/»!6Ü $$ LMS "¿UW$ÐÚïÏÚê $ÏÕò!~Ñ DS-CDMA $ahXZÄ¥
;@9¿
,É
df ,É Ñ $ $ Üá /» $¸ ) | Ñ $ ÏÕò Üá
y
y
yy
,
yyy
,
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yyy
,
yy
"Ä,É.»", yy!~ѼÂä!|Ð$ÍÖêÑ .»".»%»!|Ð, yyyDXO XZ¿IL½¾ï
Modied Leaky LMS Algorithm for Channel Estimation
in DS-CDMA Systems
y
yy
Sungkwon Jo , Jihoon Choi
, Yeon Sik Woo
yyy
, Ju Won Soh
yyy
, and Yong Hoon Lee
yy
Samsung Electronics Co., LTD.
yy Dept. of Electrical Engineering and Computer Science, KAIST
yyy
DXO Telecom Co., LTD.
y
cg #¸
FIR(nite impulse response) Wiener $¿') ÊØ:LÉÚê /»!6Ü!"* %»%»!~Ñ LMS(least mean square) 2M-¿¥ ,¸
ÏÚò ;@9¿
,É $,ÅÏÚê :L%»!~Ñ". $ÉÔç,¸ ËØ,¸ÏÚê ÒÔò?@ :L%»mÑ "¿UW$ÐÚï$ {)-Ä"
! $
´$!~Ñ df.»ÏÚê :L$!"UW
MSE(mean squared error) ,ÉÁÆòÏÚê \f!~Ñ". U[$UW .»%» ^f¥ $¿!5ØÏÚê ÒÔò?@ :L%»mÑ "¿UW$ÐÚï$ $ÐÔç¥ ;@
9¿
,É $,Å9L $?@ MSE ,ÉÁÆò$ {!"UW, $ÇÔò %»"¿$¥ ÍÔä\f9L j~Ñ2M,Æ$ $,¸ Wiener $¿')9L ¼Æç,Å!~Ñ ,É
ÁÆòÏÚê "$ÄÏÚê _f'»".
1 )ÉÔç
DS-CDMA(direct sequence code division multiple access) $ahXZÄ¥ {'»9L) .»ÍÔò '»pÉÚê ÇÔò$$¸chim ËÔäÑ!"
$ ´$?@)ÁÆç, ÍÔò'»9L) .»ÍÔò '»pÁÆç ÇÔä$Å,¸h
c m
i "
$
).Ç
ÏÚê .»ÍÔò!"UW {'»9L) "$).ÇÏÚê $ÏÕò?@ $ÄËÔê ÇÔò$, %»ÍÔò
" ÇÔò$ 9L ;@9¿ÏÚê
,É!"* _f"É?@ |)# !~Ñ". DSCDMA $ahXZÄ¥ ;@9¿
,ÉÏÚç "$¿).ÇÏÚê -¸{|Ð%»?@) ;@9¿
,É_fÉÚê lm!|Ø!~Ñ CKÄÓÚêÏÚê ,¾ÁÆç ,É $ ;@9¿ CKÄÓÚêÏÚê $¿')$É
?@) ;@9¿
,É cf"ÉÚê ÐÖê$ÁÆç ,Échim $)'»". ËÔç ÁÔç
ÊØ9L)ÁÆç 8@imÏØ $¿')$É $,ÅÏÚê \f$Å?@ "ÅÏÚï :L) ,ÉÁÆòÏÚê
ÁÔ÷$ÁÆçHL jm,ÄÏÚê ÇØ".
DS-CDMA $ahXZÄ¥ IL$V[(RAKE) {'»$¥ !~Ñ $É
)(nger)9L) "$¿).Ç '»pÉÚê -¸{|Ð%» !"/» {'» '»p x(k)ÁÆç
"ÏÚï "Í$ |)'»".
x(k) = h(k) + n(k)
(1)
$CG h(k)ÁÆç ;@9¿, n(k)ÁÆç +-ɼÅ$ 0'» "$%» BK¸CK¸ "ÅÏÚï
ÏÚê "">M»". z.» ;@9¿9L) h(k)¥ ÒÔò2M,¸ ÒÚä,ÉÏÚç $ÇÔò %»
"¿$¥ ÍÔä\f9L "" /»!"^him fx(k)gim') h(k)ÉÚê
,É!"
