㸰ḟ⤒㊰㏻㐣ᚋࡢf(n) 㐜ᘏᩘ

᫬㛫ᖹᆒ

SSCF࢔ࣝࢦࣜࢬ࣒ࡢࢫࢸࢵࣉࢧ࢖ࢬ

┦㛵㛵ᩘィ⟬⠊ᅖ

P

ANR EV(l) EA(l) )

3(n e

) (l P_Y

) ˆ (z

H_S ᭦᪂࢔ࣝࢦࣜࢬ࣒ࡢࢫࢸࢵࣉࢧ࢖ࢬ

⿵ຓ㞧㡢ᑐ㦁㡢㟁ຊẚ

⿵ຓ㞧㡢ࡢᙳ㡪ࢆ㝖࠸ࡓ㦁㡢ᡴᾘࡋ⢭ᗘ

⿵ຓ㞧㡢ࡢᙳ㡪ࢆྵࡴ㦁㡢ᡴᾘࡋ⢭ᗘ 㸰ḟ⤒㊰᥎ᐃㄗᕪ

ᖹᆒฟຊ㟁ຊ

➨ 1 ❶

ᗎㄽ

1.1 ᮏ◊✲ࡢ⫼ᬒ

⚾㐩ࡢ᪥ᖖ⏕ά࡟㡢ࡣᐦ᥋࡞⧅ࡀࡾࡀ࠶ࡿ㸬㡢ᴦࡢࡼ࠺࡞ᚰᆅࡼ࠸㡢ࡔࡅ࡛

࡞ࡃ㸪᫬࡟୙ᛌ࡟ឤࡌࡿ㦁㡢࡜ࡋ࡚⏕άࡢጉࡆ࡜࡞ࡗ࡚ࡋࡲ࠺౛ࡶ࠶ࡿ㸬୍⯡⏕

ά࡟࠾࠸࡚㸪㏆㞄ఫẸ࡜ࡢࢺࣛࣈࣝࡢཎᅉࡢ㸯఩ࡀ⏕ά㦁㡢࡛࠶ࡿ࡜ࡢሗ࿌ࡀ

࠶ࡿ[1]㸬ࡲࡓ㸪ᕤሙࡸ஦ᴗᡤ࠿ࡽⓎ⏕ࡍࡿ㦁㡢ࡣ㦁㡢つไἲࡸྛ⮬἞యࡢ᮲౛

࡟ࡼࡗ࡚ཝࡋࡃไ㝈ࡉࢀ࡚࠾ࡾ㸪ࡲࡓ⎔ቃᇶ‽ἲ➨஧᮲࡛ࡣ㦁㡢ࡣබᐖ࡜ࡋ࡚

ྲྀࡾᢅࢃࢀ࡚࠸ࡿ࡯࡝࡛࠶ࡿ㸬㦁㡢ࡢၥ㢟ࡣே㛫ࡢ⪥࡛⪺ࡇ࠼ࡿྍ⫈ᖏᇦ㡢ࡢ

ࡳࡢၥ㢟࡛ࡣ࡞࠸㸬㏆ᖺ㸪෌⏕ྍ⬟࢚ࢿࣝࢠ࣮࡜ࡋ࡚ὀ┠ࢆᾎࡧ࡚࠸ࡿ㢼ຊⓎ㟁 ᶵ࠿ࡽⓎ⏕ࡍࡿ㢼ษࡾ㡢ࡸ᣺ື➼ࡢప࿘Ἴ㡢࡟ࡼࡗ࡚㸪▱ࡽࡎ▱ࡽࡎࡢ࠺ࡕ࡟

೺ᗣ⿕ᐖࢆ⿕ࡗ࡚ࡋࡲ࠺౛ࡀ࠶ࡿ㸬ࡲࡓ㸪㦁㡢ࡀ୙ᛌ࡛࠶ࡿࡇ࡜ࢆ㏫ᡭ࡟࡜ࡾ㸪

⪥㞀ࡾ࡛࠶ࡿ㧗࿘Ἴ㡢ࢆࢃࡊ࡜Ⓨࡍࡿࡇ࡜࡟ࡼࡾ㸪῝ኪࡢබᅬタഛࡢ◚ᦆ⾜Ⅽ 㜵Ṇࡢᑐ⟇࡜ࡋ࡚⮬἞యࡀྲྀࡾ⤌ࢇ࡛࠸ࡿ౛ࡶ࠶ࡿ[2]㸬

ே㛫࡟࡜ࡗ࡚୙ᛌ࡛࠶ࡿ㦁㡢ࢆゎỴࡍࡿࡓࡵ࡟㸪ᚑ᮶࠿ࡽ྾㡢ᮦ࡞࡝ࢆ౑⏝

ࡋࡓཷື㦁㡢ไᚚ(PNC : Passive Noise Control)ࡢᢏ⾡ࡀࡼࡃ⏝࠸ࡽࢀ࡚ࡁࡓ㸬ࡋ

࡞ࡿࡓࡵࢥࢫࢺࡢၥ㢟ࡸ᪤Ꮡ᪋タ࡬ࡢタ⨨ሙᡤࡢၥ㢟ࡀ࠶ࡿ㸬PNC ࡟ᑐࡋ㸪㐺 ᛂࣇ࢕ࣝࢱ(ADF : Adaptive Digital Filter)[3]ࢆ⏝࠸ࡓᾘ㡢ᢏ⾡࡜ࡋ࡚⬟ື㦁㡢ไ ᚚ(ANC : Active Noise Control)ࡀ࠶ࡿ[4]㸬ࡇࡢᢏ⾡ࡣ㦁㡢࡟ᑐࡋ㸪ྠ᣺ᖜ࡛㏫఩

┦ࡢ␲ఝ㦁㡢ࢆⓎ⏕ࡉࡏࡿࡇ࡜࡟ࡼࡾ㦁㡢ࢆᡴࡕᾘࡍᢏ⾡࡛࠶ࡿ㸬ANC ࢩࢫࢸ

࣒࡟ࡣཧ↷࣐࢖ࢡࣟ࣍ࣥ࠿ࡽྲྀᚓࡋࡓ㦁㡢ಙྕ࡜ㄗᕪ࣐࢖ࢡࣟ࣍ࣥ࠿ࡽྲྀᚓࡋ ࡓ␲ఝ㦁㡢ࢆࡪࡘࡅࡓᚋࡢㄗᕪಙྕࡀධຊࡉࢀ㸪₇⟬ࢆ⾜࠸ᾘ㡢ࢫࣆ࣮࢝࠿ࡽ

␲ఝ㦁㡢ࢆⓎ⏕ࡉࡏ࡚ㄗᕪಙྕࡀᑠࡉࡃ࡞ࡿࡼ࠺࡟ືసࡍࡿ㸬 ANCࢆᐇ⌧ࡍࡿ

࡟ࡣ㸪」㞧࡞ࢹ࢕ࢪࢱࣝಙྕฎ⌮ࡀᚲせ࡛࠶ࡿࡀ㸪㏆ᖺࡢ༙ᑟయᢏ⾡ࡢ㐍Ṍ࡟ࡼ

ࡗ࡚㸪MPU(Micro Processing Unit)ࡢฎ⌮ᛶ⬟ࡢྥୖ㸪ᑠᆺ໬㸪పᾘ㈝㟁ຊ໬㸪ప

౯᱁໬ࡀ㐍⾜ࡋ㸪ࢹ࢕ࢪࢱࣝࢩࢢࢼࣝࣉࣟࢭࢵࢧ(DSP : Digital Signal Processor) ࡀᬑཬࡉࢀࡓࡇ࡜࡟ࡼࡾᐇ⏝ⓗ࡞ᢏ⾡࡜࡞ࡗ࡚ࡁ࡚࠸ࡿ㸬≉࡟ࢫࢸࣞ࢜࣊ࢵࢻ

