! "
#
$
%
&& '
(
)**+,-. / 0
-),12313/4. 5 6
4)+789. 5
)):) ; <
:3. 0
4),-.1 = (
)*7+ 0
34 9.-3,.3
>
,-?341-0
@ ) ;
9)+ 05
/*7 0
),89)+ 05
/*7 0
), 9AB C
B D E
8 >F
8
G
3:H I
JJ KL MNOPL QRNJNNS
TUVWX
YZ [Y\]^
_ `T [aba
c d
ce b
W [b
f \g a
hi`T [aba
c d
ce b
W [b
f \
jklmnjom
pqr st u v wvxyz{x |xyt}x | w~xqxy wt ux | u
wq |
wux |
uwx |wvxyr
yx
x w
y
xyzx
x
vwyt yr sx
~xqxy wt ux | ut |x
x wq xxy st uur y
r
yxt u
ux
y
yw|
wq |
x w
y
tq~{sxyxqx wy
q urwqr
uv wr t w yx u
r tq }xy w {t |x y wq~x yx
xq tx u t u
|x utyx | sx~xqxy wt ux |
x w
y
xy|x
vux u
yw|
wq |ut~q wtqru
wq |uz{st swyx~y
vx |tqr
rw}x
tqr xy}wu
|y w{tq~ tqv
ru y
uxq uy u{tr s
w {t |xy wvxyr
yx y {xy rw}x
wq |uz wq rw}x
tq}wyt wqr yx u
r tq t u
wstx}x | x
|x
q ur y wr x r s wr
r sx
vxy wr x u
{x
wyuurw}x
q |wytx uwq |w|
|tr tq w
wq
xqxry
wqtq yx wux vxy y
wq xwq |
yx |
x |
vx
tr{sxq
v wyx |
r
ut
twyu
wq |
wq |
wq |
|
wtq
x w
y
tq~ur y
r
yx u
mnom
yw|
wq |
x w
y
tq~
utq~ w tqx wy
qt y
uv wx | wyy w yx u
ru tq w yx
xq |xvxq |xqr uv wr t w
yx u
r tqz
utq x r sx wr xy t u
vyvyr tq w
yxwr x | r
r s
r sx wyy wu
wvxyr
yxwq |r sx yx
xq
r sxrwy
~xr
ut~q w xq x y
wq wyy w
{tr s
x | wvxyr
yxzr sx
uv wr t wyx u
r tq |x yx wux u{tr syx
xq pqy |xyr
t
tr r sx }wyt wr tq tq uv wr t w yx u
r tqz yx
xq |w
r tq u s w}x
xxq
w|xrt
trr sxvyx uutq~ ut~q wu
r wq rw}x
}xy
xr sx rw}x
wyytxyzr sx
ux |
qx
w uv wx | uxq uy wyy wu z ¡z
t
vx
xqrwr tq s wy
qt qx ur tq~ ur y
r
yx ¢z
£
wq | w
r x sqt
x
wux |qwvvy
t
wr tq~r sxt |x w qr tq
u
wvxyr
yx
¤
s w}x
xxqu
~~x ur x |
wux |
qws wy
qt wqx ur x |wyy w{tr swuwtq~tq
wvxyr
yx y|t¥xyxqrrw}xyx
xq tqr xy}wu¢z£z ¦z
r st u v wvxy|t u
uux u w~xqxyt w|wvr t}x u
wq |
wux |
yw|
wq |
x w
y
xy s w}tq~ uwx | wvxyr
yx §x
vutq~
yw|
wq |
uxq uy
ut~q wu tqr
|x t
wr x |
yx
xq
wq |u¨u
wq |u©
t u
w|}wqrw~x
utqr xy
u
yx |
tq~r sx
v
rwr tq w
vx
tr
wq |
w||tr tq w
tq yx wutq~r sx
q}xy~xq x
uvxx |
ª«
rvx
w|wvr t}x
x w
y
tq~w~ytr s
u ¬
yr sxyztqr st u v wvxy{x
|t u
uus{r sx u
wq |wvvywswq
xx
vtr x |r
®