ÁÆç .ÇÏÚç %»%»!"$ "½". $¿%»,¸chim "%»(cuto)
| "
{ ê
ÚÉ
$4@ \fÓÚê&) |"{9L "ÊÛá UW,É )-¸ ÒÔò $¿')(lowpass
lter)" ;@9¿
,É9L 9¿$ bh$ÁÆçHL, ;@9¿
,É ,ÉÁÆò$ )
-¸ ÒÔò $¿')¥ "%» |"{9L ¥?@ -¿,É$^him ,¿2M!~Ñ "
%» |"{ $¿:L $4@ \fÓÚê&) |"{" "ÉÚç -É ,ÉÁÆò
$ )!"mÑ" [1], [2]. !~Ñ+/»chim Wiener $¿') Kalman $¿
')ÉÚê $ÏÕò!~Ñ $,Å$ :L%»$,Èh
c "
[3]{[5], $).» $¿')ÁÆç ;@
9¿¥ ÒÔò2M,¸ ÒÚä,ÉÏÚê $¿cgim !"^him sv!8Ñ$ 6@ ËÔä"Å!"".
[6]9L)ÁÆç ,¸ÏÚò .»!6Ü 9MÛãù(adaptive linear prediction) $
,ÅÏÚê ;@9¿
,É9L ,¸ÏÕò!"-È". $).» 9MÛãù $,ÅÏÚç $ XU ,¸
sv!8Ñ$ %»%»!"$%» )¥ {'» CKÄÓÚêim') !8Ñ:@¥ ;@9¿ÏÚê
,É!"^him "ÉÚç KL$$É {~Ñ-É9L) ,ÉÁÆò$ )!"mÑ".
ËÔç ÁÔçÊØ9L)ÁÆç FIR Wiener $¿') ÊØ:LÉÚê /»!6Ü!"* ;@9¿
,É9L ,¸ÏÕò "ÁÆò!~Ñ 8@imÏØ ,¸ÏÚò $¿')ÉÚê :L%»!~Ñ". :L%»mÑ
;@9¿
,É$ÁÆç $$ LMS (leaky least mean square) "¿
UW$ÐÚï "!"* $,¸ Wiener $¿')9L ¼Æç,Å!~Ñ ,ÉÁÆòÏÚê "Ê
ÁÆç". "") :L%»mÑ $,ÅÏÚç $ÐÔç¥ )-¸ ÒÔò $¿')" ,¸
ÏÚò 9MÛãù$ÉÚê 4@;Q!"ÁÆç ;@9¿
,É $,Åchim :L$mÑ". "ÏÚï
Transmitte r
3 :L%»mÑ ;@9¿
,É $,Å¥ \f
Multipath Fading Channel
´
1
( pilot )
+
c1 ( k )
Transmitted
Data
´
z-
´
(1)im |)$ÁÆç {'» '»p x(k)9L 4@!~Ñ ;@9¿ h(k)¥
$¸
.»!6Ü
,É$ÁÆç "ÏÚï "Í$ |)'»".
1
h0 ( k )
´
h1 ( k )
^h(k) = wH x(k)
+
c0 ( k )
+
z-
Finger 1
c 0* ( k )
´
´
å
c1* ( k )
h1* ( k )
Recovered
Data
Finger 0
´
c 0* ( k )
å
Channel
Estimator
n (k )
1
´
å
c1* ( k )
å
Channel
Estimator
´
h0* ( k )
´
Rake Combining
U[$Ä 1: DS-CDMA $ahXZÄ¥ ÍÔò{'» $Ë "ÐÖò -Éim KL$
$É ;@9¿ (;@9¿$ x2@¥ -ÉimÉÚê "ÊÁÆç .Çchim ",É).
2,¿9L)ÁÆç ;@9¿
,ÉÏÚê UW&*!"ÁÆç DS-CDMA $
h
a XZÄ ^fVZ¿
ÏÚê %»#¸!$ ,¿-É!"UW, 3,¿9L)ÁÆç :L%»mÑ ;@9¿
,É $,ÅÏÚê
\f!"*, 4,¿9L)ÁÆç :L%»mÑ $,Å¥ {)-Ä df.» $ÉÔç,¸ ,É
ÁÆòÏÚê _f$UW, ÀÆöchim 5,¿9L)ÁÆç ;@9¿
,É9L :L%»mÑ "¿UW
(2)
´ 9L) w ÁÆç N " HKÅ "ÐÖò$ BZ¸')(tap weight vector)$
$
UW x(k) = [x(k); x(k ; 1); ; x(k ; N + 1)]T $".
