5.4 ῶ㡢㔞ᩘ್ࢩ࣑࣮ࣗࣞࢩࣙࣥ
5.4.2 ィ⟬⤖ᯝᐇ㦂⤖ᯝࡢẚ㍑
ḟࡢTable5.2ྛᐇ㦂᮲௳ࡢࣃ࣓࣮ࣛࢱࢆ♧ࡋ㸪Fig5.8Ң 5.10ྛ᮲௳ୗ࡛ࡢไᚚ
Ⅼ(ㄗᕪ࣐ࢡࣟ࣍ࣥ㸧ಙྕࡢ36ࡘ࠸࡚㸪ィ⟬⤖ᯝᐇ㦂⤖ᯝࡢẚ㍑ࢆ♧ࡍ㸬
ࡲࡓ㸪Table5.3ࡣྛᅗࡢẚ㍑ᑐ㇟㸦ኚື್ᅛᐃ್㸧ࡘ࠸࡚♧ࡍ㸬ྛᅗ♧ࡍ
Case0ࡣ㸪➨5.3.3⠇࠾ࡅࡿᐇ㦂⤖ᯝࡢ㡢ᅽࢫ࣌ࢡࢺࣝࢆࢆ⾲ࡍ㸬Case1Ң 12ࡣྛ᮲
௳ୗ࠾ࡅࡿࢩ࣑࣮ࣗࣞࢩࣙࣥ⤖ᯝࡢ㡢ᅽࢫ࣌ࢡࢺࣝࢆ⾲ࡍ㸬Fig.5.8࡛ࡣ㸪⏝
ࣝࢦࣜࢬ࣒Cˆ ࡣᅛᐃࡋ㸪Hࢆ200㸪600㸪1200[TAP]ኚࡉࡏࡿ㸬Fig5.9ࡘ࠸࡚
ࡣCˆ ࡢࡳኚືࢆ࠼ࡓ㸬Fig.5.10Fig5.11࡛ࡣ㸪ྛࣇࣝࢱHCˆ ࡢTAPࡀ㐪࠸㸪
ࣝࢦࣜࢬ࣒ࡢࡳࢆኚ᭦ࡋ㸪ẚ㍑ࡍࡿ㸬
Table 5.2 : Conditions and size of filters
Condition Number H[TAP] Cˆ [TAP] algorithm Experiment case 0 200 200 6[(1-1)-3’] ch
̭ case 1 200 ̭ ̭
̭ case 2 600 200 6[(1-1)-3’] ch
̭ case 3 1200 ̭ ̭
̭ case 4 200 ̭ ̭
̭ case 5 600 500 6[(1-1)-3’] ch
Simulation case 6 1200 ̭ ̭
̭ case 7 200 200 ̭
̭ case 8 600 ̭ 6(1-1)-6 ch
̭ case 9 500 ̭
̭ case 10 200 200 ̭
̭ case 11 600 ̭ 6-6-6 ch
̭ case 12 500 ̭
Table 5.3 : Conditions and size of filters
Figure Fig.5.8 Fig.5.9 Fig.5.10 Fig.5.11
Cases 0,1,2,3,4 0,2,5 0,1,7,10 0,5,9,12
Fixed parameter Algorithm, ˆC Algorithm,H H:200, ˆC:200 H:600, ˆC:500
Variable parameter H Cˆ Algorithm Algorithm
ḟࡢFig㸬5.8ࡣไᚚࣇࣝࢱH㸪Fig㸬5.9ࡣఝㄗᕪ⤒㊰Cˆ ࡢTAPᩘࢆኚ᭦
ࡋࡓ᮲௳࡛㸪ᮏ❶ࡢศᩓไᚚᡭἲࡼࡿῶ㡢ᛶ⬟ࢆ♧ࡍ㸬
(UURU (UURU
$1&2))
$1&21
&DVH &DVH &DVH &DVH
Fig. 5.8 : The relative sound pressure spectrum at the error point and sound pressure spectrum at the fixed point under the condition of ANC ON and OFF in Case 0㸪 1㸪2 and 3
(UURU (UURU
$1&2))
$1&21
&DVH &DVH &DVH
Fig. 5.9 : The relative sound pressure spectrum at the error point and sound pressure spectrum at the fixed point under the condition of ANC ON and OFF in Case 0㸪2 and 5