¯°±²³
´µ¶
³·²²¸¹¹
´µº »¼ º°
µ´ ¸½°º°»
¾¿À´ Á ² Ã
´µ ¹
´µ ·º »
Ä»²»·
µÅ °Æ
µ´ ½
µ ·
ÇÇ »È
y
rw}x~y
v u u
wq |uz {st s |y w{ r sxty tq
v
ruy
uxq uy uxru |t¥xyxqr uv wtq~wq |wvxyr
yx
wuw~xqxy wt uwr tq ¢z É
pqr sx
{tq~z
{xyx}tx{r sxu
wq |
wux |
yw|
wq |
x w
y
tq~
wvvyws
tq
x x
¡ tq
r y|
x ur sx
vyvux |
u
wq |
uwx |
wvxyr
yx
x w
y
xy{st s {t
xut
wr x | wq |
v wyx |r urwq
|wy |usx
x utqx £ q
utq uwyx|y w{qtqx ¤
pq
y qrwr tqz {x
ux{xy wux wq |
vvxy wux
|
wxs wy wr xy ur|xqr x}x rywq |
wr yt
wqr tr tx uz
yx uvx r t}x
Ê lkkj kjlË kËjÌÍnÌÎ
ÊÏ
ÐoÌÑ k
Ò ÓÔÕ Ö
Ô×Õ kØ
ÔÙÚÓÒ ÙÛ×Ü
Ý
x
vwyt y
w
yw|
wq |
x w
y
xyz {x sxyx
r tt ux
w
tqx wy q ur y wtqx |
tqt
}wyt wq x
ª«Þ wvvyws ßz
{st s wq
x
xàtxqr
t
vx
xqr x |
x wq u w~xqxy wt ux |ut |x
xwq xxy
sx ª«Þ vy
x
y vr t
t utq~ wyy w
{xt~sru wq
x y
wr x | wu á âwy~
tqãáänååá
u
æx r r oäá â
Ú
z {sxyx á qrwtq ur sx r xy
xàtxqru wq | nåå t u r sx }wyt wq x
wr yt
r sx
uxy}x | wyy w
|wrw sx
q ur y wtqr
wr yt
o wq | r sx
q ur y wtqtq~ }x ry
Ú t
vuxtqx wyq ur y wtqruzu
swu
r sx vyx uxy}wr tq w ut~q w tqr xyx ur t
vtq~tq~ qr
r sx wyy w y
w
uvx t |tyx r tq
wyyt}w §ç
sx vxy y
u w
vyæx r tq
r sx |wrw qr
r sx
q q ur y wtqx |
u
uv wxz{sxyx urwq |wy |
q q ur y wtqx |
vr t
t uwr tqw~ytr s
uu
swur sx x wur
x wqu
wyx u
ª« y
yx
y ut}x
x wur
u
wyx
èª w~ytr s
u
wq
x|xvx |
ÊÏÊ l
é ÖÖ
Ô×Õ Øê
ÓÙëÓìÛ í
ÛÓ×
wq |
wux |
x w
y
tq~yx
tyx ur xy
wqî ur|x
vuxr sx
yw|
wq |uxq uyut~q wu
x wq uwq w
ut ur xy
wqî utqrï|t¥xyxqryx
xq
wq |uz{st s
wq
xvxy wr x |wrwq ð r t
x u{xyuw
vtq~y wr x|
x
rr sxty yx |
x |
wq |{t |r s {x}xyz yytr t w |x t
wr tqzð âïzuvx r y wwt wutq~t
trur sxvxy y
wq x
wqvyx uutq~tq r sxu
wq ||
wtqz{st swq
x
tr t~ wr x |
rwîtq~ tqr xy
u
wq | yyxwr tq u x
vt
tr
tqr w
qru{sxq |x ut~qtq~ u
wq |
wux |
synthesis filter bank
analysis filter bank
N
N
N
N
N
N
h [n]
0
h [n]
1
h
K- 1
[n]
g [n]
0
g [n]
1
g
K- 1
[n]
n]
v[
n]
[
v
t~
yx
wq | |x
vutr tq
x wq wq wut u
wq |uqr sx ut ur xy
wqî u
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
−80
−60
−40
−20
0