E [jh(k) ; ^h(k)j2 ]ÉÚê $af !"ÁÆç $,¸¥ HKÅ "
ò
ÖÐ $
BZ¸')
woÁÆç "ÏÚï¥ Wiener-Hopf "É,É$¸ÏÚê %»ÐÔä!~Ñ".
Rwo = pxh
(3)
$CG R = E [x(k)xH (k)] , pxh = E [x(k)h (k)] $". $¿
%»,¸chim fh(k)g fn(k)gÁÆç ÇÔä$Å$^him E [h(k)n(k)] =
0 $UW pxh ÁÆç "ÏÚï "Í$ .»2@mÑ".
pxh
=
=
pxx ; E [x(k)n (k)]
pxx ; [2 ; 0; ; 0]T
(4)
$CG pxx = E [x(k)x (k)] $UW 2 ÏÚç n(k)¥ ËØ%»$".
$¸ (3)9L $¸ (4)ÉÚê 4@$Å!"/» "ÏÚï¥ j~Ñ2M" ,¾)'»".
(R + A)wo =
pxx
(5)
$¸ (5)9L) N N JKÜ)-¿ AÁÆç (1,1) ,ÉËØÏÚê :L$!~Ñ " ) $
,ÉËØ$ ^fx 0$". U[$UW (1,1) ,ÉËØ oÁÆç "ÏÚï "Í$
$ÐÚïÏÚê ,¸ÏÕò!"* $ÐÔç¥ ;@9¿
,É "¿UW$ÐÚï ,ÉÁÆòÏÚê $UX |)'»".
2
!~Ñ".
(6)
o =
2 DS-CDMA $ahXZÄ ^fVZ¿
wo;0
$CG wo;0 ÁÆç wo ¥ 7Ú.»FG ,ÉËØÏÚê "">M»". ]f!~Ñ ç
ÔË ç
ÔÁ Ø
Ê L
9
2
1
) "ÅÏÚï¥ ËØ%» ÏÚç "¿UW$ÈÁÆç "Æchim %»|!~Ñ" . $¸ (3)ÏÚç
"Éj~Ñ JKÜ)-¿ (R + A) "Éj~Ñ BZ¸') pxxim $)'» WienerHopf "É,É$¸chim ËÔê{ $ÈUW, $ÁÆç ÊÔä,¸$¸ E [jx(k);wH x(k)j2
+wH Aw]ÉÚê $af!"ÁÆç ÊØ:Lim') \fmÑ". ´$¥ ÊÔä,¸
$¸ÏÚê w 9L 4@?@ $ËØ!"/» "ÏÚï "Í".
2f;pxx + (R + A)wg
= 2E [;x(k)x (k) + (x(k)xH (k) + A)w] (7)
$¸ (7)im') $,¸ HKÅ "ÐÖò$ BZ¸') woÉÚê ,¾$ ´$!~Ñ steepest
descent "¿UW$ÐÚïÏÚç "ÏÚï "Í$ |)'»".
w(k + 1) = w(k) ; E [;x(k)x (k)
U[$Ä 1ÏÚç "$).Ç ;@9¿ÏÚê "ÊÁÆç DS-CDMA $ahXZÄ¥ ÍÔò
'», "ÐÖò -Éim ;@9¿, IL$V[ {'»ÉÚê %»#¸!$ "">M» .Ç
$". ÍÔò'»9L)ÁÆç "ÏÕò" HL$') "$).Ç '»p" ÇÔä$Å
,¸chim {|Ð%»mÑ 9L %)?@) .»ÍÔòmÑ". ÍÔò'»mÑ '»pÁÆç "ÐÖò
-Éim KL$$É ;@9¿ÏÚê -¹ÁÆçHL, $ ;@9¿ÏÚç 2M{" $%»9L ""
/»!"ÁÆç FIR $¿')im ^fVZ¿$É "ÁÆò!"". {'»mÑ '»pÁÆç "ÐÖò
-Éim KL$$É9L ¥!~Ñ '»p æ¼¾äÏÚê _f"É!"$ ´$?@ IL$V[ {
'»$im ËÔäÑ!"ÁÆçHL, IL$V[ {'»$9LÁÆç ;@9¿¥ "ÐÖò -Éim
9L 4@ÏÚò$ÁÆç $É)" $ÈUW, "¸ $É)9L) HL$') VW\h "
$¿).Ç VW\him {'» '»pÉÚê -¸{|Ð%» $'»". $¿%»,¸chim "$¿
+ (x(k)xH (k) + A)w] (8)
).Ç VW\him -¸{~Ñ%»mÑ {'» CKÄÓÚêim') ;@9¿ 2M{ÉÚê
,É!"