(UURU (UURU
$1&2))
$1&21
&DVH &DVH &DVH &DVH
Fig. 5.10 : The relative sound pressure spectrum at the error point and sound pressure spectrum at the fixed point under the condition of ANC ON and OFF in Case 0㸪1㸪7 and 10
Fig. 5.11 : The relative sound pressure spectrum at the error point and sound pressure spectrum at the fixed point under the condition of ANC ON and OFF in Case 0㸪5㸪9 and 12
Fig㸬5.8ࡼࡾ㸪ᐇ㦂ࢩ࣑࣮ࣗࣞࢩࣙࣥࡀྠ᮲௳ࡢሙྜ㸪ῶ㡢㔞ࡀࡰ୍⮴ࡋ㸪ࢩ
࣑࣮ࣗࣞࢩࣙࣥࡢᩚྜᛶࡀ☜ㄆ࡛ࡁࡿ㸬ࡲࡓ㸪ไᚚࣇࣝࢱHࡢTAPᩘࡼࡿᛶ⬟
ࡣࡰኚࢃࡽࡎ㸪ᑐ㇟࿘Ἴᩘࡢ㧗࿘Ἴഃ2[kHz]࡛ࡢቑ㡢ࡀ5[dB]⛬ᗘኚࢃࡿ㸬ࡼࡗ࡚
ไᚚࣇࣝࢱࡢTAPᩘࡣ༑ศ㊊ࡾ࡚࠸ࡿ⪃࠼ࡽࢀࡿ㸬
Fig.5.9ࡼࡾ㸪ᮏᡭἲࡢᐇ㦂᮲௳ࡢఝㄗᕪ⤒㊰Cˆ ࡢTAPᩘ࡛ไᚚࡣ༑ศ㊊ࡾ࡚࠸
ࡿ⪃࠼ࡽࢀࡿ㸬ࡲࡓ㸪Fig㸬5.8Fig㸬5.9ࡼࡾ㸪ᮏᡭἲࡢᐇ㦂࠾ࡅࡿྛࣇࣝࢱ ࡢTAPᩘࡣ༑ศ࡞ῶ㡢ᛶ⬟ࢆᚓࡿࡇࡀྍ⬟࡛࠶ࡿ㸬
⤖ᯝ㸪Fig㸬5.10Fig㸬5.11ࡼࡾ㸪ᚑ᮶ᡭἲྠ➼ࡢῶ㡢㔞ࢆ⥔ᣢࡋࡓࡲࡲ㸪ィ⟬
⏝ࡍࡿఝㄗᕪ⤒㊰Cˆ ࡢᩘࢆῶࡽࡍࡇࡀྍ⬟࡛࠶ࡿࡇࡀ᫂ࡽ࡞ࡗࡓ㸬࡞
࠾㸪6-6-6ࡢࣇࣝࢳࣕࣥࢿࣝࢩࢫࢸ࣒ẚ㍑ࡍࡿ㸪ᮏᡭἲᚑ᮶ᡭἲࡶ㸪2[kHz]
࠾ࡅࡿῶ㡢ᛶ⬟ࡢຎࡀぢࡽࢀࡿࡀ༑ศ࡞ῶ㡢㔞ࢆᚓࡿࡇࡀ࡛ࡁࡓ㸬
5.5 ⤖ゝ
ᮏ ❶ ࡛ ࡣAASࢆ つ ᶍ ࡍ ࡿ 㝿 ࢩ ࢫ ࢸ ࣒ ࡢ つ ᶍ ࢆ 㜵 ࡄ ไ ᚚ ᪉ ἲ ࡋ ࡚ 㸪 M[(1-1)-L] Filtered-X-LMSࣝࢦࣜࢬ࣒ࢆᥦࡋࡓ㸬ୖグࣝࢦࣜࢬ࣒ࡣ㸪M ࢳࣕ
ࣥࢿࣝࡢࢭࣝᩘࢆᚲせࡍࡿሙྜࢆᐃࡋ࡚࠾ࡾ㸪ྛAASࢭࣝࡣ᳨ฟ࣐ࢡࣟ࣍ࣥ
1ࡘ㸪ไᚚࢫࣆ࣮࢝㸯ࡘ㸪ࡑࡋ࡚㏆ഐࡢㄗᕪ࣐ࢡࣟ࣍ࣥLಶࡼࡾไᚚ㸦1-1-Lࡢ FX-LMS㸧ࢆ⾜࠸㸪ྛࠎࡀ⊂❧ไᚚࣇࣝࢱࢆ㐺ᛂྠᐃࡍࡿᡭἲ࡛࠶ࡿ㸬ࡲࡓㄗᕪ
࣐ࢡࣟ࣍ࣥࡣ㔜」ࡋ࡚⏝ࡋ࡚࠸ࡿࡓࡵL⾲ࡋ㸪⥲ᩘࡣMಶࡍࡿ㸬᭱⤊ⓗ
㸪ྛࢭࣝࡣ㸯ࡘࡢ᳨ฟ࣐ࢡࣟ࣍ࣥ1ࡘࡢไᚚࢫࣆ࣮࢝ࢆ1ࡘࡢᅛᐃࡋࡓࣇࣝ
ࢱ(1-1㸧ࡼࡾࣇ࣮ࢻࣇ࢛࣮࣡ࢻไᚚࡍࡿ㸬ࡇࡢᡭἲࡢ᭷ຠᛶࢆࢩ࣑࣮ࣗࣞࢩࣙࣥ
6ࢳࣕࣥࢿࣝᐇ㦂ࢆࡼࡾ☜ㄆࡋࡓ㸬ᐇ㦂࡛ࡣ⦪125[mm]ᶓ750[mm]ࡢ❆ࢆ〇స ࡋ㸪6ࡘࡢAASࢭࣝࢆ୪ไᚚࡍࡿ㸬ࢩ࣑࣮ࣗࣞࢩ࡛ࣙࣥࡣᐇ㦂⨨ࡢྛ✵㛫ࡢఏ 㐩㛵ᩘࢆィ ࡋࡓ್ࢆ⏝ࡋィ⟬ࢆ⾜࠸㸪௨ୗࡢ⤖ㄽࢆᚓࡓ㸬
࣭6[(1-1)-3’] FX-LMSࣝࢦࣜࢬ࣒ᐇ㦂ࡼࡾ㸪ไᚚⅬ࡛ࡣ500[Hz]Ң 2[kHz]ࢆ10
Ң 20[dB]ῶ㡢ྍ⬟࡛࠶ࡾ㸪ไᚚⅬᚋ᪉ࡢᗈ⠊ᅖࡢ✵㛫ࡢῶ㡢ศᕸࡀ☜ㄆࡉࢀࡓ㸬
࣭ ̭ࢩ࣑࣮ࣗࣞࢱࡼࡿ6[(1-1)-3’] FX-LMSࣝࢦࣜࢬ࣒ࡢィ⟬⤖ᯝᐇ㦂⤖ᯝ ࡢᩚྜᛶࡀ☜ㄆࡉࢀࡓ㸬
࣭6[(1-1)-3’]FX-LMSࣝࢦࣜࢬ࣒࡛ࡣ㸪ไᚚࣇࣝࢱࡢTAP㛗ࡼࡾ㸪ไᚚྍ⬟
