Signal Processing for Active Control
6. !"#$%&'(
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" 6789:;<1=->01!2345
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Signal Processing for Active Control
Y)*+,-./01!2345
1!Z:;#$[\]^_`#$aD8967bcdef0IIIIgRhij<1=->0kl`mnop
IIII[q&V-r:;#$DsNKD1=ta
!
x(n)wi
Reference
FIR Filter
Output
y(n)
d(n)
e(n)
Error Signal
Desired Signal
音響情報処理工学演習 2008 July
1
Signal Processing for Active Control
Y)*+,-./01!2345
!uv#$\]Dw[xyVz{|<}~z`��a
Signal Processing for Active Control
Y)*+,-./01!2345
!2345D�VZ2���DgRhij�J=E[e2(n)]IIII
II<1=t>02345�j wopt <��0�lp
" #$�c�V��4@KLVb�f�k���r)��b��kII�)*67b���f0p
音響情報処理工学演習 2008 July
2
Signal Processing for Active Control
Y)*+,-./01!2345
8��i��
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Signal Processing for Active Control
Y)*+,-./01!2345
! gRhij�2345�jD2���
" ^��IAI�¡�c¢$(positive definite) b�f�kIIIIgRhijr£¤D1=�<¥¦p
音響情報処理工学演習 2008 July
3
Signal Processing for Active Control
Y)*+,-./01!2345
!§3¨K (Wiener) 2345
" gRhij J <�j w b©ª^«k�f<¬l®¯�lbIIIIII��01!°
Signal Processing for Active Control
Y)*+,-./01!2345
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音響情報処理工学演習 2008 July
4
Signal Processing for Active Control
Y)*+,-./01!2345
!gRhijD1=�
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½¾D¿bÀÁ�ÂÃ
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Signal Processing for Active Control
YLMS?4@ABC
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音響情報処理工学演習 2008 July
5
Signal Processing for Active Control
YLMS?4@ABC
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:;åæ�2���bçef0�lè�k
éDêë (gradient) DìDGí-î^
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Hp
Signal Processing for Active Control
YLMS?4@ABC
!1âãä?4@ABC (Steepest Descent Algorithm)
Reference
FIR Filter
OutputError Signal
Desired Signal
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!x(n)
wiy(n)
d(n)
e(n)
音響情報処理工学演習 2008 July
6
Signal Processing for Active Control
YLMS?4@ABC
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Signal Processing for Active Control
YLMS?4@ABC
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FilterError Signal
Desired Signal
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!
x(n)w(n)
d(n)
e(n)!
音響情報処理工学演習 2008 July
7
Signal Processing for Active Control
YLMS?4@ABC
! LMS ?4@ABCDÝÞÚ½
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Signal Processing for Active Control
YLMS?4@ABC
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音響情報処理工学演習 2008 July
8
Signal Processing for Active Control
YLMS?4@ABC
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Signal Processing for Active Control
YLMS?4@ABC
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音響情報処理工学演習 2008 July
9
Signal Processing for Active Control
YLMS?4@ABC
! LMS?4@ABCDÝÞÚ½
��-k b��kTEtefkFGGí-
HIef_�jDÝÞDJK<ç>�jb�0p
Signal Processing for Active Control
YLMS?4@ABC
! LMS?4@ABCDÝÞÚ½
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l`mQR<S_ï�k¬-ÝÞ>0p
音響情報処理工学演習 2008 July
10
Signal Processing for Active Control
YLMS?4@ABC
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I<äD��b�0p
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Signal Processing for Active Control
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YLMS?4@ABC
音響情報処理工学演習 2008 July
11
Signal Processing for Active Control
YLMS?4@ABC
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r?cD1!2345b-�f0�¹� `ab>`p
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Signal Processing for Active Control
YLMS?4@ABC
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)cjbç^«¿0p
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音響情報処理工学演習 2008 July
12
Signal Processing for Active Control
YLMS?4@ABC
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Signal Processing for Active Control
YLMS?4@ABC�op¶eúqrC
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音響情報処理工学演習 2008 July
13
Signal Processing for Active Control
今回の課題
! LMS.m によるデモを参考に,中心周波数 63 Hz のバンドノイズ(band63.mat)を5秒間以内に消去する適応フィルタを作成せよ。" サンプリング周波数は 1000 Hz とする。" 適応フィルタのタップ数は 512 とする。" 結果の表示法として時系列データの減衰の様子と,スペクトラムの減衰の様子を示すこと。
" プログラムと,結果の図を,repo12というsubject のメールに添付して送ってください。
Signal Processing for Active Control
今回の課題
!消去システムのブロックダイアグラム
Reference
512 tapFIR Filter
Error Signal
!x(n)
wi
d(n)
e(n)
63 Hz バンドノイズ
100 taps Delay
音響情報処理工学演習 2008 July
14
Signal Processing for Active Control
Y 23KL2MNKLOP
!23KL2MNKLlr
エラーセンサー
騒音源
適応アルゴリズム
適応フィルタ
音速:340 m/s
光速:3×108 m/s
適応フィルタの調整のためだけに用いられる
Signal Processing for Active Control
エラーセンサー
騒音源
適応アルゴリズム
適応フィルタ
音速:340 m/s
光速:3×108 m/s
適応フィルタの調整のためだけに用いられる
Y 23KL2MNKLOP
!¶3s54+,bDc�t
x(n)W(z)
Reference
Digital
Controller
Disturbance
Signal
d(n)
e(n)
Error Signal
Sampled Plant
G(z)
2�xtè��rKuùøKÏbD"v<
Plant l%ºk�Düc<wxe¶4
(Internal Model) l^«y�z¿k!"?4@ABCb³`0
u(n)!