normalized frequency
Ω
/
π
20log
10
|H
k
(e
j
Ω
)|
t~
yx
tr xy
wqî s wy wr xyt ur t y ï â ¤ wq |
ð â¢
wux |
q
w
vyrrvx
{tr s
⢢¬
xàtxqru
ytr s
u ¡ ut
vxy wvvyws t u r}xy uw
vxu
wq |uztx|x t
wr x
wwry ð ï ¢z
{st s
wqxàtxqru
vvyx uuwt wutq~tqu
wq |uwq |vxy
tr
u
wq |ur
xvyx uux |tq |xvxq |xqr
wq | |x
vutr tq u wyx vxy y
x |
wq wut u
r xy
wqî uu
s wuus{qtq t~
zq ut ur tq~ wux
ytx u
wq wut u r xy u
z
â
ßï
z wq | |x
t
wr tq
w
wry
ð
qr sx ut u
t u wstx}x |
v
uw
vtq~
w
wry
ð
{x |
wvvyvyt wr x
tq
r xyvwr tq r xy u
y }xy uw
vx | r xy
wqî u
çu
{tr s ð ï
z{st s wyx
q ut |xyx |
sxyxzr sx
r xy u
wq |
wq
x
xàtxqr
|x ut~qx | wq |
t
vx
xqr x |
wux | q r sx
|
wr tq wutq~x vy
rrvx{v wuur xy pq
y {yîz{xx
vr sx ~xq
xy wt ux | |t uyxr x
ytxy r y wq u y
§ y
|
wr tqz{st sw|
truwur y wt~sr y{wy ||x ut~qwy |tq~
r ¤
u wq x
w
vxzr sx
w~qtr
|x s wy wr xyt ur t u
y
wq ç {tr s ï â ¤wq |
ð â¢
utq~wr xy xq~r s
⢢¬xàtxqrut u
~t}xq tq t~ r x r s wr r sx yx u
r tq~ u
wq | ut~
q wuwyx
vx
}w
x |zwq |r s wr yyx w}w
x |wyy w
ut~q wur sx us{q ï â¬u
wq |u wyx
vx
q
æ
~ wr x}xy utq ur sxyx
wtqtq~
wq |uz{st swyxr sxyx
yx
yx |
q |wqrwq |wq
x
trr x |
y
vyx uutq~
ÊÏ l
é ÖÖ
Ô×Õ kØ
ÔÙÚÓÒ Ù Ø
Ò
sx
î |t w~y w
w urwq |wy | u
wq |
x w
y
xyvyx uutq~
x |wvxyr
yxwyy w|wrwt uus{qtq
t~¡¬z ¦
sx wq wut uçuzw
xx | jz|x
vuxr sx
yw|
wq |wyy wut~q wutqru
wq |utr stq
x ws u
wq |zwqtq |xvxq |xqr
yw|
wq |
x w
y
xyz
sxyxx
x
vwytw z
t u
vxy wr x | sx
x w
y
xy
[
n
]
e
[
n
]
M
−1
x
[
n
]
1
x
[
n
]
x
0
GSC
GSC
GSC
A
A
S
A
t~
yx ¡
wq | w|wvr t}x
x w
y
xy {tr s
x |
wvxyr
yx
0.2
0.4
0.6
0.8
−60
−40
−20
0
20
40
60
−60
−50
−40
−30
−20
−10
0
10
|Α(Ω,ϑ)|
/[dB]
ϑ/ο
t~
yx¢ §tyx r t}trv wrr xyq
x w
y
xy{tr s
x |
wvxyr
yx
r v
ru
y
r sx
wut u
w
yx q ur y
r x |
wq |
x w
y
xy
r v
r
x wq u
w
uqr sx ut u ç |xqr x |
wu l
sx
uv wr t w yx u
r tq
t u
yx tvywvyvyr tq wr
r s
wvxyr
yxwq |r sx yx
xq
r sxt
vtq~tq~{w}x
y
u
u
sz
y
r sx
x w
y
tq~ur y
r
yxtq
t~
¡z
vy yx u
r tq
t u xq
qr xyx | wr r sx
{xy yx
xq
tx u st ux¥x r
t u tq |t wr x |
r sx
|tyx r t}tr