࿘Ἴᩘࡢ㧗࿘Ἴഃ࡛ࡢᙳ㡪ࡀ࠶ࡾ㸪ไᚚࣇࣝࢱࡀ200TAP࡛ࡣ1200TAPࡃ
ࡽ࡚2[kHz]࡛ࡢ5Ң 10[dB]ࡢῶ㡢ᛶ⬟ࡢຎࡀ⏕ࡌࡿ㸬
࣭6[(1-1)-3’]FX-LMSࣝࢦࣜࢬ࣒࡛ࡣ㸪ఝㄗᕪ⤒㊰ࣇࣝࢱCˆࡢTAP㛗ࡢኚ
࡛ࡣᛶ⬟ࡢຎࡣⓎ⏕ࡋ࡞࠸㸬
࣭ ࢩ࣑࣮ࣗࣞࢩࣙࣥࡼࡾ㸪6[(1-1)-3’] FX-LMSࣝࢦࣜࢬ࣒௨እ㸪ᚑ᮶ᡭἲࡢ 6(1-1)-6 FX-LMSࣝࢦࣜࢬ࣒6-6-6FX-LMSࡢῶ㡢㔞ࡢẚ㍑ࡀྍ⬟࡞ࡗࡓ㸬
࣭6[(1-1)-3’]FX-LMSࣝࢦࣜࢬ࣒ࡣ㸬6-6-6FX-LMSẚ࿘Ἴᩘᖏᇦ࡛ࡣ1.5[kHz]
Ң 2[kHz]࡛5Ң 10[dB]ࡢຎࡀ⏕ࡌࡿ㸬
௨ୖࡢ⤖ᯝࡼࡾ㸪M[(1-1)-L] Filtered-X-LMSࣝࢦࣜࢬ࣒ࡼࡿῶ㡢ຠᯝࡣ2000Hz(w/λ
=0.75㸧㏆࡛ࡢ5Ң 10dBࡢຎࡀ࠶ࡿࡶࡢࡢࢩࢫࢸ࣒ࡣᏳᐃࡋᗈ⠊ᅖ࡛ࡢῶ㡢ຠᯝ
ࢆᚓࡿࡇࡀ࡛ࡁࡓ.ࡑࡢ⤖ᯝ㸪Fig.5.12♧ࡍࡼ࠺㸪ศᩓไᚚࡼࡿྛࢭࣝ⊂❧
ไᚚࡀྍ⬟࡞ࡾ㸪❆ࡀᣑࡋ࡚ไᚚࢭࣝࡀቑ࠼ࡓ❆ࡘ࠸࡚ࡶ㸪つᶍࡋࡓ㝿 ࡢᨵၿᡭἲࡋ࡚᭷ຠ࡛࠶ࡿࡇࡀ᫂ࡽ࡞ࡗࡓ㸬
Fig. 5.12 : AAS window by decentralized system
➨ 6 ❶
⥲ᣓ
̭⎔ቃព㆑ࡢ㧗ࡲࡾࡼࡾ㸪⮬ື㌴࣭㕲㐨➼ࡢ㏻㦁㡢ࡸⓎ㟁ࣉࣛࣥࢺ࣭ᕤሙ➼
ࡽࡢᕤሙ㦁㡢ࡽᐙᗞ㟁ჾ〇ရ➼⮳ࡿࡲ࡛ᵝࠎ࡞㟼⢔ࡀ⾜ࢃࢀ㸪ᵝࠎ࡞✀㢮ࡢ㦁 㡢ᑐࡋ࡚㦁㡢పῶࡀᮃࡲࢀ࡚࠸ࡿ㸬ࡑࡢ⤖ᯝ㸪ᶵᲔ࡞ࡢ㡢※⮬యࡢ㟼㡢㸪ཷ
ࡅᡭഃࡢᑐ⟇ࡀ㐍ࡳࡘࡘ࠶ࡿࡀ㸪㟼⢔ᛶຍ࠼࡚┬࢚ࢿࣝࢠ࣮ᛶࡸᛌ㐺࡞㡢㡪✵㛫
ᑐࡍࡿせᮃࡀቑ࠼㸪㧗ᗘ࡞㦁㡢ᑐ⟇ᢏ⾡ࡀせồࡉࢀ࡚࠸ࡿ㸬ࡑࡢ୰࡛ࡶ㸪ぢ㏻ࡏ
ࡿሙᡤࡽ⪺ࡇ࠼ࡿ㦁㡢ࡢపῶࡀᣲࡆࡽࢀࡿ㸬ලయⓗࡣ㸪❆ࡽධࡿ㦁㡢ࢆ❆ࢆ
㛢ࡵࡎ㟼ࡋࡓ࠸࠸࠺せᮃ࡛࠶ࡿ㸬ࡑࡢゎỴ᪉ἲࡋ࡚ᮏ◊✲࡛ࡣ㸪㡢࡛㡢
ࢆไᚚࡍࡿ㸪⬟ື㦁㡢ไᚚ㸦Active Noise Control :ANC)ࢆ⏝ࡋࡓ㸪ࠕ㢼ࡣ㏻ࡍࡀ㡢 ࡣ㏻ࡉ࡞࠸❆ࠖࡢᐇ⌧ࢆ┠ᶆࡋࡓ㸪ࢡࢸࣈ㡢㡪ࢩ࣮ࣝࢹࣥࢢ(Active Acoustic
Shielding:AAS)ࢆᥦࡋࡓ㸬̭ᮏㄽᩥ࡛ࡣ㸪ᥦࡋࡓAASࡢࢥࣥࢭࣉࢺ⌮ㄽࢆド
᫂ࡍࡿࡓࡵ㸪ࢩ࣑࣮ࣗࣞࢩࣙࣥᐇ㦂ࡼࡾ᳨ドࡋ㸪ᐇ⌧ᛶࢆ᫂ࡽࡋࡓ㸬ࡲࡓ AASࢆᐇ⏝ࡍࡿ࠶ࡓࡾၥ㢟࡞ࡿ㸪ᑐ㇟ྍ⬟࡞࿘Ἴᩘᖏᇦࡘ࠸࡚ࡢᨵၿᡭἲࢆ
ᥦࡋ㸪ᐇ㦂ࡼࡾຠᯝࢆ᳨ドࡋࡓ㸬᭱ᚋ㸪ࡶ࠺୍ࡘࡢၥ㢟ࡋ࡚㸪❆ࡢࢧࢬ ࡀኚࢃࡗࡓ㸦つᶍࡋࡓ㸧ሙྜ㸪ศᩓไᚚࢆ⏝ࡋࡓM[(1-1)-L]Filtered-X-LMS
ࣝࢦࣜࢬ࣒ࡼࡾࢩࢫࢸ࣒ࡢ」㞧࣭つᶍࢆ㜵ࡄᡭἲࢆᥦࡋ㸪ࢩ࣑࣮ࣗࣞࢩࣙ
ࣥᐇ㦂ࡼࡾ㸪ࡑࡢῶ㡢ᛶ⬟ࢆ᳨ドࡋࡓ㸬
➨1❶࡛ࡣ㸪◊✲ࡢ⫼ᬒ࣭ὶࢀ࣭ᴫせࡑࡋ࡚AASࡢࢥࣥࢭࣉࢺࡘ࠸࡚㏙ࡓ㸬➨
2❶࡛ࡣ㸪ࢩ࣑࣮ࣗࣞࢩࣙࣥࡼࡾ⌮ㄽⓗ࡞ῶ㡢ຠᯝࢆィ⟬ࡋ㸪✵㛫ࡢῶ㡢ศᕸࢆண ࡋࡓ㸬ࣔࢹࣝࡣ3ḟඖ✵㛫ࡋ㸪୍ḟ㡢※(㦁㡢㸧ࢆἼ㛗λ㹙m㹛ࡢᖹ㠃Ἴࡋ㡢ᅽ
ࢆ࠼㸪xyᖹ㠃ࡣไᚚ⏝ࡢⅬ㡢※ࢆ᱁Ꮚ≧w㹙m㹛㛫㝸࡛㓄⨨ࡋᚋ᪉d㹙m㹛
⨨㸦ไᚚⅬ㸧࡛ࡢ㡢ᅽࡀ0࡞ࡿࡼ࠺ಙྕࢆ࠼ࡓ㸬ᐇ㦂᮲௳ࡋ࡚㸪λ㸪dࢆw
࡛㝖⟬ࡋࡓ↓ḟඖ್ᩚ⌮ࡋࡓ್ࢆኚືࡉࡏ㸪ࡉࡽ୍ḟ㡢※ࡢධᑕゅθࡘ࠸࡚
ࡶẚࡓ㸬⤖ᯝ㸪ไᚚⅬᚋ᪉ࡢᗈ⠊ᅖ࡛ࡢῶ㡢ศᕸࡀ☜ㄆࡉࢀ㸪ไᚚ㡢※ࡢ㓄⨨
ᑐ㇟ྍ⬟࡞Ἴ㛗ࡢ㛵ಀࡣw/λ ≤ 0.5㸪ไᚚⅬ⨨ࡘ࠸࡚ࡣd/w=1௨ୖ࡛㸪ධᑕ ゅᗘࡘ࠸࡚ࡣθ≤60[deg]࡛ࡢῶ㡢ࡀྍ⬟࡛࠶ࡿࡇࡀண ࡉࢀࡓ㸬