UW $ÉÚê $ÏÕò!"* HL$')¥ ;@9¿ æ¼¾äÏÚê _f"É!~Ñ". "") ´$¥ $¸ (8)9L) $4@"Æ E []ÉÚê :L)!"/» "ÏÚï¥ LMS "¿UW
Ð $ \fmÑ".
"ÐÖò -Éim KL$$É ;@9¿9L) DS-CDMA $ahXZÄ¥ ,ÉÁÆò !#Ü $Úï
"ÉÏÚê ´$?@) ,É{|Ð!~Ñ ;@9¿
,É$ cgsvmÑ".
w(k + 1) = (I ; A)w(k)
+x(k)fx(k) ; wH (k)x(k)g (9)
ÏÚç {'» '»pÉÚê ^fÇÚç "ÏÕò" VW\h $¸UX'» VW\him -¸{|Ð!~Ñ
ËØ%»ÏÚê 2M%»!"*
,É!|Ô { $È" [8].
1 2
$¸ (9)9L) k" ÐÚò"!"/» w(k)ÁÆç wo9L ,żÆç!~Ñ". ´$¥ HKÅ "
! /» (k)9L 4@!~Ñ "Éj~ÑJKÜ)-¿ K(k) = E [(k)H (k)]ÁÆç "ÏÚï
,¸ÏÚò$¸ÏÚê ,¸ÏÕò!"$ ´$?@)ÁÆç o(ÜÝùÏÚç A)ÉÚê "¿UW $È)# !"
"Í$ ,É$mÑ".
^him, $ÉÚê $!"$ ´$?@ $%» k9L) o "ÆÏÚê (k)"UW ln
K(k + 1) = (I ; R)K(k)(I ; R)
!8Ñ!"UW "ÏÚï¥ $¸9L "" w(k) ÇÔò$9L =KÉ'»$\fÉÔä !~Ñ".
2
2
H
2
(k) =
w0 (k )
(10)
$CG w0 (k)ÁÆç w(k)¥ 7Ú.»FG ,ÉËØ$". :L%»mÑ ;@9¿
,É
"¿UW$ÐÚïÏÚê cg#¸!"/» "ÏÚï "Í".
1. ;@9¿
,É:
h^ (k) = wH (k)x(k)
3.
(16)
$CG Jmin = E [jeo (k)j2 ]ÁÆç Wiener $¿')¥ MSEÉÚê ""
>M»". !~Ñ+/»
,É cf" e(k)ÁÆç "ÏÚï "Í$ ln!8ÑmÑ".
(11)
e(k) = h(k) ; wH x(k)
= h(k) ; woH x(k) ; H (k)x(k)
= eo (k) ; H (k)x(k)
(12)
eo(k) H (k)x(k)" ÇÔä$Å$"UW ",É!"/» k.»FG HKÅ =KÉ'»
$¥ MSE'» J (k)ÁÆç "ÏÚï "Í$ .»2@mÑ".
2.
,É cf" 2M%»:
e(k) = x(k) ; h^ (k)
+ f(Jmin + )R + cc g
HKÅ "ÐÖò$ =KÉ'»:
(17)
J (k) = E [je(k)j2 ]
= Jmin + E [H (k)x(k)xH (k)(k)]
= Jmin + tr[RK(k)]
(18)
w(k + 1) = (I ; A^ (k))w(k) + x(k)e (k) (13)
$ (13)9L) N N JKÜ)-¿ A^ (k)ÁÆç (1,1) ,ÉËØ$ (k)$UW ´$9L) tr[]ÁÆç JKÜ-¿¥ 4@"¸!|ÙÏÚê "">M»". $¸ (16),(18)im
¸
")$ ,ÉËØÏÚç ^fx 0$". :L%»mÑ "¿UW$ÐÚïÏÚç $$ LMS
"¿UW$ÐÚï "!"^him /»!6Ü $$ LMS" ioUW oÁÆç $
,¸ uvÛßú 2M{" io$im !~Ñ".