v wrr xyq
z yx y |tq~ r sx
x w
y
xyu ~ wtq tq |xvxq
|xq r sxqy
wt ux |wq~
wyyx
xq wq |w§ç
ztqt~¢z{st s|x
q ur y wr x uw
x w
y
xyu~ wtqyx
uvq uxwuw
q r tqyx
xq wq |§ç }xy
x
r st uzr sx u
wq |
wux | uwx |wvxyr
yx
x w
y
xyt u
tqr y|
x |
ÎËËnjÐlË lkkj kjlË
lojÐË jËnmnË kËjÌÍnÌËn
sx
u
wq |
wux |uwx |wvxyr
yx
wvvyws
ux u
w|t¥xyxqr wyy w wvxyr
yx{tr stq x ws rw}xz tx
vy
~yx uut}x
{xyyx
xq
rw}x u
wyx
vyx uux |
yx u
r tqt u
wtqrwtqx |y
rw}xrrw}x¢z É
x
xq x{tr s wq x
w
vx tq x ¡zwq |~xqxy wt ux
r sxur y
r
yxtq x ¡
Ï Ë
ÔÙë Ø
qx
w
vxr sxvyvux |ur y
r
yx ywqwyy wvxy
wr tq~}xywy wq~x â¡rw}x u
r tt utq~ â¢uxq
uy uvxyrw}xt uvy}t |x |tqt~£ sx uxrw}x uwq
xyx u}x |
uvtrr tq~w
yw|
wq |ut~q wtqrï â¬
qt y
u
wq |u §t uwy |tq~
r sx §
vqxqr tq
u
wq | ßz r sx {x ur yx
xq rw}x t u qrwtqx |
tq u
wq | z {stx u
wq |u wq | ¡ s|
r sx
ux q | rw}x
wq | r sx st~sx ur yx
xq
rw}x
uv wq u
u
wq |u¢ r¦
pq
y |xyr
xqs wq x
uv wr t wyx u
r tq
zr sx wyy w
wvxyr
yxt u
|
x |
{sxq
qxy
r sx
st~sxy
rw}x~x ur
r sxqx
r
{xyqx É
pq t~
£z
r sxu
wq |
x w
y
xyvxy wr x uqr sx{
x ur
wq |wq ||y w{ utrutqv
ry
r sxwy~x urwvxyr
yx
sx vyx uuy u wq | ¡ vxy wr x q r sx qx
r
st~sxyrw}xz{tr s r sxyx
wtqtq~¢ vyx uuy uyx uvq
ut
x y r sxst~sx ur rw}x
wq | }xytq~¢ u
wq |u
sxwvxyr
yxutx yr sxr syxxrw}x
wq |uwyx â¡z
â¤wq |â yx uvx r t}xz{tr s
xtq~r sx|t u
rwq x
xr{xxqw|æwxqruxq uy uuwr t utq~r sxytr xyt wr
w}t |uv wr t wwt wutq~ yr sxu
wx ur
{w}xxq~r s
sx
ux qx ur x | wyy wuu
s wu us{q tq t~
£t u
x q
t wzutq xuxq uy uwq
x yx
ux | wq |
xv wyr
ux}xy wu
wyy wuzu
swur sx uxq uy
ut~q wu
z
wq |
tq r sx w
}x
x
w
vxz{st s yx
tyx uw
rrw
â ¬ qx ur x |
wyy w xx
xqru p
r sx ux uxq uy
vutr tq u
{xyxx
r y wr x |
y
w
tqx wy
qt y
uv wx |
wyy wz
tr {
| qrwtq
â ¡ u
s
xx
xqru
x yxr stqqtq~
ÏÊ ÎØ
× Ø
Ò ÔÛìÔ í
ÛÓ×
u
w
~xqxy wt uwr tq
r sx w
}x
x
w
vxz
tr wq
x
us{q r s wr r sx uxq uy ut~q wu qxx | r
x |x
vux |
tqr
ïâ
qt y
u
wq |utq
y |xyr
uxr
v w u
wq |
x w
y
xy{st swq
yx u}xrw}x u
yr sxyzr sx~xqxy
wt uwr tq u y
wq |
wq
xus{qr
x
â
wq |
â
|« ¡
{sxyx
!