࣍ࣥࡣࣀ࢖ࢬ࢟ࣕࣥࢭࣝᶵ⬟ࡀᦚ㍕ࡉࢀࡓ〇ရࡀᩘከࡃᕷ㈍ࡉࢀ࡚࠸ࡿ㸬ࡓࡔ ࡋ㸪࣊ࢵࢻ࣍ࣥ࡟ࡘ࠸࡚ࡣᑠࡉ࡞✵㛫࡛ືసࡍࡿࡓࡵ⤒㊰ࡢ㡢㡪≉ᛶࢆ⪃៖ࡋ

࡞ࡃ࡚ࡶືసྍ⬟࡛࠶ࡿࡀ㸪ᕤሙ➼࡟タ⨨ࡋࡓ᫬ࡢࡼ࠺࡞኱ࡁ࡞✵㛫࡛ࡣཧ↷

࣐࢖ࢡࣟ࣍ࣥ࠿ࡽㄗᕪ࣐࢖ࢡࣟ࣍ࣥࡲ࡛ࡢ⤒㊰(㸯ḟ⤒㊰)ࡸᾘ㡢ࢫࣆ࣮࢝࠿ࡽ

ㄗᕪ࣐࢖ࢡࣟ࣍ࣥࡲ࡛ࡢ⤒㊰(㸰ḟ⤒㊰)ࡢ≉ᛶࢆ⪃៖ࡋ࡚ANC ࢩࢫࢸ࣒ࢆᵓ⠏

ࡍࡿᚲせࡀ࠶ࡿ㸬

㸯ḟ⤒㊰࡜㸰ḟ⤒㊰ࢆ⪃៖ࡍࡿᚲせࡀ࠶ࡿANCࢩࢫࢸ࣒࡛ࡣࣇ࢕࣮ࢻࣇ࢛࣡

࣮ࢻไᚚࡢ㐺ᛂ࢔ࣝࢦࣜࢬ࣒࡜ࡋ࡚Filtered-x࢔ࣝࢦࣜࢬ࣒ࡀࡼࡃ౑⏝ࡉࢀ࡚࠸

ࡿ[6] - [8]㸬ࡋ࠿ࡋ㸪Filtered-x࢔ࣝࢦࣜࢬ࣒ࡣ㸰ḟ⤒㊰ࡢ≉ᛶࡢኚື࡟ࡼࡗ࡚ࣔ

ࢹࣝ໬ㄗᕪࡀⓎ⏕ࡋไᚚᛶ⬟ࡢຎ໬ࡸᏳᐃᛶ࡟኱ࡁ࡞ᙳ㡪ࢆ୚࠼ࡿ[9]㸬ࡇࡢࣔ

ࢹࣝ໬ㄗᕪࢆゎᾘࡍࡿࡓࡵ࡟⿵ຓ㞧㡢ὀධἲ[10] - [14]ࡀ࠶ࡿࡀ㸪㸰ḟ⤒㊰ࡢ≉

࠶ࡿ㸬ࡇࢀ࡟ࡼࡾไᚚࣇ࢕ࣝࢱࡢ㐺ᛂ࢔ࣝࢦࣜࢬ࣒࡟⏝࠸ࡿධຊಙྕ࡜ࡋ࡚㸪㸰 ḟ⤒㊰ࡢఏ㐩㛵ᩘࢆ᭷ࡍࡿࣇ࢕ࣝࢱࡢ௦ࢃࡾ࡟ᐃ㐜ᘏࢆస⏝ࡉࡏࡓಙྕࢆ⏝࠸

ࡿࡇ࡜ࡀྍ⬟࡜࡞ࡾ㸪୙Ᏻᐃᛶࢆゎᾘࡍࡿ㸬ࡋ࠿ࡋ㸪 Pre-inverseᆺANCࢩࢫࢸ

࣒࡛ࡣ㸰ḟ⤒㊰ࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱࡢ᭦᪂࢔ࣝࢦࣜࢬ࣒࡛ồࡵࡿホ౯㛵ᩘ

ࡢ໙㓄࡟እ஘ᡂศࡀྵࡲࢀࡿࡇ࡜࡟ࡼࡾࣂ࢖࢔ࢫࢆᣢࡗࡓㄗᕪࡀⓎ⏕ࡋ㸪᥎ᐃ

⢭ᗘࡀຎ໬ࡋ࡚ࡋࡲ࠺ၥ㢟ࡀ࠶ࡿ㸬᥎ᐃ⢭ᗘࢆྥୖࡉࡏࡿࡓࡵ࡟ࡣ⏝࠸ࡿ⿵ຓ

㞧㡢ࡢ㟁ຊࢆ኱ࡁࡃࡍࡿᚲせࡀ࠶ࡾ㸪ࡇࡢ⿵ຓ㞧㡢ࡀࢩࢫࢸ࣒඲యࡢ㦁㡢ᡴᾘ ࡋᛶ⬟ࡢຎ໬ࢆᘬࡁ㉳ࡇࡋ࡚ࡋࡲ࠺㸬ࡇࡢࡼ࠺࡞ၥ㢟ࢆゎỴࡍࡿࡓࡵ࡟⿵ຓ㞧 㡢ࢆ๐ῶࡍࡿ᪂ࡓ࡞ᡭἲࡀồࡵࡽࢀ࡚࠸ࡿ㸬

1.2 ◊ ◊✲┠ⓗ࡜◊✲ᴫせ

๓⠇࡛㏙࡭ࡓࡼ࠺࡞ᢏ⾡ⓗ⫼ᬒࡢࡶ࡜࡟㸪ᮏㄽᩥ࡛ࡣ㸪㦁㡢ၥ㢟ࢆゎỴࡍࡿࡓ

ࡵࡢᡭẁ࡜ࡋ࡚Pre-inverseᆺANCࢩࢫࢸ࣒ࡢ᥎ᐃ⢭ᗘᨵၿࢆ┠ⓗ࡜ࡋ࡚◊✲ࢆ

⾜ࡗࡓ㸬

➨㸰❶࡛ࡣ㸪ࢩࢫࢸ࣒඲యࡢ᥎ᐃ⢭ᗘຎ໬ࢆᘬࡁ㉳ࡇࡍཎᅉ࡜࡞ࡿ⿵ຓ㞧㡢

ࢆ⏝࠸࡞࠸Pre-inverseᆺANCࢩࢫࢸ࣒[21]ࢆᥦ᱌ࡍࡿ㸬Pre-inverseᆺANCࢩࢫ ࢸ࣒ࢆᵓᡂࡍࡿ࡟࠶ࡓࡾ㸪㸰ḟ⤒㊰ࡢ㏫ఏ㐩㛵ᩘࢆồࡵࡿᚲせࡀ࠶ࡿࡀ㸪㸰ḟ⤒

㊰ࡢఏ㐩㛵ᩘࡣ᭱ᑠ఩┦⣔࡜ࡣ㝈ࡽ࡞࠸ࡓࡵ㸪༢⣧࡟㸰ḟ⤒㊰ࡢఏ㐩㛵ᩘࢆ᥎ ᐃࡋ࡚ศẕศᏊࢆ཯㌿ࡋ࡚ࡋࡲ࠺࡜Ⓨᩓࡋ࡚ࡋࡲ࠺ྍ⬟ᛶࡀ࠶ࡿ㸬ࡑࡇ࡛㸪㐺ᛂ ᣦᩘࣇ࢕ࣝࢱࢆ⏝࠸ࡿࡇ࡜࡛㸪㸰ḟ⤒㊰ఏ㐩㛵ᩘࡢ᭱ᑠ఩┦㒊࡜᭱኱఩┦㒊ࢆ

ศ㞳ࡋ࡚᥎ᐃࢆ⾜࠸㸪ࡑࢀࡒࢀࡢ㏫ఏ㐩㛵ᩘࢆồࡵࡿࡇ࡜࡛Pre-inverseᆺANC

ࢆᵓᡂࡍࡿ㸬ィ⟬ᶵࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟ࡼࡗ࡚Filtered-x࢔ࣝࢦࣜࢬ࣒࡜ẚ㍑ࢆ

⾜࠸ᥦ᱌ᡭἲࡢ᭷⏝ᛶࢆ☜ㄆࡋ࡚࠸ࡿ㸬

➨㸱❶࡛ࡣ㸪ᚑ᮶◊✲ࡉࢀ࡚ࡁࡓPre-inverseᆺANC࡟࠾࠸࡚㸰ḟ⤒㊰ࡢఏ㐩 㛵ᩘࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱࡢ᭦᪂࢔ࣝࢦࣜࢬ࣒࡛ồࡵࡿホ౯㛵ᩘࡢ໙㓄࡟እ

஘ᡂศࡀྵࡲࢀࡿࡇ࡜࡟ࡼࡾࣂ࢖࢔ࢫࢆᣢࡗࡓㄗᕪࡀⓎ⏕ࡋ㸪᥎ᐃ⢭ᗘࡀຎ໬

ࡍࡿၥ㢟࡟╔┠ࡋ㸪ࣂ࢖࢔ࢫㄗᕪࡀ⌮ㄽୖⓎ⏕ࡋ࡞࠸ᡭἲࢆᥦ᱌ࡍࡿ[22],[23]㸬 እ஘࡟ࣟࣂࢫࢺ࡞࢔ࣝࢦࣜࢬ࣒࡜ࡋ࡚ SSCF(Square Sum of Correlation Function) 㐺ᛂ࢔ࣝࢦࣜࢬ࣒ࡀᥦ᱌ࡉࢀ࡚࠸ࡿ[15]㸬SSCF 㐺ᛂ࢔ࣝࢦࣜࢬ࣒ࡣ㦁㡢※࡜㸰

࡜ࡀ࡛ࡁࡎእ஘ࡢᙳ㡪ࢆཷࡅ࡚ࡋࡲ࠺㸬ࡑࡇ࡛㸪ࡇࡢၥ㢟ࢆゎỴࡍࡿࡓࡵ࡟⿵ຓ

ࣇ࢕ࣝࢱ࡟ࡼࡿ㸰ḟ⤒㊰㏫ఏ㐩㛵ᩘ᥎ᐃࢆ⏝࠸ࡿPre-inverseᆺANCࢩࢫࢸ࣒ࢆ

ᥦ᱌ࡍࡿ[19],[20]㸬ᮏᡭἲࡣ㸰ḟ⤒㊰࡟ᑐࡋ࡚⿵ຓࣇ࢕ࣝࢱࢆ୪ิ࡟㓄⨨ࡋࢩࢫ

ࢸ࣒ྠᐃࢆ⾜࠸㸪⿵ຓࣇ࢕ࣝࢱ࡟ᑐࡋ㸪⦪⥆࡟㸰ḟ⤒㊰ࡢ㏫ఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿ

ࣇ࢕ࣝࢱࢆ㓄⨨ࡍࡿ㸬ࡇࢀ࡟ࡼࡾ㸰ḟ⤒㊰ࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱࡢ᭦᪂࢔ࣝ

ࢦࣜࢬ࣒࡛⏝࠸ࡿホ౯㛵ᩘࡢ໙㓄࡟㸪እ஘࡟ࡼࡿಙྕᡂศࡀྵࡲࢀ࡞ࡃ࡞ࡿࡓ

ࡵ㸪ࣂ࢖࢔ࢫㄗᕪࡀ⌮ㄽୖⓎ⏕ࡋ࡞࠸㸬ᚑࡗ࡚㸰ḟ⤒㊰ࡢ᥎ᐃ࡟౑⏝ࡍࡿ⿵ຓ㞧 㡢ࡢ㟁ຊࢆపῶࡉࡏࡿࡇ࡜ࡀྍ⬟࡜࡞ࡾ㸪ࢩࢫࢸ࣒඲యࡢᾘ㡢ᛶ⬟ࢆྥୖࡉࡏ

ࡿࡇ࡜ࡀྍ⬟࡜࡞ࡿ㸬ࢩ࣑࣮ࣗࣞࢩࣙࣥᐇ㦂࡛ᚑ᮶ἲ࡜ࡢẚ㍑ࢆ⾜࠸㸪ࡲࡓ㸪ᐇ

⿦ᐇ㦂ࢆ⾜࠺ࡇ࡜࡟ࡼࡾᥦ᱌ᡭἲࡀᐇ⎔ቃୗ࡛ືసྍ⬟࡛࠶ࡿࡇ࡜ࢆ☜ㄆࡋ࡚

࠸ࡿ㸬

᭱ᚋ࡟➨㸲❶࡛ࡣ㸪ࡇࢀࡲ࡛࡟ᚓࡓᡂᯝࢆ⤫ᣓࡋ㸪௒ᚋ࡟ṧࡉࢀࡓㄢ㢟ࢆᣦ᦬

ࡋ࡚࠸ࡿ㸬

➨

➨ 2 ❶

⿵ຓ㞧㡢ࢆ⏝࠸࡞࠸ Pre-inverse ᆺ ANC ࢩࢫࢸ࣒

2.1 ⥴ゝ

⌧ᅾ㸪ANC ࢩࢫࢸ࣒࡛ࡣࣇ࢕࣮ࢻࣇ࢛࣮࣡ࢻᆺࡢ㐺ᛂ࢔ࣝࢦࣜࢬ࣒࡜ࡋ࡚

Filtered-x࢔ࣝࢦࣜࢬ࣒ࡀࡼࡃ⏝࠸ࡽࢀ࡚࠸ࡿ[6] - [8]㸬Filtered-x࢔ࣝࢦࣜࢬ࣒ࡣ 㸰ḟ㡢※ࢆⓎࡍࡿࢫࣆ࣮࢝࠿ࡽᾘ㡢ຠᯝࡢほ ࡟⏝࠸ࡿㄗᕪ᳨ฟ࣐࢖ࢡࣟ࣍ࣥ

ࡲ࡛ࡢ㡢㡪⣔(㸰ḟ⤒㊰)ࡢఏ㐩㛵ᩘࢆ஦๓࡟᥎ᐃࡋ㸪ࡑࡢ≉ᛶࢆ᭷ࡍࡿࣇ࢕ࣝࢱ

࡟㦁㡢ࢆ㏻㐣ࡉࡏࡓಙྕࢆไᚚࣇ࢕ࣝࢱ࡛࠶ࡿ㐺ᛂࣇ࢕ࣝࢱ(ADF : Adaptive

Digital Filter)ࡢࢱࢵࣉධຊ࡜ࡋ࡚⏝࠸ࡿ㸬ࡋ࠿ࡋ㸪ࡇࡢ஦๓࡟᥎ᐃࡋࡓ㸰ḟ⤒㊰

ࡢఏ㐩㛵ᩘࡀኚືࡍࡿࡇ࡜࡟ࡼࡾࣔࢹࣝ໬ㄗᕪࡀ⏕ࡌࡿ㸬ࡇࡢࣔࢹࣝ໬ㄗᕪࡣ ANC ࢩࢫࢸ࣒ࡢไᚚᛶ⬟ࡢຎ໬ࢆᘬࡁ㉳ࡇࡍࡔࡅ࡛࡞ࡃ㸪Ᏻᐃᛶ࡟኱ࡁ࡞ᙳ㡪

ࢆ୚࠼ࡿ[9]㸬ࡑࡇ࡛㸪ࣔࢹࣝ໬ㄗᕪࢆ㍍ῶࡍࡿࡓࡵ㸪㸰ḟ⤒㊰ࡢኚື࡟㏣ᚑࡍࡿ

ᡭἲ࡜ࡋ࡚࢜ࣥࣛ࢖࡛ࣥ㸰ḟ⤒㊰᥎ᐃࢆ⾜࠺⿵ຓ㞧㡢ὀධἲࡀ࠶ࡿ[10] - [14]㸬

⿵ຓ㞧㡢ὀධἲࡣไᚚࣇ࢕ࣝࢱࡢฟຊಙྕ࡟పࣞ࣋ࣝࡢᗈᖏᇦ⿵ຓಙྕࢆ௜ຍ ࡍࡿࡇ࡜࡟ࡼࡾไᚚືస୰࡟㸰ḟ⤒㊰ࡢఏ㐩㛵ᩘࡢ᥎ᐃࢆ⾜࠺㸬ࡋ࠿ࡋ࡞ࡀࡽ㸪

ࡇࡢᡭἲ࡛ࡣ㸰ḟ⤒㊰ࡢኚື࡟㏣ᚑࡍࡿࡇ࡜ࡣྍ⬟࡛࠶ࡿࡀ㸪㏣ᚑࡀ㐜࠸ሙྜ

ࡸ⤒㊰ኚືࡀ኱ࡁ࠸ሙྜ࡟ࢩࢫࢸ࣒ࡀⓎᩓࡋ࡚ࡋࡲ࠺ྍ⬟ᛶࡀ࠶ࡿ㸬

ࡑࡇ࡛㸪Filtered-x࢔ࣝࢦࣜࢬ࣒ࢆ౑⏝ࡋ࡞࠸ ANCࢩࢫࢸ࣒࡜ࡋ࡚Pre-inverse ᆺANCࢩࢫࢸ࣒ࡀᥦ᱌ࡉࢀ࡚ࡁࡓ[15]㸬Pre-inverseᆺANCࢩࢫࢸ࣒ࡣ㸰ḟ⤒㊰

ࡢ㏫ఏ㐩㛵ᩘࢆ᥎ᐃࡋ㸪ࡑࡢ᥎ᐃ್ࢆ㸰ḟ⤒㊰ࡢ๓ẁ࡟ࣇ࢕ࣝࢱ࡜ࡋ࡚㓄⨨ࡋ㸪 㸰ḟ⤒㊰ࡢไᚚࢆ⾜࠺ࡶࡢ࡛࠶ࡿ㸬ࡇࢀ࡟ࡼࡾ㦁㡢ไᚚࣇ࢕ࣝࢱࡣ㸯ḟ⤒㊰ࡢ

ࡳࢆ୪ิᆺࢩࢫࢸ࣒ྠᐃ࡜ࡋ࡚᥎ᐃࡍࢀࡤࡼ࠸㸬ࡘࡲࡾ㸪Pre-inverse ᆺANCࢩ ࢫࢸ࣒ࡣ㸪㦁㡢ไᚚࣇ࢕ࣝࢱࡢ㐺ᛂ࢔ࣝࢦࣜࢬ࣒࡟⏝࠸ࡿධຊಙྕ࡜ࡋ࡚㸪㸰ḟ

⤒㊰ࡢఏ㐩㛵ᩘࢆ᭷ࡍࡿࣇ࢕ࣝࢱࡢ௦ࢃࡾ࡟ᐃ㐜ᘏࢆస⏝ࡉࡏࡓಙྕࢆ⏝࠸ࡿ

ࡇ࡜࡟ࡼࡾ㸪୙Ᏻᐃᛶࢆゎᾘࡍࡿ㸬ࡋ࠿ࡋ㸪Pre-inverse ᆺANCࢩࢫࢸ࣒࡛ࡣ㸰 ḟ⤒㊰ࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱࡢ᭦᪂࢔ࣝࢦࣜࢬ࣒࡛ồࡵࡿホ౯㛵ᩘࡢ໙㓄࡟

እ஘ᡂศࡀྵࡲࢀࡿࡇ࡜࡟ࡼࡾࣂ࢖࢔ࢫࢆᣢࡗࡓㄗᕪ㸦௨ୗ㸪ࣂ࢖࢔ࢫㄗᕪ࡜࿧

ࡪ㸧ࡀⓎ⏕ࡋ㸪᥎ᐃ⢭ᗘࡀຎ໬ࡋ࡚ࡋࡲ࠺ၥ㢟ࡀ࠶ࡿ㸬᥎ᐃ⢭ᗘࢆྥୖࡉࡏࡿࡓ

ࡵ࡟ࡣ⏝࠸ࡿ⿵ຓ㞧㡢ࡢ㟁ຊࢆ኱ࡁࡃࡍࡿᚲせࡀ࠶ࡾ㸪ࡇࡢ⿵ຓ㞧㡢ࡀࢩࢫࢸ

࣒඲యࡢ᥎ᐃ⢭ᗘࡢຎ໬ࢆᘬࡁ㉳ࡇࡋ࡚ࡋࡲ࠺㸬

ᮏ❶࡛ࡣ㸪ࡇࡢࢩࢫࢸ࣒඲యࡢ᥎ᐃ⢭ᗘຎ໬ࢆᘬࡁ㉳ࡇࡍཎᅉ࡜࡞ࡿ⿵ຓ㞧 㡢ࢆ౑⏝ࡋ࡞࠸Pre-inverseᆺANCࢩࢫࢸ࣒ࢆᥦ᱌ࡍࡿ㸬ࡑࡋ࡚㸪ィ⟬ᶵࢩ࣑ࣗ

࣮ࣞࢩࣙࣥᐇ㦂ࢆ⾜࠸ᥦ᱌ᡭἲࡢ᭷ຠᛶࢆ☜ㄆࡍࡿ㸬

2.2 ᇶ ᇶᮏཎ⌮

ᮏ⠇࡛ࡣ⿵ຓ㞧㡢ࢆ౑⏝ࡋ࡞࠸Pre-inverseᆺANCࢩࢫࢸ࣒ࡢᇶᮏཎ⌮࡟ࡘ࠸

࡚ㄝ᫂ࡍࡿ㸬 ᅗ 2. 1࡟ᮏࢩࢫࢸ࣒ࡢᵓᡂࢆ♧ࡍ㸬ྛಙྕࢆ௨ୗ࡟♧ࡍ㸬

) (n

g _㸸㦁㡢

) (n

p 㸸㸯ḟ⤒㊰㏻㐣ᚋࡢ㦁㡢 )

(n

y _{㸸ほ ಙྕ}

) (n

f _{㸸ไᚚಙྕ}

) (n

d 㸸㸰ḟ⤒㊰㏻㐣ᚋࡢไᚚಙྕ

)

ec(n _{ࡣ㐺ᛂࣇ࢕ࣝࢱH}^ˆ_{SMc (z)㸪H}^ˆ_{SAc (z)}ࡢ㐺ᛂ࢔ࣝࢦࣜࢬ࣒᭦᪂ࡢࡓࡵࡢㄗᕪಙ

ྕ࡛࠶ࡿ㸬

ᅗ 2. 1 ⿵ຓ㞧㡢ࢆ⏝࠸࡞࠸Pre-inverseᆺANCࢩࢫࢸ࣒ᵓᡂᅗ ( )