➨3❶࡛ࡣ㸪2❶ࡢ⤖ᯝࢆࡶᑠᆺࡢAAS❆ࢆసᡂࡋ㸪ṇ㠃ධᑕ㡢※㸪ᩳࡵධᑕ 㡢※㸪」ᩘ㡢※㸪⛣ື㡢※㸪ᐊෆࡢᑕ㡢㸪ෆ㒊㡢※ࡘ࠸࡚ࣔࢹࣝࢆసᡂࡋ㸪ࣔ
ࢹࣝヨ㦂ࢆ⾜ࡗࡓ㸬ࡑࡢ⤖ᯝ㸪ྛ᮲௳ୗ࡛ࡢῶ㡢ຠᯝ㸪ῶ㡢ศᕸࢆᚓࡿࡇࡀ࡛ࡁ㸪 AASࡢ᭷⏝ᛶࢆ☜ㄆࡍࡿࡇࡀ࡛ࡁࡓ㸬
➨4❶ࡢప࿘Ἴᖏᇦࡢᛶ⬟ᨵၿ࠾࠸࡚ࡣ㸪ప࿘Ἴ⏝ࣘࢽࢵࢺ㧗࿘Ἴ⏝ࣘࢽࢵࢺ
ྠసືࡼࡗ࡚300[Hz]Ң 2[kHz]ࡢᖏᇦ࡛5Ң 18[dB]ࡢῶ㡢ຠᯝࢆᚓࡿࡇࡀ࡛ࡁ㸪
┠ᶆࡢ500[Hz]௨ୗࡢῶ㡢ᛶ⬟ࡢᨵၿࡀྍ⬟࡞ࡗࡓ㸬ࡲࡓ㸪ྠ୍ࣇࣝࢱࡢᐇ㦂
࡛ࡶྠᵝ࡞⤖ᯝࢆᚓࡓ㸬ࡋࡋ㸪ప࿘Ἴ⏝㸪㧗࿘Ἴ⏝㸪ࢯࣟࡒࢀ༢⊂࡛ࡢῶ㡢ຠᯝ
ẚ㸪୧⪅ࢆྠసືࡋࡓሙྜࡢῶ㡢ຠᯝࡣຎࡀぢࡽࢀࡿ㸬ࡑࡇ࡛㸰✀㢮 ࡢAASࣘࢽࢵࢺᮏ᮶ࡢᛶ⬟ࢆ᭱㝈ࡍࡿࡓࡵࡣ㸪౽ᐅⓗ⏝ࡋࡓ2ࣘࢽࢵࢺ
ࢆྠไᚚࡍࡿᡭἲࡢᨵၿࡋ࡚㸪ྛࣘࢽࢵࢺࡢࢡࣟࢫࢺ࣮ࢡᡂศࢆ⪃៖ࡋࡓᡭ ἲࡀᚲせ࡛࠶ࡿ㸬
➨5❶ ࡛ ࡣAASࢆ つ ᶍ ࡍ ࡿ 㝿 ᚲ せ ࡞ ࡿ ไ ᚚ ᪉ ἲ ࡋ ࡚ 㸪M[(1-1)-L]
Filtered-X-LMSࣝࢦࣜࢬ࣒ࢆᥦࡋࡓ6ࢳࣕࣥࢿࣝAASࣔࢹࣝࢆ〇సࡋ㸪᪂ᡭἲ
ࡢ᭷ຠᛶࢆᐇ㦂ⓗ᳨ドࡋࡓ㸬ࡲࡓ㸪ࢩ࣑࣮ࣗࣞࢩࣙࣥࡼࡗ࡚㸪ไᚚⅬ࠾ࡅࡿῶ 㡢ຠᯝࢆ㸪ᡭἲẚ㍑᳨᳨࣭ウࡋ㸪᪂ᡭἲࡢ᭷ຠᛶࢆ᳨ドࡋࡓ㸬⤖ᯝ㸪ྛไᚚࢭ
ࣝࢆ⊂❧ไᚚࡍࢀࡤྛࢭࣝᚲせ࡞ఏ㐩㛵ᩘࢆ㐺ᛂྠᐃ࡛ࡁࡿᡭἲ࡞ࡾ㸪ࢭࣝ
ᩘࡀቑ࠼ࡓࡋ࡚ࡶྛࢭࣝࡣ1-1-LࡢFiltered-X-LMSࣝࢦࣜࢬ࣒ࡢไᚚ࡛ᗈ࠸ῶ 㡢ศᕸࢆᚓࡿࡇࡀྍ⬟࡞ࡗࡓ㸬
௨ୖࡼࡾ㸪ㄢ㢟ࡋ࡚ᣲࡆࡓ㸪᳨ฟ࣐ࢡࣟ࣍ࣥไᚚࢫࣆ࣮࢝⨨ࡼࡿྠ୍
⨨㸪ᐇ㝿ࡢ㓄⨨㊥㞳ࡼࡿᙳ㡪ࡘ࠸࡚ࡣ㸪ᩳࡵධᑕ㡢※࠾࠸࡚㸪ྠ୍
⨨ࡍࡿሙྜࡢ㊥㞳ᕪࡼࡾ㸪⏕ᡂࡍࡿ㡢ἼࡢἼ㠃ࡀ㦁㡢࡞ࡿ㡢ἼࡢἼ㠃ࡎ
ࢀࡀ⏕ࡌ㸪ῶ㡢ຠᯝࡢⱝᖸࡢຎࡀ☜ㄆࡉࢀࡓࡀ㸪యⓗࡣ༑ศ࡞ῶ㡢ຠᯝࢆᚓ
ࡿࡇࡀ࡛ࡁࡓ㸬ࡲࡓ㸪㧗ࢧࣥࣉࣜࣥࢢ࿘Ἴᩘࢆ࠺ࡇ࡛㸪᳨ฟ࣐ࢡࣟ࣍ࣥ
ไᚚࢫࣆ࣮࢝ࢆ㏆㊥㞳㓄⨨ࡋ࡚ࡶ㸪ᅉᯝᚊࢆ‶ࡓࡍࡇࡀྍ⬟࡞ࡗࡓ㸬
ῶ㡢ྍ⬟࡞ᑐ㇟࿘Ἴᩘᖏᇦfࡘ࠸࡚ࡣ㸪2✀㢮ࡢࣘࢽࢵࢺࢆྠ⊂❧ไᚚࡍ
ࡿᡭἲࡼࡾప࿘Ἴᡂศࡢᛶ⬟ᨵၿࡀྍ⬟࡞ࡗࡓ㸬
ࡑࡋ࡚㸪ไᚚࢭࣝࡢᩘࡀቑຍࡼࡿࢩࢫࢸ࣒ࡢ」㞧࣭つᶍ㜵Ṇࡘ࠸࡚ࡣ㸪
ྛࢭࣝࡀ⊂❧ไᚚࡉࢀ㸪㏆ഐࡢไᚚⅬࢆᑐ㇟ࡍࡿศᩓไᚚᡭἲࢆ⏝ࡍࡿࡇ
࡛㸪AASࡢᛶ⬟ࢆຎࢆᢚ࠼㸪ከࢳࣕࣥࢿࣝไᚚྠ➼ࡢῶ㡢ຠᯝ࣭ศᕸࢆᚓࡿࡇ
ࡀ࡛ࡁࡓ㸬
ᚋࡢㄢ㢟ࡋ࡚ࡣ㸪ࡲࡎ㸪᳨ฟ࣐ࢡࣟ࣍ࣥไᚚࢫࣆ࣮࢝ࡢ㊥㞳ࢆࡼࡾ㏆࡙
ࡅࡿࡇ࡛㸪ᩳࡵධᑕ㡢※ᑐࡍࡿᛶ⬟ࢆྥୖࡍࡿᚲせࡀ࠶ࡿ㸬ࡑࡢࡓࡵ㸪ࡼࡾ㧗
㏿࡞ಙྕฎ⌮ࢆྍ⬟ࡍࡿࢥࣥࢺ࣮ࣟࣛ㛤Ⓨࡀᚲせ࡛࠶ࡾ㸪FPGAࢆ⏝࠸ࡓ㧗㏿ಙ
ྕฎ⌮࣮࣎ࢻ㛤Ⓨࡀ⾜ࢃࢀ࡚࠸ࡿ[52]㸬ࡲࡓ㸪㧗ࢧࣥࣉࣜࣥࢢ࿘Ἴᩘࢆ࠺ࡇ࡛☜
ಖ࡛ࡁ࡞ࡗࡓࣥࣃࣝࢫᛂ⟅ࡢࣇࣝࢱ㛗ࡉࡶ㸪FPGAࡼࡾᨵၿࡉࢀప࿘Ἴᖏ ᇦࡢᛶ⬟ࡀྥୖࡍࡿ[51]㸬ࡼࡗ࡚㸪FPGAࡢ㛤Ⓨᬑཬࡼࡾᖜ࡞ᨵၿࡀぢ㎸ࡲࢀ
ࡿ㸬ḟ㸪ᑐᛂྍ⬟࡞࿘Ἴᩘᣑࡢㄢ㢟ࡋ࡚ࡣ㸪ࡼࡾᑠᆺࡘప࿘ἼࡢⓎ㡢ᛶ⬟
ࡢ㧗࠸ࢫࣆ࣮࢝ࡢ㛤Ⓨࡀᚲせ࡛࠶ࡿ㸬ࡉࡽᮏㄽᩥ࡛Ⓨࡋࡓ2✀㢮ࡢࣘࢽࢵࢺࢆ
⏝ࡍࡿᡭἲࡢไᚚ᪉ἲࢆᨵၿࡍࡿᚲせࡀ࠶ࡿ㸬ࡲࡓ㐺ษ࡞ྛࣘࢽࢵࢺࡢ㐺ษ࡞ᑐ
ᛂ࿘Ἴᩘࡢ㑅ᐃ㸦ࢭࣝ㛫㝸ࢫࣆ࣮࢝㸧ࡀᚲせ࡞ࡿ㸬᭱ᚋ㸪ᮏㄽᩥ࡛Ⓨࡋࡓ㸪 ࢩࢫࢸ࣒ࡢつᶍࢆ㜵ࡄAASศᩓไᚚᡭἲࡘ࠸࡚ࡣ㸪5❶ᮎ♧ࡋࡓFig.5.12