t ur sx"yvxy wrywq |
|
yxvyx uxqrur sx
|
vxy wr tqtr s wq |¡z{xwq|x ut~qwq
y wq q
xy rw}x u wq |uxq uyxx
xqru
vxy rw}x r x r s wr r sx ï urwr x | tq t u r sx
tqt
q
xy u
wq |u yx
tyx | r yx u}xr sx
|x utyx |q
xy rw}x u#x
vtq~wqtqr x~xy
r t
vxr st uït uvxy
t uut
xwq |
ws w}xw|}wqrw~x utq
r xy
u w~ytr s
t
vx
trwq |q}xy~xq xuvxx |
wq w|wvr t}x
w~ytr s
GSC
[ ]
n
x
1
GSC
GSC
GSC
GSC
GSC
GSC
0
x
d
d
d
d
A
[ ]
n
e
A
A
A
7
5
4
1
6
3
2
[ ]
n
[ ]
n
2
x
[ ]
n
x
3
[ ]
n
x
[ ]
n
x
4
[ ]
n
x
5
[ ]
n
x
6
[ ]
n
x
7
2d
2d
4d
A
A
S
A
A
A
t~
yx £
wq | w|wvr t}x
x w
y
xy {tr s uwx |
wvxyr
yx
$
oÌmjmjÐ oÌÐË%m&
$Ï Í
é Ö
Ô×Õ o
Ôì Ø
ì
wq |
x |wvxyr
yx
x w
y
xyx
vtq~
w
|yt}xq
w qy
wt ux | x wur
x wq u
wyx
ª« w
~ytr s
yx
tyx uw
v
rwr tq w
vx
tr
r tv w
wr x« vxy wr tq u ytru
îtq~
wr yt
wq |
tx uxqr}x rywq |¡ ¡ ytruw|wv
r t}x v wyrz {tr s yxvyx uxqr tq~r sx r x
vy w |t
xq utq
txr sxrwv |xw tqx xq~r s
r sx
x w
y
xy
st uwy
x ur
'
()*+
,-â
¡ ¡ ¢
p
{x
ux |wqx ur x |wyy wwq |
r tt uxww}wtw
x
uxq uy
ut~q wrvxy wr x
w
wq |
z
'
()
,.,-â
¡
¡
£
{
|yx u
rz{tr s
wy |tq~r ¡
$ÏÊ l
é ÖÖ
Ô×Õ o
Ôì Ø
ì
y w u
wq | |x
vutr tqz wq xàtxqr
|
wr x |
ç
wq wut uyuqr sx ut ur xy
wqît uwuut wr x |{tr s
'
(
/ â
0
¢ï~ï¢ï
z
{tr s
xtq~r sx
xq~r s
r sx
vyrrvx r xy £ sxyx yx
w
wvxyr
yx u
wq |
x w
y
xy w
ux u x
r y w
v
rw
r tq w
vx
trtqr sx y
r xy
wqî u y
|x
vutr tq wq | u
ux
xqr yx q ur y
r tq ut~
q wu wy |tq~r t~ ¡
v
rwr tq w uw}tq~ u wyt ux
tqr sxu
wq ||
wtq|
xrwqð r t
x u{xy
v|wr x
y wr x wq | wq wvvy
t
wr x ð r t
x u usyr xy r x
vy w
|t
xq utq yx
tyx | y wq
x w
y
xyzwr s
~sq{
ï v wy wxyx wt uwr tq us w}xr
xvxy wr x |
¬ sxyxz
r sx ur
w
x |wvxyr
yxu
wq |
x w
y
xywq
x
|xqr x |
wu wvvy
t
wr x
'
.()*+ ,-â
ï
ð
ð
¡
ð
! '
(
/ ¤
yr sxvyvux |
x w