$ ,¿9L)ÁÆç $¸ (11){(13)im |)$ÁÆç ,¸ÏÚò "¿UW$ÐÚï¥
{)-Ä df.» MSE ,ÉÁÆòÏÚê $ÉÔç,¸chim \f!~Ñ". U[$UW
\fmÑ -¿ÉÚê .»%» ^f¥ $¿!5Ø -¿¥ $UXÉÚê ÒÔò?@ ,ÄÐÚò!~Ñ
.
"
$ÉÔç,¸
MSE
,ÉÁÆò \f
$¸ (10)im') HKÅ ,¸ÏÚò$¸ (13)ÏÚç "ÏÚï "Í$ ,'»".
w(k + 1) = w(k) + x(k)fx(k) ; wH (k)x(k)g ; c
(14)
$CG c = [2 ; 0; ; 0]T $".
DG/» "ÏÚï "Í$ ,É$mÑ".
(k + 1)
0<< 2
max
4 ,ÉÁÆò ËØ,¸
4.1
') [7, p.397]¥ ,Échim .»2@!"/» J (k)" "É{im {)-Ä
!"$ ´$!~Ñ $¿cgÛßòËØ df.»ÏÚç "ÏÚï "Í$ |)'»".
$¸ (14)¥ #É /»9L) woÉÚê
= (I ; x(k)xH (k))(k)
+fx(k)(x(k) ; woH (k)x(k)) ; cg
= (I ; x(k)xH (k))(k)
+fx(k)(eo(k) + n(k)) ; cg (15)
´$9L) (k) = w(k);wo $UW eo (k) = h(k);woH (k)x(k)$
". (k) x(k)" "Éj~Ñ,É$ ,ÆUW E [(k)] = 0$"UW ",É
(19)
$CG max ÁÆç R¥ $4@ UW$(eigenvalue)$". [
U $
W
U
$¸ (19)" %»ÐÔä!|Ô CG J (k)ÁÆç "ÏÚï "Í$ sv?@'»".
J (k) = Jmin + T fBk (x(0) ; x(1)) + x(1)g (20)
´$¥ $¸9L 4@ÏÚò$ÁÆç "¸ /»{ÁÆç "ÏÚï "Í$ ,É¥mÑ".
N 1BZ¸') ÁÆç R¥ UW$ÇÚêÏÚê ,ÉËØchim "ÊÁÆç".
N N( JKÜ)-¿ BÁÆç "ÏÚï "Í$ sv,ÉmÑ".
(1 ; i )2 ; i = j
bij =
2 i j ;
i=
6 j
Q" R¥ UWBZ¸')(eigenvector)ÇÚêim sv,É$
ç
ÆÁ %»´$
JKÜ)-¿$"UW !|ÔCG x(0)ÏÚç "ÏÚï "Í$ |)'»".
x(0) = diagfQH (w(0) ; wo)(w(0) ; wo)H Qg
x(1) = 2 (I;B);1 f(Jmin +2 )+[4 ; 0; ; 0]T g.
]f!~Ñ $¸ (20)im') ,É"É "É=@9L)¥ MSEÁÆç "ÏÚï "Í$
|)'»".
J (1) = Jmin + T 2 (I ; B);1
f(Jmin + 2 ) + [4 ; 0; ; 0]T g:
(21)
0.4
0
10
Prediction−based
LPF(cutoff freq.=0.05)
LPF(cutoff freq.=0.03)
Proposed
Wiener filter
0.35
Experiment
MSE
MSE
0.3
0.25
Theory
0.2
−1
10
0.15
0.1
0
100
200
300
400
500
Number of iterations
600
700
800
0
0.005
0.01
0.015
0.02
0.025
fd⋅T
0.03
0.035
0.04
0.045
0.05
0.03
0.035
0.04
0.045
0.05
(a)
(a)
0.3
0
10
Prediction−based
LPF(cutoff freq.=0.05)
LPF(cutoff freq.=0.03)
Proposed
Wiener filter
0.25
Theory
MSE
MSE
0.2
Experiment
0.15
0.1
−1
10
0.05
0
0
100
200
300
400
500
Number of iterations
600
700
800
0
0.005
0.01
0.015
0.02
0.025
fd⋅T
(b)
(b)
U[$Ä 2: :L%»mÑ ;@9¿
,É $,Å¥ $ÉÔç,¸ ,ÉÁÆò $¿!5Ø,¸ ,É
ÁÆò $UX (fdT = 0:03, N = 5, = 0:0025). (a) SNR= 0
dB
4.2
(b) SNR= 5 dB.