ࡼ࠺㸪ᮏ᮶ࡢ㓄⨨࡛࠶ࡿ᱁Ꮚ≧୪㸪ᆺࡢ❆㐺ᛂࡍࡿࡇࢆ┠ᣦࡍ㸬ࡑࡢ ࡓࡵ㸪M[(1-1)-L]Filtered-X-LMSࣝࢦࣜࢬ࣒ࡢL㒊ศࡣቑࡸࡍᚲせࡀ࠶ࡾ㸪Lࡢ 㑅ᐃ㸦㏆ഐࡢㄗᕪಙྕࢆࡇࡲ࡛ᑐ㇟ࡍࡿ㸧㸪ไᚚࢭࣝࡢຠ⋡ⓗ࡞㓄⨨᪉ἲ࡞
᳨ウࡍࡿᚲせࡀ࠶ࡿ㸬ࡉࡽ㸪ࢩࢫࢸ࣒ࡢつᶍࢆ㜵ࡄᡭἲࡋ࡚㸪❆ᯟ࿘㎶
୰ኸ㒊㏆࡛ࡢไᚚࣇࣝࢱࡢ᮰್㸦ᅛᐃࣇࣝࢱ㸧ࢆồࡵ㸪ሙᡤࡼࡾ✀㢮 ࡢ㐪࠺ྠ୍ᅛᐃࣇࣝࢱࢆ⏝ࡍࡿ᪉ἲࡼࡾ㸪㐺ᛂྠᐃ㒊ศࡢ┬␎࡛ࡁࡿྍ⬟ᛶ ࡀᣲࡆࡽࢀࡿ㸬ࡇࢀࡽࡘ࠸࡚ࡶ᳨ウࡋ࡚࠸ࡃᚲせࡀ࠶ࡿ㸬
̭ᮏ◊✲ࢆ㐙⾜ࡍࡿ࠶ࡓࡾ㸪◊✲᪉㔪ࢆ࠼࡚࠸ࡓࡔࡁ㸪࠸ࡘࡶᑀ࡞ࡈᣦᑟ㸪 ࡈᣦࢆ࠸ࡓࡔ࠸ࡓすᮧṇ≉௵ᩍᤵ㸪す⏣ಙ୍㑻ᩍᤵ,ᚋ⸨▱ఙᩍᤵ࡞ࡽࡧᱜ㛫
୍ᚨᩍᤵ῝ࡃឤㅰ࠸ࡓࡋࡲࡍ㸬
ࡲࡓ㸪ᬑẁࡽከࠎᚚ༠ຊ࠸ࡓࡔࡁࡲࡋࡓไᚚ࣭ࣟ࣎ࢸࢡࢫ◊✲ᐊࡢⓙᵝᑐ ࡋ࡚㸪ᚰࡽᚚ♩⏦ࡋୖࡆࡲࡍ㸬
ཧ⪃ᩥ⊩
[1] ♫ᅋἲே᪥ᮏ㦁㡢ไᚚᕤᏛ⦅͆ 㦁㡢⏝ㄒ ͇(ᰴ㸧ᢏሗᇽฟ∧㸦2010㸧 [2] ஂ ಖ ⚈ ୕ 㸪ᮌ ᮧ ோ ⨾ 㸪͆ ㏻ 㦁 㡢 ၥ 㢟 ࡢ ⾜ ᨻ ⓗ ྲྀ ࡾ ⤌ ࡳ ͇᪥ ᮏ 㡢 㡪 Ꮫ ㄅ 㸪
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ࡢཎᅉᚋࡢㄢ㢟ࡘ࠸࡚ ͇᪥ᮏ㦁㡢ไᚚᕤᏛᖹᡂ24ᖺ⛅Ꮨ◊✲Ⓨ⾲ㅮ
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⟇ࡢ࠶ࡺࡳࡽࡳࡓ㟼㡢㌴୧ࡢᙳ㡪ࡘ࠸࡚ ͇᪥ᮏ㦁㡢ไᚚᕤᏛᖹᡂ22ᖺ⛅
Ꮨ◊✲Ⓨ⾲ㅮ₇ㄽᩥ㞟㸪pp.1-4㸦2010㸧
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[35] ᑿᮏ ❶, ⸨ཎ ᜤྖ㸪,͆ 㜵㡢ሟ࢚ࢵࢪ࣏ࢸࣥࢩࣕࣝࡢ⬟ືᾘཤ ͇,᪥ᮏ㡢㡪Ꮫ
ㄅ,Vol.47㸪No.11㸪pp. 801-808(1991)
[36] ๓⏣ᑗኴ㑻㸪すᮧṇ㸪ᒣཱྀ㐩ஓ㸪ⱱᮌᘓ͆ ከࢳࣕࣥࢿࣝἼᙧྠᮇἲࢆ⏝࠸
ࡓANCࡢᇶ♏◊✲ ͇᪥ᮏᶵᲔᏛD&D2011,CD-ROM㸦2011㸧
[37] Ლᕝᘏ͆MR㦁㡢ࡢࡓࡵࡢࢡࢸࣈࣀࢬࢥࣥࢺ࣮ࣟࣝࢩࢫࢸ࣒ࡢ᳨ウ ͇,
᪥ᮏ㦁㡢ไᚚᕤᏛᖹᡂ22ᖺᏘ◊✲Ⓨ⾲ㅮ₇ㄽᩥ㞟,pp.5-8㸦2010㸧
[38] ᒣᕝ⯟ᖹ㸪Ლᕝᘏ͆MRᐊෆእ࡛ࡢ㡢ኌヰࢆ┠ⓗࡋࡓ࣊ࢵࢻ࣐࢘ࣥࢺᆺANC ࢩࢫࢸ࣒ ͇,᪥ᮏ㦁㡢ไᚚᕤᏛᖹᡂ25ᖺᏘ◊✲Ⓨ⾲ㅮ₇ㄽᩥ㞟,pp.117-120 㸦2013㸧
[39] M.Nishimura,K.Ohnishi,W.P.Patrick and A.C.Zander,͆Decelopment of Active Acoustic Treatment (Phase1,Basic concept and development of AAT-Cell)͇,Proc.of ACTIVE’97,pp.319-330(1997)
[40] W.P.Patrick㸪A.C.Zander㸪P.G.Mehta and M.Nishimura,K.Ohnishi,͆Decelopment of Active Acoustic Treatment (Phase2,Duct Test of AAT Sheet)͇,Proc.of ACTIVE’97,pp.331-344(1997)