音響情報処理工学演習 2008 July
15
Signal Processing for Active Control
Y 23KL2MNKLOP
!c�t-Ì^«D`¯¦èDÕc
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Signal Processing for Active Control
Y 23KL2MNKLOP
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" ^úrùh��kz�mb��f«.�k^è 1=��DQRS
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音響情報処理工学演習 2008 July
16
Signal Processing for Active Control
Y 23KL2MNKLOP
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Signal Processing for Active Control
Y 23KL2MNKLOPEÌDúrùhDw
xyVzúrùh W�Vzúrùh
音響情報処理工学演習 2008 July
17
Signal Processing for Active Control
Y 23KL2MNKLOP
!�����?qrC[��h�D!³wa
' 6æ¡
±²#$uùøK
s(t) H(s)
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Signal Processing for Active Control
Y23KL2MNKLOP
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音響情報処理工学演習 2008 July
18
Signal Processing for Active Control
Y23KL2MNKLOP
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Signal Processing for Active Control
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x(n) W(z) G(z)
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x(n) W(z)G(z)
d(n)
! e(n)r(n)
音響情報処理工学演習 2008 July
19
Signal Processing for Active Control
Y23KL2MNKLOP
!«¡j+,bDOVDz`1!t
" Z��^_#$b}~0l
" ��b®X^m01bDgh¯rk
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Signal Processing for Active Control
Y23KL2MNKLOP
!¥x#$l±²#$Dg°K�ùR
" A«¡j w bD:;#$<<äD¹m-ç|^«k
" sNKR²�h4³m See <÷«¡jb1=t>0p
音響情報処理工学演習 2008 July
20
Signal Processing for Active Control
Y23KL2MNKLOP
!¥x#$l±²#$Dg°K�ùR
" See r´EVz W -i>0£���b��k�f<1=t>0
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Signal Processing for Active Control
Y23KL2MNKLOP
!¥x#$l±²#$Dg°K�ùR
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• "xd2(#) = 0.99 bk20 dB Dgh
音響情報処理工学演習 2008 July
21
Signal Processing for Active Control
Y23KL2MNKLOP
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Signal Processing for Active Control
Y23KL2MNKLOP
!±¸½l@Vz�e<}¹^_)*+,1!2345
" OP¢�FIR 2345bWXef«`0 Dl>0
x(n) W(z)G(z) !
d(n)
e(n)
±²#$ OP¢úrùh :;#$
r(n)
音響情報処理工学演習 2008 July
22
Signal Processing for Active Control
Y23KL2MNKLOP
!±¸½l@Vz�e<}¹^_)*+,1!2345
" gRhij<:;#$D2967�l>0
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Signal Processing for Active Control
! Filtered Reference LMS ?4@ABC
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±²#$ OP¢úrùh
:;#$
x(n) W(z)G(z) !
d(n)
e(n)r(n)
音響情報処理工学演習 2008 July
23
Signal Processing for Active Control
Y23KL2MNKLOP
! Filtered Reference LMS ?4@ABC:;#$
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x(n) W(z) G(z) !
d(n)
e(n)
$G(z)%
Signal Processing for Active Control
Y23KL2MNKLOP
! Filtered Reference LMS ?4@ABC
" uv#$\]D��DLMSlD�`rk�jòó-úrùh"v G
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#$D)*<¿~«k¡^`���i<-0l`mno��0p
LMS
Filtered Reference LMS
音響情報処理工学演習 2008 July
24
Signal Processing for Active Control
Y23KL2MNKLOP
! Filtered Reference LMS ?4@ABC
" �D?4@ABCD�c½À½ÃrkúrùhD"v�`è-�m
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Signal Processing for Active Control
Y23KL2MNKLOP
! Filtered Reference LMS ?4@ABC
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音響情報処理工学演習 2008 July
25
Signal Processing for Active Control
Y23KL2MNKLOP
! Filtered Reference LMS ?4@ABC
" �D��kÛAXªD?@� &i �kÓi^ Ejbrz`p
" ÝÞDQRl^«rk<äD¹m-z0p
" ?4@ABCD�c½rkIIIIIIIIIIl`m��D?@�Ex
D¢$-¹0�l-z0p�f�ìDEx<¥¦lkÇÈ>0pÉD
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ücD��:;� 90°<w-ÝÏñ«`f��ÍbÎÏb�0p
Signal Processing for Active Control
今回の課題
!ある音場において,中心周波数 63 Hz のバンドノイズ(band63.mat)を消去する適応フィルタを作成せよ。" サンプリング周波数は 1000 Hz とする。" 適応フィルタのタップ数は 512 とする。" 音場のインパルス応答は onba.mat とする。" 結果の表示法として時系列データの減衰の様子と,スペクトラムの減衰の様子を示すこと。
" プログラムと,結果の図を,repo13というsubject のメールに添付して送ってください。
音響情報処理工学演習 2008 July
26