$ÉÔç $¿!5Ø -¿¥ $UX
U[$Ä 3: ;@9¿
,É $,Å¥ MSE ,ÉÁÆò $UX (N = 5, =
0:0025). (a) SNR= 0 dB (b) SNR= 5 dB.
ÏÚê _f*ÐØ". U[$Ä9L) $¿!5Ø,¸'» ¼¾ä.»ÏÚç 100.»¥ ÇÔä$Å,¸
'» $¿!5Ø9L) ,¾)'» :L¼¾ð cf""ÆÏÚê +-ɼÅ!"* ,¾,È". U[$Ä
2¥ -¿im') $ÉÔç"Æ $¿!5Ø,¸'» -¿" 6@ ,É{|Ð!$ $¿
$!|ØÏÚê "¿{ $È".
$¸ (20)chim ,¾)'» $ÉÔç,¸ -¿ÉÚê ,ÄÐÚò!"$ ´$?@ :L%»mÑ
/»!6Ü $$ LMS "¿UW$ÐÚïÏÚê ;@9¿
,É9L ,¸ÏÕò!"* $¿!5Ø,¸
'» MSE "ÆÏÚê sv!"-È". $¸ (1)¥ '»p x(k)ÁÆç h(k)" ,É 5 /»!6Ü $$ LMSÉÚê $ÏÕò!~Ñ ;@9¿
,É
swmÑ $4@ \fÓÚê&) |"{ fd T = 0:03ÏÚê "ÊÁÆç Rayleigh
KL$$ÉÏÚê -¹UW n(k)" ËÔäaf BK¸CK¸ "$%» "ÅÏÚï$"ÁÆç "
$¸ (1)¥ '»p x(k)ÁÆç 4.2,¿9L) "ÍÏÚç "É,Åchim ¿" ÉKC $
,É!"9L "¿CKÉ$-È"2. .»%» f^ ¥ $¿!5Ø9L) /»!6Ü $$ LMS $$, "%» fdT " 09L) 0:05 "$9L) /»!"\fÉÔä !"-È".
"¿UW$ÐÚï¥ -É HKÅ{ N = 5, jm$ HKÅ "ÐÖò$ BZ¸') w(0) = L
: %»mÑ svdf9L 4@!~Ñ ^f¥ $¿!5Ø ""$')ÁÆç 4.2,¿9L) ÇÔò
T
[1=N; 0; ; 0] , = 0:0025chim !"-È". U[$Ä 2ÁÆç SNR= $¿
!"". :L%»mÑ $,Å¥ ,ÉÁÆò $UXÉÚê ´$?@) fdT = 0:03,
0 dB $¿ CG SNR= 5 dB $¿CG :L%»mÑ $,Å¥ !|ÐÍÚð ¼¾ä.» fdT = 0:059L ,¸!|Ù!~Ñ )-¸ ÒÔò $¿')ÉÚê ,¿2M!"-ÈUW, ,¸ÏÚò
W-CDMA¥ -É }Ù .»ÍÔòÏ×ê$ 3.84 Mcps, $ÄËÔê .»ÍÔòÏ×ê$ 15.0 .»!6Ü 9MÛãù$ $,¸ Wiener $¿')ÉÚê UW&*!"-È". )-¸ ÒÔò
ksps, %»ÍÔò" |"{" 2.0 GHz, $ÇÔò %»"¿$¥ $4@ ÍÔä\f" 300 $¿'), .»!6Ü 9MÛãù$, Wiener $¿')9L 4@!~Ñ "¸ ""$')ÁÆç :L
km/h"UW !|ÔCG fd T = 0:037$".
2
%»mÑ "¿UW$ÐÚï¥ ""$') ÇÔò$¿!"". )-¸ ÒÔò $¿')¥
-É Park-McClellan "¿UW$ÐÚïchim ,¿2M!"-ÈUW, Wiener
$¿')ÁÆç ;@9¿¥ fdT /»9L "Ê
)) ,¿2M!"* MSE ,ÉÁÆò
¥ $af"ÆÏÚê ""3@\fÉÔä !"-È". :L%»mÑ $,Å ,¸ÏÚò .»!6Ü
9MÛãù$¥ $¿!5Ø,¸ MSE "ÆÏÚç ,É"É "É=@9L)¥ :L¼¾ð cf"ÉÚê
+-ɼÅ!"* 2M%»!"-È".
U[$Ä 3ÏÚç fdT 9L /»9L "ÉÚç "¸ ;@9¿
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