[41] M.Nishimura,T.Goto and N.Kanamori,͆Basic Research of Active Sound Insulation Unit͇,Proc. of ICA 2004,III pp.2169-2172(2004)
[42] Y.Umebayashi㸪M.Nishimura㸪N.Kanamori and N.Furuyashiki,͆Basic Research of Active Sound Insulation Unit for Fllor Impact Noise͇,Proc. of INTERNOISE 2006,CD-ROM(2006)
[43] ᭷ᮏ΅㸪すᮧṇ㸪⏣ಙᩗ,͆ ᖹ㠃ࢫࣆ࣮࢝ࢆ⏝࠸ࡓࢡࢸࣈ㐽㡢ࣘࢽࢵࢺ ࡢ㛤Ⓨ㸦᭱㐺ᵓ㐀ࡢ᳨ウ㸧͇,᪥ᮏᶵᲔᏛD&D,CD-ROM(2010)
[44] K.Ohnishi, T.Saito, S.Teranishi,Y.Namikawa,T.Mori,K.Kimura and K.Uesaka͆ De-celopment of proto-type active soft edge noise barrier͇,Proc.of ICA 2004,II pp.1041-1044(2004)
[45] K.Ohnishi, S.Teranishi㸪M.Nishimura㸪K.Uesaka㸪K.Hachimine and H.Ohnishi͆ De-celopment of the Noise Barier Using Active Soft Edge, Part 1: Control Algorithm, Consistency with Active and Passive Performance and 2m Length Prototype Test in Anechoic Room͇,Proc. of ACTIVE99㸪pp.596-606(1999)
[46] す୕㸪ᑎす㐍㸪すᮧṇ㸪ୖᆏඞᕭ㸪す༤ᩥ͆ ࢡࢸࣈࢯࣇࢺ࢚ࢵࢪ㐽 㡢ቨࡢᇶᮏࢥࣥࢭࣉࢺ↓㡪ᐊᐇ㦂ࡼࡿῶ㡢ຠᯝ ͇,᪥ᮏ㡢㡪Ꮫㄅ,Vol.57㸪 No.2㸪pp.129-138(2001)
[47] ୖᆏඞᕭ㸪ᮌᮧ㸪୪ἙⰋ㸪す༤ᩥ㸪す୕㸪ᑎす㐍㸪すᮧṇ㸪͆ ࢡࢸࣈࢯࣇࢺ࢚ࢵࢪ㐽㡢ቨࡢ㛤Ⓨῶ㡢ຠᯝࡢホ౯ ͇,᪥ᮏ㡢㡪Ꮫㄅ,Vol.58㸪 No.12㸪pp.753-760(2002)
[48] Ἑᓮ༤⛅㸪すᮧṇ㸪㔠᳃┤ᕼ㸪Ώ㎶ᩄᖾ͆ 㜵㡢ቨ⏝ANCࢩࢫࢸ࣒ࡢ㧗ᛶ⬟
㛵ࡍࡿᇶ♏᳨ウ㸦➨2ሗ㸸↓㡪ᐊᐇ㦂 ͇,᪥ᮏᶵᲔᏛ➨18ᅇ⎔ቃᕤᏛ⥲ྜࢩ
࣏ࣥࢪ࣒࢘2008㸪CD-ROM(2008)
[49] S.M.Kuo,D.R.Morgan,͆Active Noise Control Systems algorithmes and DSP imple-mentations͇,Wiley-Interscience(1996)
[50] 㕥ᮌḟ㸪すᮧṇ㸪㞡ᮏಙဢ㸪ᚚἲᕝᏛ͆ ᶵᲔ㡢㡪ᕤᏛ ͇,㸦ᰴ㸧ࢥࣟࢼ♫(2004) [51] 㐩 ྍ ⿱ ᕫ 㸪す ᮧ ṇ 㸪ⱱ ᮌ 㸪͆FPGAࢆ ⏝ ࠸ ࡓANC⏝ 㧗 ㏿ ಙ ྕ ฎ ⌮ ࣎ ࣮ ࢻࡢ㛤Ⓨ㸦ప࿘Ἴᇦ࡛ࡢῶ㡢ຠᯝࡢᨵၿ㸧͇᪥ᮏᶵᲔᏛDynamics and Design Conference2011(㧗▱㸧CD-ROMㄽᩥ㞟, No.627㸦2011㸧
[52] すᮧṇ㸪すᙳ◊୍㸪ᮧᑿ㐩ஓ㸪⏣ಙᩗ͆ ᳨ฟ࣐ࢡ࣭ࣟ࣍ࣥไᚚࢫࣆ࣮࢝