LMS

( ) Q( )

g( )

( ) ( )

( )

g′ ( ) ( ) _{( )}

LMS

( ) 㞧㡢※

( ) ′ ( )

ཧ↷䝬䜲䜽 ㄗᕪ䝬䜲䜽

஧ḟ㡢※

LMS ( )

′ ( )

( )

′( ) ( )

( )

′( )

2.2.1 㸰㸰ḟ⤒㊰ࡢ᥎ᐃ

ᮏ⠇࡛ࡣ⿵ຓ㞧㡢ࢆ⏝࠸࡞࠸Pre-inverseᆺANCࢩࢫࢸ࣒ࡢ㸰ḟ⤒㊰ࡢ᥎ᐃ࡟

ࡘ࠸࡚ㄝ᫂ࡍࡿ㸬ᅗ 2. 2ࡣᥦ᱌ᡭἲࡢᵓᡂᅗ࡛࠶ࡿᅗ 2. 1࠿ࡽ㸰ḟ⤒㊰ࢆᢳฟ ࡋࡓᅗ࡛࠶ࡿ㸬

ᅗ 2. 2 ⿵ຓ㞧㡢ࢆ⏝࠸࡞࠸Pre-inverseᆺANCࢩࢫࢸ࣒ࡢ㸰ḟ⤒㊰ᵓᡂᅗ

( )

Q( )

( )

g′ ( )

( )

( )

LMS ′( ) ′ ( )

ㄗᕪ䝬䜲䜽

஧ḟ㡢※

′ ( )

LMS

㸰ḟ⤒㊰ࡢఏ㐩㛵ᩘH_S(z)ࡣ୍⯡ⓗ࡟᭱኱఩┦㒊࡜᭱ᑠ఩┦㒊࡟ศࡅࡿࡇ࡜

ࡀྍ⬟࡛࠶ࡾ㸪ḟᘧ࡛⾲ࡉࢀࡿ㸬

) ( ) ( )

(z H z H z

H_{S SM SA} ^㸦 2.1 㸧

ࡇࡇ࡛㸪H_SM(z)^㸪H_SA(z)ࡣࡑࢀࡒࢀ㸰ḟ⤒㊰ࡢ᭱ᑠ఩┦㒊㸪᭱኱఩┦㒊ࡢఏ㐩 㛵ᩘ࡛࠶ࡿ㸬㸰ḟ⤒㊰ࡢ᭱ᑠ఩┦㒊ࡢ㏫ఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿᣦᩘᆺ㐺ᛂࣇ࢕ࣝ

ࢱHˆ_SMc (z)ࡣḟᘧ࡛୚࠼ࡽࢀࡿ㸬

¦

c

N k

k k SM

z n g z

G

z G z

H

1

) ( )

(

) ( exp ) ˆ (

㸦 2.2 㸧

) (z

G ࡣࢺࣛࣥࢫࣂ࣮ࢧࣝᆺࡢࣇ࢕ࣝࢱ࡛࠶ࡾ㸪N ^ࡣG(z)ࡢࢱࢵࣉᩘ㸪g_k(n)^ࡣ )

(z

G ^ࡢk␒┠ࡢࢱࢵࣉಀᩘ࡛࠶ࡿ㸬᭦᪂࢔ࣝࢦࣜࢬ࣒ࡣ

>

@

) ( ) 1

(n g n Ee n d n k

g_{k k} D c ^㸦 2.3 㸧

࡜࡞ࡿ㸬ࡇࡇ࡛㸪Dࡣ㐺ᛂࣇ࢕ࣝࢱࡢࢫࢸࢵࣉࢧ࢖ࢬ࡛࠶ࡾ㸪^E

> @

࠶ࡿ㸬ᣦᩘᆺ㐺ᛂࣇ࢕ࣝࢱHˆ_SMc (z)ࡣࡍ࡭࡚ࡢᴟ࡜㞽Ⅼࡀ༢఩෇ෆ࡟Ꮡᅾࡍࡿࡓ

ࡵ[16]㸪ᚲࡎ᭱ᑠ఩┦ఏ㐩㛵ᩘ࡜࡞ࡿ㸬ᣦᩘᆺ㐺ᛂࣇ࢕ࣝࢱHˆ_SMc (z)ࡣ࣐ࢡ࣮ࣟࣜ

ࣥᒎ㛤࡟ࡼࡗ࡚ḟᘧࡢࡼ࠺࡟㏆ఝࡉࢀࡿ㸬

) ( 1 )

ˆ (z G z G z ² G z r

H_SMc ^r 㸦 2.4 㸧

ࡇࡇ࡛㸪rࡣ㏆ఝࡢ㡯ᩘ࡛࠶ࡿ㸬ᣦᩘᆺ㐺ᛂࣇ࢕ࣝࢱHˆ_SMc (z)ࡢᵓᡂᅗࢆᅗ 2. 3

࡟♧ࡍ㸬

ᅗ 2. 3 Hˆ_SMc (z)ᵓᡂᅗ

1

z

Adaptive Algorithm

1

z z¹

1

z z¹ z¹

1/2!

1/r!

1

z z¹ z¹

) (n q

)

2(n

g g_N1(n) g_N(n)

) (n f )

1(n g

)

2(n

g g_N1(n) g_N(n) )

1(n g

)

2(n

g g_N1(n) g_N(n) )

1(n g

㸰ḟ⤒㊰ࡢ᭱኱఩┦㒊ࢆ᥎ᐃࡍࡿࢺࣛࣥࢫࣂ࣮ࢧࣝᆺࡢ㐺ᛂࣇ࢕ࣝࢱHˆ_SAc (z) ࡣḟᘧ࡛⾲ࡉࢀࡿ㸬

M j j

j

SA z w n z

H^c

¦

0

) ( )

ˆ ( _{㸦 2.5 㸧}

ࡇࡇ࡛㸪M ࡣHˆ_SAc (z)ࡢࢱࢵࣉᩘ࡛࠶ࡾ㸪w_j(n)ࡣHˆ_SAc (z)ࡢ j␒┠ࡢࢱࢵࣉಀᩘ࡛

࠶ࡿ㸬᭦᪂࢔ࣝࢦࣜࢬ࣒ࡣ

>

@

) ( ) 1

(n w n E e n q n j

w_{j j} E c 㸦 2.6 㸧

࡜࡞ࡿ㸬ࡇࡇ࡛㸪Eࡣ㐺ᛂࣇ࢕ࣝࢱࡢࢫࢸࢵࣉࢧ࢖ࢬ࡛࠶ࡾ㸪^E

> @

࠶ࡿ㸬㐺ᛂࣇ࢕ࣝࢱHˆ_SAc (z)ࡢᵓᡂࢆᅗ 2. 4࡟♧ࡍ㸬

ᅗ 2. 4 Hˆ_SAc (z)ᵓᡂᅗ

1

z z¹ z¹

) (n q

w2 w_M1 w_M

w1

w0

) (n a

ᅗ 2. 5 Hˆ_SMc (z)࡜Hˆ_SAc (z)ࡢ᥎ᐃ᫬ࡢಙྕࡢὶࢀ

㸰ḟ⤒㊰᭱ᑠ఩┦㒊ࡢ㏫ఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿᣦᩘᆺ㐺ᛂࣇ࢕ࣝࢱHˆ_SMc (z)࡜ 㸰ḟ⤒㊰᭱኱఩┦㒊ࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱHˆ_SAc (z)ࡢ᥎ᐃࡢືస࡟ࡘ࠸࡚ㄝ᫂

ࢆ⾜࠺㸬ᅗ 2. 5࡟Hˆ_SMc (z)࡜Hˆ_SAc (z)ࡢ᥎ᐃ᫬ࡢಙྕࡢὶࢀࢆ♧ࡍ㸬Hˆ_SMc (z)ࡣಙ

ྕq(n)ࢆ౑⏝ࡋ࡚┤ิᆺࡢࢩࢫࢸ࣒ྠᐃ࡜ࡋ࡚H_SM(z)^{ࡢ㏫ఏ㐩㛵ᩘ࡛࠶ࡿ}

) ( /

1 H_SM z ࡢ᥎ᐃࢆ⾜࠺㸬୍᪉㸪Hˆ_SAc (z)ࡣಙྕq(n)ࢆ౑⏝ࡋ࡚୪ิᆺࡢࢩࢫࢸ࣒

ྠᐃ࡜ࡋ࡚H_SA(z)^{ࡢ᥎ᐃࢆ⾜࠺㸬}

( )

Q( )

( )

g′ ( )

( )

( )

LMS ′( ) ′ ( )

ㄗᕪ䝬䜲䜽

஧ḟ㡢※

′ ( )

LMS ( )

( )

)

( )

)

′

㸰ḟ⤒㊰ఏ㐩㛵ᩘࡢ᭱኱఩┦㒊ࡢ㏫ఏ㐩㛵ᩘ࡛࠶ࡿQ(z)^{ࡣḟᘧ࡛⾲ࡉࢀࡿ㸬}

¦

c

V q

q q

SA M V

z n b

z H z

z Q

0

) 1 (

) (

) ˆ ( )