୍యᆺANCࣘࢽࢵࢺࡢ㛤Ⓨ ͇,᪥ᮏᶵᲔᏛ➨20ᅇ⎔ቃᕤᏛ⥲ྜࢩ࣏ࣥࢪ࣒࢘
2010㸪CD-ROM(2010)
㛵㐃ሗ࿌
➨ 1,2,3 ❶
(1) ᮧᑿ 㐩ஓ㸪すᮧ ṇ㸪⏣ಙᩗ͆ ࢡࢸࣈ㡢㡪ࢩ࣮ࣝࢹࣥࢢ㛵ࡍࡿᇶ♏
◊✲̭➨2ሗ̭ᑠ❆タ⨨ࡋࡓሙྜࡢῶ㡢ᛶ⬟ ͇㸪᪥ᮏ㦁㡢ไᚚᕤᏛᖹᡂ22 ᖺᏘ◊✲Ⓨ⾲ㅮ₇ㄽᩥ㞟㸪pp.13-16㸦2010㸧
(2) Masaharu Nishimura㸪Tatsuya Murao and Nobutaka Wada㸪Basic Study on Active Acoustic Shielding : Phase 2 Noise Reducing Performance for a Small Open Win-dow㸪Proc. of INTER NOISE 2010㸪CD-ROM㸦2010㸧
(3) Tatsuya Murao and Masaharu Nishimura㸪͆Basic Study on Active Acoustic Shielding
͇Journal of Environment and Engineering㸪Vol.7㸪No.1㸪pp㸬76-91㸦2012㸧
➨ 4 ❶
(4) Tatsuya Murao and Masaharu Nishimura㸪Basic Study on Active Acoustic Shielding:
phase 3 Improving Noise Reducing Performance in Low Frequency Region㸪Proc.
of INTER NOISE 2011㸪CD-ROM㸦2011㸧
(5) Tatsuya Murao㸪Masaharu Nishimura and Kazunori Sakurama㸪͆Basic Study on Active Acoustic Shielding: Phase 4 improving noise reducing performance in low frequency-2͇㸪Proc. of INTER NOISE 2012㸪CD-ROM㸦2012㸧
(6) Tatsuya Murao㸪Masaharu Nishimura㸪Kazunori SAKURAMA and Shin-ichiro Nishida
͆Basic study on active acoustic shielding (Improving noise-reducing performance in low-frequency range)͇Mechanical Engineering Journal㸪Vol.1㸪No.6㸪pp㸬EPS0065 㸦2014㸧
➨ 5 ❶
(7) ᮧᑿ 㐩ஓ㸪すᮧ ṇ㸪͆ ࢡࢸࣈ㡢㡪ࢩ࣮ࣝࢹࣥࢢ㛵ࡍࡿᇶ♏◊✲̭➨3 ሗ̭ప࿘Ἴᖏᇦ࠾ࡅࡿῶ㡢ᛶ⬟ᨵၿ ͇㸪᪥ᮏ㦁㡢ไᚚᕤᏛᖹᡂ25ᖺᏘ◊
✲Ⓨ⾲ㅮ₇ㄽᩥ㞟㸪pp.101-104㸦2013㸧̭̭
(8) Tatsuya Murao㸪Masaharu Nishimura and Kazunori Sakurama͆Basic study on active acoustic shielding: phase 5 improving the method to enlarge AAS window͇Proc.
of INTER NOISE 2013㸪CD-ROM㸦2013㸧̭
(9) Tatsuya Murao㸪Masaharu Nishimura㸪Kazunori SAKURAMA and Shin-ichiro Nishida
͆Basic study on active acoustic shielding: phase 6 improving the method to enlarge AAS window-2͇Proc. of INTER NOISE 2014㸪USB flash memory㸦2014㸧
㘓 A
ᇶ♏ไᚚᡭἲ
ᮏ❶࡛ࡣ㸪㐺ᛂࣇࣝࢱࡢཎ⌮ࣝࢦࣜࢬ࣒ࡘ࠸࡚⤂ࡋ㸪୍ḟඖࢲࢡࢺ
࠾ࡅࡿANCไᚚࢩࢫࢸ࣒ࢆᣲࡆ㸪ᇶ♏ไᚚᡭἲࡘ࠸࡚㏙ࡿ㸬
A.1 㐺ᛂࣇࣝࢱࡢཎ⌮
̭ᮏ❶࡛ࡣ㸪㐺ᛂࣇࣝࢱࡋ࡚ከࡃ⏝࠸ࡽࢀ࡚࠸ࡿ᭷㝈ࣥࣃࣝࢫᛂ⟅㸦Finite Impulse Response㸸FIR㸧ᆺ㐺ᛂࢹࢪࢱࣝࣇࣝࢱࢆ⪃࠼ࡿ㸬ᮏ᮶㸪NhḟࡢFIRࣇ
ࣝࢱࡢሙྜ㸪Nhḟ㐃❧᪉⛬ᘧࡢゎࡋ࡚ࣇࣝࢱಀᩘࡀᑟࡁฟࡉࢀࡿ㸬ࡇࡢ᪉⛬ᘧ
ࢆFIRࣇࣝࢱࡢṇつ᪉⛬ᘧࡧ[15]㸪┤᥋ゎࡃᡭἲ࡛ࡣ㸪ࣇࣝࢱࡢḟᩘࡀከࡃ
࡞ࡿ₇⟬㔞ࡀቑࡍࡿ㸬ࡇࡢၥ㢟ࢆゎỴࡍࡿࡓࡵ㏲ḟⓗ᭱㐺ゎࢆồࡵࡿ᪉ἲ ࡀᥦࡉࢀ࡚࠾ࡾ㸪ࡑࡢ୍ࡘ᭱ᛴ㝆ୗἲࡀ࠶ࡿ㸬᭱ᛴ㝆ୗἲࡣ㸪࠶ࡿࣇࣝࢱ ಀᩘᑐࡋ࡚ᖹᆒㄗᕪࡢ୍ḟᑟ㛵ᩘࡽ໙㓄ࢆồࡵ㸪ࡑࡢ໙㓄ࡀ㈇ࡢ᪉ྥಀ
ᩘࢆ᭦᪂ࡍࡿࡇ࡛㸪᭱ᑠᖹᆒ฿㐩ࡍࡿࡇࢆ⏝ࡋ࡚࠸ࡿ㸬ࡋࡋ㸪໙㓄
࣋ࢡࢺࣝࢆồࡵࡿ㝿ㄗᕪࡢᮇᚅ್ࡀᚲせ࡞ࡾ㸪₇⟬㔞ࡣᑡ࡞ࡃࡣ࡞࠸㸬ࡑ ࡇ࡛㸪௦ࢃࡾᆒㄗᕪࡢ▐್ࢆ⏝࠸ࡓࣝࢦࣜࢬ࣒ࡀLMSࣝࢦࣜࢬ࣒࡛࠶
ࡿ㸬Fig.A.1(a)ࡣ࠶ࡿ┠ᶆಙྕd(n)ࢆ㐺ᛂࣇࣝࢱࡢฟຊಙྕy(n)࡛᥎ᐃࡍࡿࢆ
♧ࡍ㸬㐺ᛂࣇࣝࢱࡢᙺࡣ㸪ࡑࡢఏ㐩≉ᛶࡍ࡞ࢃࡕࣇࣝࢱಀᩘࢆኚ࠼࡞ࡀࡽy(n)
ࢆd(n)㏆࡙ࡅࡿࡇ࡛࠶ࡿ㸬ࡍ࡞ࢃࡕ㸪Fig.A.1(b)ࡢ᥎ᐃㄗᕪಙྕe(n)ࡣ
e(n) =d(n)−y(n) (A.1)
ࢆ᭱ᑠࡍࡿࡇࡀ㐺ᛂࣇࣝࢱࡢᙺ࠸࠼ࡿ㸬࠸ࡲ㐺ᛂࣇࣝࢱࡋ࡚㸪Fig.A.2 ࡢhkࢆಀᩘࢆࡍࡿFIRࣇࣝࢱࢆ⏝࠸ࡿࡍࡿࡑࡢฟຊಙྕy(n)ࡣ㸪ࡓࡓࡳ㎸ࡳ
࡛⾲ࡉࢀ㸪
y(n) =
N−1
k=0
hkx(n−k) (A.2)
࡞ࡿ㸬̭Eq.(A.2)ࡼࡾ㸪ྠࡌධຊಙྕx(n) ࡛ࡶಀᩘ ࢆኚ࠼ࡿࡇࡼࡾ㸪ࣇ
ࣝࢱฟຊy(n)ࡀኚࡍࡿࡇࡀศࡿ㸬̭ࡇࢁ࡛ㄗᕪホ౯㔞ࡀ㸪Eq.(A.1)ࡢㄗᕪ ಙྕe(n)ࡢࡲࡲ࡛࠶ࡿ㸪e(n) = 0࡞ࡿࣇࣝࢱಀᩘhkࡢ⤌ࡳྜࢃࡏࡣᩘከࡃᏑ ᅾࡍࡿ㸬ࡑࡇ࡛㸪e(n)ࡢ⮬್e2(n)ࢆ᥎ᐃㄗᕪࡢホ౯㔞ࡋ࡚ࡳࡿ㸬
Fig. A.1 : Presumption of the Signal Using Adaptive Filter
Fig. A.2 : FIR Adaptive Filter
e2(n) ={d(n)−y(n)}2 =d2(n)−2d(n)y(n) +y2(n) (A.3) Eq.(A.3)Eq.(A.2)ࡢy(n)ࢆ௦ධࡍࡿ
e2(n) =d2(n)−2d(n)
N−1
k=0
hkx(n−k)
+
N−1
k=0 N−1
m=0
hkx(n−k)hmx(n−m) (A.4)
࡞ ࡿ 㸬 ࠼ ࡤ 㸪N=2 ࡋ 㸪ࣇࣝ ࢱ ಀ ᩘ ࡀh0㸪h1 ࡢ ࡘ ࡛ ࠶ ࡿ ࡍ ࡿ 㸪Eq㸬 (A.4)ࡣ
e2(n) = d2(n)−2d(n){h0x(n) +h1x(n−1)}
+x2(n)h20+x2(n−1)h21+ 2h0h1x(n)x(n−1) (A.5)
࡞ࡾ㸪ࣇࣝࢱಀᩘh0㸪h1ࢆኚᩘࡍࡿḟ㛵ᩘ࡞ࡗ࡚࠸ࡿ㸬ㄗᕪホ౯㔞e2(n) ࡀḟ㛵ᩘ࡛࠶ࡿ࠸࠺ࡇࡣ㸪Fig.A.3♧ࡍࡼ࠺ୗฝ࡞ࡍࡾࡤࡕ≧ࡢḟ᭤
㠃⪃࠼ࡽࢀ㸪ㄗᕪࡢ᭱ᑠⅬe2min(n)ࡀ၏୍Ꮡᅾࡍࡿ࠸࠺ࡇ࡛࠶ࡿ㸬e2min(n)
࠾ࡅࡿಀᩘhopt0 㸪hopt1 ࡀ㸪้n࠾ࡅࡿ᭱㐺࡞ࣇࣝࢱಀᩘ࡞ࡿ㸬
ࡇࢁ࡛㸪Eq.(A.3)࡛ࡣ᭱㐺ಀᩘ್ࡀ㛫ⓗኚࡋ࡚ࡋࡲ࠺ࡢ࡛Eq.(A.3)௦
ࢃࡿูࡢㄗᕪホ౯㔞ࡋ࡚㸪ᖹᆒㄗᕪE[e2(n)]ࢆ⏝࠸ࡿ[15]㸬
Ee2(n)=
n k=0
e2 =
n k=0
{d(k)−y(k)}2 (A.6)
Fig. A.3 : The Amount of Evaluations of Square Error