(

㸦 2.7 㸧

VࡣQ(z)ࡢࢱࢵࣉᩘ࡛࠶ࡾ㸪b_q(n)ࡣQ(z)ࡢq␒┠ࡢࢱࢵࣉಀᩘ࡛࠶ࡿ㸬᭱኱఩

┦ఏ㐩㛵ᩘࡢ㏫ఏ㐩㛵ᩘࡣᅉᯝᛶࢆ‶ࡓࡉ࡞࠸ࡓࡵ㸪༢⣧࡟ಀᩘࢆ཯㌿ࡉࡏ࡚

㏫ࣇ࢕ࣝࢱࢆᵓᡂࡍࡿ࡜ࢩࢫࢸ࣒ࡀⓎᩓࡋ࡚ࡋࡲ࠺㸬ࡑࡇ࡛㸪㐜ᘏࢆᤄධࡍࡿࡇ

࡜ࡼࡾ㏫ఏ㐩㛵ᩘQ(z)^{ࢆᐇ⌧ࡍࡿ㸬}

㐺ᛂࣇ࢕ࣝࢱHˆ_SAc (z)ࡣ᭱኱఩┦㒊ࡢఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱࡢࡓࡵ㸪 ᥎ᐃᚋࡢఏ㐩㛵ᩘ ˆ ( )

, z

H_Oc_SA ࡢఏ㐩㛵ᩘࡢ㞽Ⅼࡣࡍ࡭࡚༢఩෇እ࡟Ꮡᅾࡍࡿ㸬ࡼࡗ

࡚

0

m ࡢࡳ࡟Ꮡᅾࡍࡿࡇ࡜࡜࡞ࡾ㸪┤᥋⟬ฟࡍࡿࡇ࡜ࡣ୙ྍ⬟࡛࠶ࡿ㸬௒㸪S(z)

ࢆ㸪

) ˆ (

)

( 1

,

c z

H z z S

SA O

M

㸦 2.8 㸧

࡜ᐃ⩏ࡍࢀࡤ㞽Ⅼࡣࡍ࡭࡚༢఩෇ෆ࡟Ꮡᅾࡍࡿࡓࡵ㸪ࡑࡢ㏫zኚ᥮

¦

i si m i

m s

0

) ( )

( G ^㸦2.9 㸧

ࡣ⟬ฟྍ⬟࡛࠶ࡿ㸬ࡲࡓ㸪

¦

i si m i

m v

0

) ( )

( G _{㸦 2.11 㸧}

࡜ࡋ࡚⟬ฟྍ⬟࡛࠶ࡿ㸬ࡇࡇ࡛v(m)ࡣᅉᯝᛶࢆ‶ࡓࡉ࡞࠸ࡓࡵ㸪㐜ᘏV ^ࢆᤄධ ࡍࡿࡇ࡜࡟ࡼࡾ㸪

¦

^V

i si m i V

V m v

0

) (

)

( G _{㸦 2.12 㸧}

࡜ࡋ࡚ᐇ⌧ࡍࡿ㸬ࡍ࡞ࢃࡕ㸪

) ) (

(

, ) 1 (

z H z z

S z

A O

M

V V

㸦 2.13 㸧

࡛࠶ࡾ㸪┠ⓗ࡜ࡍࡿ[(m)^࡟ᑐࡋ㸪(M V)^{ࡢ㐜ᘏಙྕࢆᤄධࡋࡓ}[(mM V)^࡜ ࡋ࡚ᐇ⌧ྍ⬟࡛࠶ࡿ㸬ᅗ 2. 6 ࡟s(m)^{ࡢ⟬ฟᅇ㊰ࢆ㸪ᅗ} 2. 7 ࡟s(m)^㸪v(m)^㸪

) (m V

v ^{ࡢ㛵ಀᛶࢆᅗ♧ࡍࡿ㸬}

ᅗ 2. 6 s(m)^⟬ฟᅇ㊰

1

z

1

z

1

z

)

G(m ^(wO,M)1

1 ,M

wO

1 ,

wO

0 ,

wO

) (m s )

(z S

m

0 m ) (m

v s(m)

)

(m V m M V

v [

V

) ˆ (z

H_SMc 㸪Hˆ_SAc (z)ࡀ᭱㐺ゎ࡟཰᮰ࡋࡓሙྜ㸪㸰ḟ⤒㊰ఏ㐩㛵ᩘ࡜ࡑࡢ㏫ఏ㐩㛵

ᩘ࡛࠶ࡿQ(z)^㸪Hˆ_SMc (z)㸪Hˆ_SAc (z)㸪H_SA(z)࡛ᵓᡂࡉࢀࡿఏ㐩㛵ᩘH_T(z)ࡣḟᘧ࡜

࡞ࡿ㸬

) (

) ( ) ( ) ˆ ( ) ( ) (

M V

SA SM

SM T

z

z H z H z H z Q z H

c 㸦 2.14 㸧

ࡼࡗ࡚㸪

)) (

( )

(n g n V M

d _Cc 㸦 2.15 㸧

࡛࠶ࡾ㸪㸰ḟ⤒㊰ࡢฟຊd(n)ࡣ㸰ḟ⤒㊰ࡢධຊg_Cc(n)ࡢ㐜ᘏಙྕ࡜࡞ࡿ㸬

2.2.2 㸯㸯ḟ⤒㊰ࡢ᥎ᐃ

ᅗ 2. 8ࡣ㸰ḟ⤒㊰ࡀ᭱㐺್࡟཰᮰ࡋࡓሙྜࡢᵓᡂᅗ࡛࠶ࡿ㸬㸯ḟ⤒㊰ࢆ᥎ᐃ

ࡍࡿไᚚࣇ࢕ࣝࢱHˆ_Cc (z)ࡣࢺࣛࣥࢫࣂ࣮ࢧࣝᆺࡢ㐺ᛂࣇ࢕ࣝࢱ࡛࠶ࡾ㸪ḟᘧ࡛

୚࠼ࡽࢀࡿ㸬

F i

i i

C z p n z

H

¦

0

) ( )

ˆ ( 㸦 2.16 㸧

ࡇࡇ࡛㸪F ࡣHˆ_C(z)ࡢࢱࢵࣉᩘ࡛࠶ࡾ㸪p_i(n)ࡣHˆ_C(z)ࡢi␒┠ࡢࢱࢵࣉಀᩘ࡛࠶

ࡿ㸬᭦᪂࢔ࣝࢦࣜࢬ࣒ࡣ

>

@

) ( ) 1

(n p n Ee₂ n g n i

p_{i i}

J

࡜࡞ࡿ㸬ࡇࡇ࡛㸪J ࡣ㐺ᛂࣇ࢕ࣝࢱࡢࢫࢸࢵࣉࢧ࢖ࢬ࡛࠶ࡾ㸪^E

> @

࠶ࡿ㸬ࢩࢫࢸ࣒ࡢฟຊ࡛࠶ࡿy(n)^ࡣ㸪

) ( ) ( )

(n p n d n

y ^㸦 2.18 㸧

࡛࠶ࡿ㸬

㐺ᛂࣇ࢕ࣝࢱHˆ_C(z)ࡣ୪ิᆺࡢࢩࢫࢸ࣒ྠᐃ࡟ࡼࡗ࡚H_P(z)z^VMࢆ᥎ᐃࡍ

ࡿࡇ࡜࡟࡞ࡾ㸪㦁㡢 p(n)^ࡣd(n)࡟ࡼࡾᢚᅽࡉࢀ㸪㦁㡢ࡀᡴࡕᾘࡉࢀࡽࢀࡿ㸬

ᅗ 2. 8 㸰ḟ⤒㊰཰᮰᫬ࡢࣈࣟࢵࢡᅗ ( )

LMS ( )

g( )

( ) ( )

( )

g′ ( ) 㞧㡢※

ཧ↷䝬䜲䜽 ㄗᕪ䝬䜲䜽

஧ḟ㡢※ ^{( )}

( )

( )

2.2.3 㸯㸯ḟ⤒㊰࡜㸰ḟ⤒㊰ྠ᫬᥎ᐃ᫬ࡢၥ㢟Ⅼ

๓⠇ࡲ࡛࡟㸯ḟ⤒㊰࡜㸰ḟ⤒㊰ࡢ᥎ᐃ᪉ἲ࡟ࡘ࠸࡚㏙࡭ࡓ㸬㸰ḟ⤒㊰ࡢࡳ࡛

᥎ᐃࡍࡿሙྜၥ㢟࡜࡞ࡽ࡞࠿ࡗࡓࡀ㸪㸯ḟ⤒㊰࡜ྜࢃࡏ࡚ࢩࢫࢸ࣒඲య࡛᥎ᐃ

ࢆ⾜࠺ሙྜ㸪㸰ḟ⤒㊰ࡢ㐺ᛂ࢔ࣝࢦࣜࢬ࣒࡟ධຊࡍࡿㄗᕪಙྕec(n)࡟p(n)^ࢆྵ

ࢇ࡛ࡋࡲ࠺㸬ࡇࡢ᫬ࡢㄗᕪಙྕec(n)ࡣ

) ( ) ( ) ( )

(n y n a n p n

ec 㸦 2.19 㸧

࡜࡞ࡿ㸬㸰ḟ⤒㊰ࡢ㐺ᛂ࢔ࣝࢦࣜࢬ࣒࡟࡜ࡗ࡚p(n)ࡣእ஘࡜࡞ࡿࡓࡵ㸪㸰ḟ⤒

㊰ࡢ᥎ᐃࡀṇࡋࡃ⾜ࢃࢀ࡞࠸㸬ࡑࡇ࡛㸪

) ( ) ( ) ( ) ( )

(n y n a n p n p n

ec c 㸦 2.20 㸧

࡜ࡋ㸪p(n)^ࡢᙳ㡪ࢆpc(n)࡛┦ẅࡍࡿࡇ࡜࡛㸰ḟ⤒㊰ࡢ᥎ᐃ⢭ᗘࡀྥୖࡋ㸪⿵ຓ

㞧㡢ࢆ౑⏝ࡍࡿࡇ࡜࡞ࡃ᭱㐺್࡟᥎ᐃࡍࡿࡇ࡜ࡀྍ⬟࡜࡞ࡿ㸬

2.3 ィ ィ⟬ᶵࢩ࣑࣮ࣗࣞࢩࣙࣥ

ᮏ⠇࡛ࡣ㸪ᥦ᱌ᡭἲࡢ㦁㡢ᢚᅽຠᯝࢆ☜ㄆࡍࡿࡓࡵ࡟㸪ィ⟬ᶵ࡟ࡼࡿࢩ࣑ࣗࣞ

࣮ࢩࣙࣥᐇ㦂ࢆ⾜࠺㸬

ᮏࢩ࣑࣮ࣗࣞࢩࣙࣥᐇ㦂࡟࠾࠸࡚㸪㦁㡢※g(n)࡜ࡋ࡚ᖹᆒ್ࡀ㞽ࡢⓑⰍᛶ࢞

࢘ࢫ㞧㡢ࢆ⏝࠸ࡓ㸬

ᮍ▱ࡢ⤒㊰࡜ࡋ࡚㸪㸯ḟ⤒㊰ࡢఏ㐩㛵ᩘH_P(z)ࡣ㸪

12 , 2

) (

)

( ^{( ) *}_{0 1}^{* 1} ₂^{* 2} V

M

z p z p p z

z

H_P ^{V M}

㸦 2.21 㸧

࡛୚࠼ࡽࢀࡿ㸬ࡲࡓ㸪㸰ḟ⤒㊰ࡢ᭱ᑠ఩┦㒊ఏ㐩㛵ᩘH_SM(z)^{࡜᭱኱఩┦㒊ఏ㐩} 㛵ᩘH_SA(z)^ࡣ㸪

6 / ,

5 . 1 , cos 2 ,

) (

* 1 2

* 0

2 1

* 1

* 0

S T T

R R

a R a

z z a a z H_SA

㸦 2.22 㸧

¦

|

5

1

*

*

* 2

*

*

*

) (

8

,

! / )) ( (

! 2 / )) ( ( ) ( 1

)) ( exp(

) (

i

i i

r M

S

z g z

G r

r z G z

G z G

z G z

H

㸦 2.23 㸧

࡛୚࠼ࡽࢀࡿ㸬ᮏࢩ࣑࣮ࣗࣞࢩ࡛ࣙࣥࡣ⤒㊰ኚື࡟ᑐࡍࡿホ౯ࢆ⾜࠺ࡓࡵ㸪ࢩ࣑

࣮ࣗࣞࢩࣙࣥ㛤ጞ࠿ࡽࡢヨ⾜ࣈࣟࢵࢡᅇᩘl=1500࡛⤒㊰ࢆኚືࡉࡏࡿ㸬⾲࡟g^*_i㸪

*

pi ࡢタᐃ್ࢆ♧ࡍ㸬

⾲ 2.1 G^*(z)࡜H_P(z)ࡢタᐃ್

Number of blocks, l

)

*(z

G H_P(z)

*

g1 g^*₂ g₃^* g^*₄ g₅^* p^*₀ p₁^* p₂^* 0 - 1499 0.5 0.5 0.3 -0.5 0.1 1.0 1.0 1.0 1500 - 3000 -0.5 0.5 0.3 -0.5 0.1 1.0 -1.0 1.0

㐺ᛂࣇ࢕ࣝࢱHˆ_SMc (z)㸪Hˆ_SAc (z)㸪Hˆ_C(z)ࡢࢱࢵࣉಀᩘࡢ᭦᪂࡟⏝࠸ࡿ㐺ᛂ࢔ࣝ

ࢦࣜࢬ࣒ࡣḟᘧ࡛♧ࡍblock normalized least mean square(BNLMS)[17]࢔ࣝࢦࣜࢬ

࣒ࢆ౑⏝ࡍࡿ㸬

> @

¦ ¦

¦

c

_N

m L l

lL n L l

lL n k

k

m n e

k n e n e l

g l

g

0 1 ) 1

( 2

1 1 ) 1 (

1

) (

)) ( ) ( ( )

( ) 1 (

D

㸦 2.24 㸧

> @

¦ ¦

¦

c

_M

m L l

lL n

L l

lL n j

j

m n e

j n e n e l

w l

w

0 1 ) 1

( 2

1 1 ) 1 (

1

) (

)) ( ) ( ( )

( ) 1 (

E

㸦 2.25 㸧

> @

¦ ¦

¦

_{F l L}

L l

lL n i

i

m n y

i n y n e l

p l

p _{( 1) 1}

2 1

) 1 (

2

) (

) ( ) ( )

( ) 1 (

J

㸦 2.26 㸧

ᮏࢩ࣑࣮ࣗࣞࢩࣙࣥ࡟࠾࠸࡚㸪㐺ᛂࣇ࢕ࣝࢱHˆ_SMc (z)㸪Hˆ_SAc (z)㸪Hˆ_C(z)ࡢึᮇ

್ࡣHˆ_C(z)ࡢࢱࢵࣉಀᩘp₀(0) 1࡜ࡋ㸪ࡑࡢ࡯࠿ࡢࢱࢵࣉಀᩘࡣࡍ࡭࡚0࡜ࡋࡓ㸬 ᥦ᱌ᡭἲࡢᛶ⬟ࢆホ౯ࡍࡿࡓࡵ࡟㸪࢔ࢡࢸ࢕ࣈࣀ࢖ࢬࢥࣥࢺ࣮ࣟࣝࢩࢫࢸ࣒

࡜ࡋ࡚ࡼࡃ⏝࠸ࡽࢀࡿ⿵ຓ㞧㡢ࢆ౑⏝ࡋࡓFiltered-x࢔ࣝࢦࣜࢬ࣒࡜ẚ㍑ࢆ⾜࠺㸬

Filtered-x࢔ࣝࢦࣜࢬ࣒ࡢᵓᡂᅗࢆᅗ 2. 9࡟♧ࡍ㸬ྛ㐺ᛂࣇ࢕ࣝࢱࡢ᭦᪂࢔ࣝࢦ

ࣜࢬ࣒࡟ࡣᥦ᱌ᡭἲ࡜ྠᵝ࡟BNLMS࢔ࣝࢦࣜࢬ࣒ࢆ౑⏝ࡍࡿ㸬

ᅗ 2. 9 Filtered-x࢔ࣝࢦࣜࢬ࣒

( )

( )

LMS ′ ( )

( ) g( )

( ) ( )

( )

g′ ( ) ( )

LMS ′( )

㞧㡢※

( )

ཧ↷䝬䜲䜽 ㄗᕪ䝬䜲䜽

஧ḟ㡢※

( )

ᮏࢩ࣑࣮ࣗࣞࢩࣙࣥࡢタᐃ್ࢆ⾲ 2.2࡟♧ࡍ㸬

⾲ 2.2 ࢩ࣑࣮ࣗࣞࢩࣙࣥタᐃ್

Filtered-x

࢔ࣝࢦࣜࢬ࣒

ᥦ᱌ᡭἲ

) ˆ (z

H_C ࡢࢱࢵࣉᩘ 16 16

) ˆ (z

H_C ࡢࢫࢸࢵࣉࢧ࢖ࢬJ _{0.5 0.5}

) (z

G ࡢࢱࢵࣉᩘ 16

) ˆ (z

H_SMc ࡢࢫࢸࢵࣉࢧ࢖ࢬD _0.5

) ˆ (z

H_SAc ࡢࢱࢵࣉᩘ 3

) ˆ (z

H_SAc ࡢࢫࢸࢵࣉࢧ࢖ࢬE _0.1

) (z

Q ࡢࢱࢵࣉᩘ 12

) (z

A ࡢࢱࢵࣉᩘ 40

) (z

A ࡢࢫࢸࢵࣉࢧ࢖ࢬ 0.5

ࣈࣟࢵࢡ㛗L 128 128

ࣀ࢖ࢬ㝖ཤᛶ⬟ࡢホ౯ࡍࡿࡓࡵ࡟ḟᘧ࡟♧ࡍ㦁㡢ᡴᾘࡋ⢭ᗘEV(l)ࢆᐃ⩏ࡍࡿ㸬

] [ ) (

) ( log

10 )

( ( 1) 1

2 1 ) 1

( 2

10 dB

n p E

n y E

l

EV l L

lL n

L l

lL n

»¼

« º

¬ ª

»¼

« º

¬ ª

¦

¦

㸦 2.27 㸧

ࡇࡇ࡛㸪y(n)^ࡣFiltered-x࢔ࣝࢦࣜࢬ࣒ࡢሙྜ㸪⿵ຓ㞧㡢ࡢᡂศࢆྵࡲ࡞࠸ಙྕ

࡛࠶ࡿ㸬ᮏࢩ࣑࣮ࣗࣞࢩ࡛ࣙࣥࡣ⊂❧࡞ 200 ᅇࡢヨ⾜⧞ࡾ㏉ࡋ㸪ᖹᆒࢆ࡜ࡗ࡚

EV(l)ࢆồࡵࡓ㸬

ᅗ 2. 10 ࡟ᮏࢩ࣑࣮ࣗࣞࢩࣙࣥᐇ㦂ࡢ⤖ᯝࢆ♧ࡍ㸬ᐇ⥺ࡀᥦ᱌ᡭἲ㸪◚⥺ࡀ

Filtered-x ࢔ࣝࢦࣜࢬ࣒ࡢ EV(l)ࢆ♧ࡋ࡚࠸ࡿ㸬ᥦ᱌ᡭἲࡣ Filtered-x ࢔ࣝࢦࣜࢬ

࣒࡜ẚ㍑ࡋ࡚ᾘ㡢ᛶ⬟࡛࠶ࡿ EV(l)ࡀ⣙-25dB ᨵၿࡉࢀ࡚࠸ࡿ㸬ࡲࡓ㸪ヨ⾜ࣈࣟ

ࢵࢡᅇᩘ l=1500࡟࡚㸯ḟ⤒㊰࠾ࡼࡧ㸰ḟ⤒㊰ࡢఏ㐩㛵ᩘࢆኚ໬ࡉࡏࡓᚋࡶ㸪ᥦ

᱌ᡭἲࡣ㠀ᐃᖖ࡞⤒㊰࡟㏣ᚑྍ⬟࡛࠶ࡿࡢ࡟ᑐࡋ㸪Filtered-x ࢔ࣝࢦࣜࢬ࣒ࡣ㏣

ᚑ୙ྍ⬟࡛࠶ࡿ㸬

ᅗ 2. 10 ࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝ

0 1000 2000 3000

-50 -40 -30 -20 -10 0

Number of blocks, l

EV ( l ) [dB]

Filtered-x

࢔ࣝࢦࣜࢬ࣒

2.4 ⤖ ⤖ゝ

ᮏ❶࡛ࡣ㸪⿵ຓ㞧㡢ࢆ⏝࠸࡞࠸Pre-inverseᆺANCࢩࢫࢸ࣒ࢆᥦ᱌ࡋ㸪ィ⟬ᶵ ࢩ࣑࣮ࣗࣞࢩ࡛ࣙࣥᮏᡭἲࡢ᭷ຠᛶࢆ☜ㄆࡋࡓ㸬

ᮏᡭἲࡣ㸪㸰ḟ⤒㊰ࡢ㏫ఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿࡓࡵ࡟㸪㐺ᛂᣦᩘࣇ࢕ࣝࢱࢆ⏝࠸

࡚᭱ᑠ఩┦㒊࡜᭱኱఩┦㒊࡟ศゎࡋ࡚᥎ᐃࢆ⾜࠸㸪ࡑࢀࡒࢀ࡟ᑐࡋ࡚㏫ఏ㐩㛵

ᩘࢆィ⟬ࡍࡿᡭἲ࡛࠶ࡿ㸬ィ⟬ᶵࢩ࣑࣮ࣗࣞࢩࣙࣥᐇ㦂࡟࠾࠸࡚ࡣ㸪ࣇ࢕࣮ࢻࣇ

࢛࣮࣡ࢻᆺࡢ ANC ࢩࢫࢸ࣒࡜ࡋ࡚ࡼࡃ⏝࠸ࡽࢀࡿ Filtered-x ࢔ࣝࢦࣜࢬ࣒࡜ࡢ ᥎ᐃ⢭ᗘ࡜⤒㊰ኚື࡟ᑐࡍࡿ㏣ᚑᛶ⬟ࡢẚ㍑ࢆ⾜࠸㸪⢭ᗘࡢྥୖ࡜⤒㊰ኚື࡬

ࡢ㏣ᚑᛶ⬟ྥୖࢆ☜ㄆ࡛ࡁ㸪ᮏᡭἲࡢ᭷ຠᛶࡀ♧ࡉࢀࡓ㸬

➨

➨ 3 ❶

⿵ຓࣇ࢕ࣝࢱ࡟ࡼࡿ㸰ḟ⤒㊰㏫ఏ㐩㛵ᩘ

᥎ᐃࢆ⏝࠸ࡿ Pre-inverse ᆺ ANC ࢩࢫࢸ࣒

3.1 ⥴ゝ

๓❶࡟࡚ㄝ᫂ࡋࡓ⿵ຓ㞧㡢ࢆ⏝࠸࡞࠸Pre-inverseᆺANCࢩࢫࢸ࣒ࡣ㸰ḟ⤒㊰

㏫ఏ㐩㛵ᩘࢆồࡵࡿࡓࡵ࡟㸪㸰ḟ⤒㊰ࡢ᭱኱఩┦㒊࡜᭱ᑠ఩┦㒊ࢆศ㞳ࡋ࡚᥎ ᐃࡋ㸪ࡑࢀࡒࢀࡢ㏫ఏ㐩㛵ᩘࢆồࡵࡿࡇ࡜࡛ANCࢩࢫࢸ࣒ࢆᐇ⌧ࡋࡓ㸬ࢩ࣑ࣗ

࣮ࣞࢩࣙࣥᐇ㦂࡛Filtered-x࢔ࣝࢦࣜࢬ࣒࡜ẚ㍑ࢆ⾜࠸ᥦ᱌ᡭἲࡢ᭷ຠᛶࡀ☜ㄆ

࡛ࡁࡓ㸬ࡋ࠿ࡋ㸪ࢩ࣑࣮ࣗࣞࢩࣙࣥᐇ㦂࡛ࡣᮍ▱ࡢ㸰ḟ⤒㊰ࡢఏ㐩㛵ᩘࢆ᭱኱఩

┦㒊࡜᭱ᑠ఩┦㒊࡟ศ㞳ࡋࡓࡶࡢࢆ౑⏝ࡋࡓࡀ㸪ࡼࡾᐇ⎔ቃ࡟㏆࠸⤒㊰࡛ࡢࢩ

࣑࣮ࣗࣞࢩࣙࣥᐇ㦂ࢆ⾜ࡗࡓ࡜ࡇࢁṇᖖ࡟ືసࡋ࡞࠸ၥ㢟ࡀ⏕ࡌࡓ㸬ࡇࢀࡣ㸪㸰 ḟ⤒㊰ࡢ᭱ᑠ఩┦㒊ࢆ᥎ᐃࡍࡿ㐺ᛂᣦᩘࣇ࢕ࣝࢱࡀṇ☜࡟᥎ᐃ࡛ࡁ࡞࠿ࡗࡓࡓ

ࡵ࡟᭱኱఩┦㒊ࢆ᥎ᐃࡍࡿ㐺ᛂࣇ࢕ࣝࢱࡀ᭱ᑠ఩┦㒊ࢆྵࢇࡔఏ㐩㛵ᩘࢆ᥎ᐃ ࡋ࡚ࡋࡲ࠸㸪ࡑࡢ㏫ఏ㐩㛵ᩘࢆồࡵࡿ࡜ᅉᯝᛶࢆ‶ࡓࡏ࡞ࡃ࡞ࡗ࡚ࡋࡲࡗࡓࡓ

ࡵ࡟ࢩࢫࢸ࣒ࡀⓎᩓࡋ࡚ࡋࡲࡗࡓ࡜⪃࠼ࡽࢀࡿ㸬㐺ᛂᣦᩘࣇ࢕ࣝࢱࡀṇࡋࡃ᥎ ᐃ࡛ࡁ࡞࠿ࡗࡓཎᅉ࡜ࡋ࡚㸪㸰ḟ⤒㊰ࡢ᭱ᑠ఩┦㒊ࢆᣦᩘࣇ࢕ࣝࢱ࡛෌⌧࡛ࡁ

࡞࠿ࡗࡓࡇ࡜ࡸ㸪⿵ຓ㞧㡢ࢆ౑⏝ࡋ࡚࠸࡞࠸ࡓࡵ㸰ḟ⤒㊰ࡢ᥎ᐃ࡟౑⏝ࡍࡿಙ

ྕࡀ᭷Ⰽ໬ࡋ࡚ࡋࡲࡗࡓࡇ࡜࡟ࡼࡿ᥎ᐃ⢭ᗘࡢຎ໬ࡀ⪃࠼ࡽࢀࡿ㸬

ࡑࡇ࡛㸪ᮏ❶࡛ࡣ᪂ࡓ࡞Pre-inverseᆺANCࢩࢫࢸ࣒ࡢᥦ᱌ࢆ⾜࠺㸬Pre-inverse ᆺANCࢩࢫࢸ࣒࡛ࡣ๓㏙ࡢ㏻ࡾእ஘࡟ࡼࡿࣂ࢖࢔ࢫㄗᕪࡢᙳ㡪࡛᥎ᐃ⢭ᗘࡀຎ

໬ࡋ࡚ࡋࡲ࠺ၥ㢟ࡀ࠶ࡗࡓ㸬ࡑࡇ࡛㸪እ஘࡟ࣟࣂࢫࢺ࡞㐺ᛂ࢔ࣝࢦࣜࢬ࣒࡜ࡋ࡚

SSCF(Square Sum of Correlation Function)㐺ᛂ࢔ࣝࢦࣜࢬ࣒ࡀᥦ᱌ࡉࢀ࡚࠸ࡿ[15]㸬 SSCF 㐺ᛂ࢔ࣝࢦࣜࢬ࣒ࡣ㦁㡢※࡜㸰ḟ⤒㊰ࢆ᥎ᐃࡍࡿࡓࡵ࡟௜ຍࡍࡿ⿵ຓ㞧 㡢ࡀ⊂❧ᛶ࡟ࡼࡾ↓┦㛵࡛࠶ࡿᛶ㉁ࢆ฼⏝ࡋ㸪⿵ຓ㞧㡢࡜ㄗᕪಙྕࡢ┦஫┦㛵 㛵ᩘࢆホ౯㛵ᩘ࡜ࡍࡿࡇ࡜࡟ࡼࡾ㸪እ஘ࡢᙳ㡪ࢆᢚ࠼ࡓ㸰ḟ⤒㊰᥎ᐃࢆྍ⬟࡜

ࡍࡿ㸬ࡋ࠿ࡋ㸪┿ࡢ┦஫┦㛵㛵ᩘࢆィ⟬ࡍࡿࡓࡵ࡟ࡣ㛗᫬㛫 ᐃࡀᚲせ࡛࠶ࡾ㸪 ᐇ⏝ୖࣂ࢖࢔ࢫㄗᕪࢆ᏶඲࡟ᢚᅽࡍࡿࡇ࡜ࡀ࡛ࡁࡎ㸪እ஘ࡢᙳ㡪ࢆཷࡅ࡚ࡋࡲ

࠺㸬ࡇࡢၥ㢟ࢆゎỴࡍࡿࡓࡵ࡟㸪⿵ຓࣇ࢕ࣝࢱ࡟ࡼࡿ㸰ḟ⤒㊰㏫ఏ㐩㛵ᩘ᥎ᐃࢆ

⏝࠸ࡿPre-inverseᆺANCࢩࢫࢸ࣒ࢆᥦ᱌ࡍࡿ㸬ᮏᡭἲࡣ㸪㸰ḟ⤒㊰࡟ᑐࡋ⿵ຓ

ࣇ࢕ࣝࢱࢆ୪ิ࡟㓄⨨ࡋࢩࢫࢸ࣒ྠᐃࢆ⾜࠸㸪⿵ຓࣇ࢕ࣝࢱ࡟ᑐࡋ⦪⥆࡟㸰ḟ

⤒㊰ࡢ㏫ఏ㐩㛵ᩘࢆ᥎ᐃࡍࡿࣇ࢕ࣝࢱࢆ㓄⨨ࡍࡿ㸬ࡇࢀ࡟ࡼࡾ㸰ḟ⤒㊰ࢆ᥎ᐃ ࡍࡿ㐺ᛂࣇ࢕ࣝࢱࡢ᭦᪂࢔ࣝࢦࣜࢬ࣒࡛ồࡵࡿホ౯㛵ᩘࡢ໙㓄࡟እ஘࡟ࡼࡿಙ

ྕᡂศࢆྵࡲ࡞࠸ᅇ㊰ᵓᡂ࡜࡞ࡿࡓࡵ㸪ࣂ࢖࢔ࢫㄗᕪࡀ⌮ㄽୖⓎ⏕ࡋ࡞࠸㸬ࡲࡓ㸪 ࡇࢀ࡟ࡼࡾ㸰ḟ⤒㊰ࡢ᥎ᐃ࡟౑⏝ࡍࡿ⿵ຓ㞧㡢ࡢ㟁ຊࢆపῶࡉࡏࡿࡇ࡜ࡀྍ⬟

࡜࡞ࡾ㸪ࢩࢫࢸ࣒඲యࡢᾘ㡢ᛶ⬟ࢆྥୖࡉࡏࡿ㸬ᮏ❶࡛ࡣᚑ᮶ᆺࡢPre-inverseᆺ ANC ࢩࢫࢸ࣒࡜ࡋ࡚ SSCF 㐺ᛂ࢔ࣝࢦࣜࢬ࣒ࡢㄝ᫂ࢆ⾜࠸㸪ḟ࡟ᥦ᱌ᡭἲࡢㄝ

᫂ࢆ⾜࠺㸬ࡲࡓ㸪ࢩ࣑࣮ࣗࣞࢩࣙࣥᐇ㦂࡟࡚ᥦ᱌ᡭἲࡢ᭷ຠᛶࢆ☜ㄆࡋ㸪ᐇ⿦ᐇ 㦂࡛ᐇ⎔ቃୗ࡟࡚ၥ㢟࡞ࡃືసࡍࡿࡇ࡜ࢆ☜ㄆࡍࡿ㸬

3.2 SSCF ࢆ ࢆ⏝࠸ࡓ Pre-inverse ᆺ ANC ࢩࢫࢸ࣒

ᅗ 3. 1࡟ Pre-inverse ᆺ ANCࡢᵓᡂࢆ♧ࡍ㸬ࡇࡇ࡛㸪H_P(z)^㸪H_S(z)^ࡣࡑࢀ

ࡒࢀ㸯ḟ⤒㊰࡜㸰ḟ⤒㊰ࡢఏ㐩㛵ᩘࢆ⾲ࡋ࡚࠸ࡿ㸬ࡲࡓ㐺ᛂࣇ࢕ࣝࢱHˆ_C(z)ࡣ )

(z H z^M _P

ࢆ᥎ᐃࡍࡿไᚚࣇ࢕ࣝࢱ㸪Hˆ_Sc(z)ࡣ㸰ḟ⤒㊰H_S(z)^{ࡢ㏫ఏ㐩㛵ᩘࢆ}

᥎ᐃࡍࡿࡓࡵࡢ㐺ᛂࣇ࢕ࣝࢱ࡛࠶ࡿ㸬ྛಙྕࢆ௨ୗ࡟♧ࡍ㸬

) (n

g ^㸸㦁㡢

) (n

p 㸸㸯ḟ⤒㊰㏻㐣ᚋࡢ㦁㡢 )

(n

y ^{㸸ほ ಙྕ}

) (n

w ^{㸸⿵ຓ㞧㡢} )

(n

f ^{㸸ไᚚಙྕ}

) (n

d 㸸㸰ḟ⤒㊰㏻㐣ᚋࡢไᚚಙྕ

࡞࠾㸪㦁㡢g(n)^{ཬࡧ㸪⿵ຓ㞧㡢}w(n)ࡣ஫࠸࡟⊂❧↓┦㛵࡞ಙྕ࡛࠶ࡿ㸬ࡲ

ࡓ㸪⿵ຓ㞧㡢w(n)ࡣᑐ㇟࡜ࡍࡿ࿘Ἴᩘ㡿ᇦ࡛ⓑⰍࡢಙྕ࡛࠶ࡿ㸬ec(n)ࡣ㐺ᛂ

ࣇ࢕ࣝࢱHˆ_Sc(z)ࡢ㐺ᛂ࢔ࣝࢦࣜࢬ࣒᭦᪂ࡢࡓࡵࡢㄗᕪಙྕ࡛࠶ࡿ㸬

ᅗ 3. 1 Pre-inverse ᆺANCࡢᵓᡂᅗ ( )

( )

NLMS

′ ( ) ′ ( )

( ) g( )

( ) ( )

( ) g′ ( ) ( ) ( )

NLMS ′( )

㞧㡢※

′ ( )

ཧ↷䝬䜲䜽 ㄗᕪ䝬䜲䜽

஧ḟ㡢※

ྛ㐺ᛂࣇ࢕ࣝࢱ࡟ࡘ࠸࡚㸪ไᚚࣇ࢕ࣝࢱHˆ_C(z)ࡣ㸪

¦

i

i i C

C z h n z

H

0

, ( ) ) ˆ

ˆ ( _{㸦 3.1 㸧}

ࡇࡇ࡛㸪N_CࡣHˆ_C(z)ࡢࢱࢵࣉᩘ㸪ˆ ( )

, n

h_Ci ࡣHˆ_C(z)ࡢi␒┠ࡢࢱࢵࣉಀᩘ࡛࠶ࡿ㸬

ࡲࡓ㸪㐺ᛂࣇ࢕ࣝࢱHˆ_Sc(z)ࡣ㸪

¦

c ^NS

i

i i S

S z h n z

H

0 ,( ) ) ˆ

ˆ ( _{㸦 3.2 㸧}

࡟ࡼࡾ⾲ࡉࢀࡿ㸬ࡇࡇ࡛㸪N_ScࡣHˆ_Sc(z)ࡢࢱࢵࣉᩘ㸪ˆ ( )

, n

h_Sc_i ࡣHˆ_Sc(z)ࡢi␒┠ࡢࢱ

ࢵࣉಀᩘ࡛࠶ࡿ㸬ࡲࡓ㸪ࡍ࡭࡚ࡢ㐺ᛂࣇ࢕ࣝࢱ࡟࠾࠸࡚NLMS (Normalized Least

Mean Square) ࢔ࣝࢦࣜࢬ࣒[18]ࢆ⏝࠸࡚࠾ࡾ㸪ྛࢱࢵࣉಀᩘࡢ᭦᪂ࡣ㸪

) ( ) (

) ( ) ) (

ˆ ( ) 1 ˆ (

n n

n n n y

n _{C C T}

C g g

h g

h P 㸦 3.3 㸧

) ( ) (

) ( ) ) (

ˆ ( ) 1 ˆ (

n n

n n n e

n _{S S T}

S y y

h y

hc c Pc c 㸦 3.4 㸧

࡜࡞ࡿ㸬ࡇࡇ࡛㸪P_C࡜P_Scࡣࡑࢀࡒࢀࡢ㐺ᛂࣇ࢕ࣝࢱࡢࢫࢸࢵࣉࢧ࢖ࢬ㸪T ࡣ㌿

⨨ࢆ⾲ࡍ㸬ࡲࡓ㸪

T N C C

C

C(n) [hˆ (n),hˆ (n),...,hˆ _C(n)]

ˆ ,0 ,1 ,

h ^㸦 3.5 㸧

T

NC

M n g M

n g M n g

n) [ ( ), ( 1),..., ( )]

(

g 㸦 3.6 㸧

T N S S

S

S(n) [hˆ (n),hˆ (n),...,hˆ _S(n)]

ˆc c,0 c,1 c, c

h ^㸦 3.7 㸧

T

NS

n y n

y n y

n) [ ( ), ( 1),..., ( )]

( c

y 㸦 3.8 㸧

ᅗ 3. 2 Hˆ_Sc(z)᥎ᐃ᫬ࡢಙྕࡢὶࢀ

ᅗ 3. 2࡟㐺ᛂࣇ࢕ࣝࢱHˆ_Sc(z)᥎ᐃ᫬ࡢಙྕࡢὶࢀࢆ♧ࡍ㸬Hˆ_Sc(z)ࡣ⿵ຓ㞧㡢 )

(n

w ࢆ౑⏝ࡋ㸪┤ิᆺࡢࢩࢫࢸ࣒ྠᐃ࡜ࡋ࡚㸰ḟ⤒㊰ࡢ㏫ఏ㐩㛵ᩘz^M H_S(z)

ࢆ᥎ᐃࡍࡿ㸬᥎ᐃࡋࡓ⤖ᯝࡣไᚚࣇ࢕ࣝࢱᚋẁࡢࣇ࢕ࣝࢱHˆ_Sc(z)࡟ࢥࣆ࣮ࡍࡿ㸬 ࡇࢀ࡟ࡼࡾ㸪㸰ḟ⤒㊰H_S(z)ࡣ┦ẅࡉࢀ㸪

M S

S z H z z

Hˆc( ) ( ) 㸦 3.9 㸧

࡜࡞ࡿ㸬㐺ᛂࣇ࢕ࣝࢱHˆ_C(z)࡛ࡣz^MH_P(z)ࢆ᥎ᐃࡍࡿࡇ࡜࡟࡞ࡾ㸪㸯ḟ⤒㊰ࢆ

㏻㐣ࡋࡓ㦁㡢 p(n)࡜㸰ḟ⤒㊰ࢆ㏻㐣ࡋࡓไᚚಙྕ d(n)ࡣᡴࡕᾘࡋ࠶࠺ࡇ࡜࡟࡞

ˆ z^MH (z) NLMS

g

g

SSCF 㞧㡢※

ཧ↷䝬䜲䜽 ㄗᕪ䝬䜲䜽

஧ḟ㡢※