y
xyzr sxq
xywr t}x
uxq uyut~q wuvxyrw}xt uqrs wq~x |
v wyx |rr sx
x |wvxyr
yxusx
xz
rwst~sxyq
xy wq wut u
r xy
wqî us wur
xt
vx
xqr x |wy |tq~r t~
£z
yx u
r tq~tq
'
.()
,.,-â ï
ð
ð
¡
ð
! '
(
/
¦
« u
vxy
wq |uw
vtq~
vxyt|
lÌÐjmlj nËlÐml
pq r sx
{tq~z
{x wuux uu wq |
v wyxr sx
vyvux |
yw|
wq |
x w
y
xy tq r xy
u
r sx wstx}x |
|tyx r t}trv wrr xyqwq |trurw}x
tq}wyt wqryx u
r tqztq
r xy
u tqr xyxyxq xu
vvyx uutq wq |q}xy~xq xzwq |
tq r xy
u
vx
trr r sxy
wq | wq | u
wq |
usx
x u|y w{tq~r sxtytqv
ruy
uxq uy u{tr s w
x |
wvxyr
yx
Ï
ÛÒ Øêí
Û Û í
Ô ííØ
Ò ×
sx" x
t
ttr r sx
x w
y
xy y }wyt
u uxq
uyxx
xqrq
xy u wq |rw}x u t u t
ur y wr x |tq
t~¤
r sxx
w
vx âwq | â¢zyx
tytq~
w|x
vutr tqtqrïâ¤u
wq |u
v wytq~r sx
us{q |tyx r t}trv wrr xyq{tr s t~¢zwut~qtwqr t
vy}x
xqrtq
wtqrwtqtq~rw}x
tq}wyt wqrwq |r sxyx yx
qx wy yx
xq
tq}wyt wqryx u
r tq wyuuw{t |x uvx
r y
wq
x
qr x |
sx
x w
y
xy {tr s w|wvr t}x
r xy u tq yv
y wr x | xq w
x u
r
ur xxy q
u
r{wy |u tqr xyxyxy u
t
t
q wr tq~r sx
wyy wy
|tyx r tq ur sxy
r s wqr sx î
|t
yx r tq
|x
q ur y wr x
r st u x¥x rz
{x
wvvr{
yw|
wq |
tqr xyxyxy u
t
vtq~tq~
qr
r sx
wyy wy
wq~x u
¡ß wq |
ß
yx uvx r t}xz {stx r sx ut~q w tqr xyx ur
tx u wr
yw|ut |x sx ut
wr tq
r tt ux u â ¡
rw}x u{tr s âuxq uy uvxyrw}xwq |u
ux
xqr
ï â ¤ sx r xy
wqî u wyx r sx qx u s wy wr xyt ux |
tq t~ z
wux | q wvyrrvx xq~r s ⢢¬
vxy
trr tq~w|x t
wr tqwryð ⢠r xyw|wvrw
r tqzr sx|tyx r t}trv wrr xyqtqt~¦t
ur y wr x ur sxu
x uu
q
tq~ r sx r{
yw|
wq | tqr xyxyxy u st u
qr y wuru {tr s t~
¤z {sxyx q w|wvrwr tq t u wvvtx |
wq |u
ux
xqrr sx
tx uxqr
x w
v wrr xyqt uqruxr
r
u vvyx uuwq
uvx ttqr xyxyxy u
0.2
0.4
0.6
0.8
−60
−40
−20
0
20
40
60
−60
−50
−40
−30
−20
−10
0
10
|Α(Ω,ϑ)|
/[dB]
Ω/π
ϑ/ο
t~
yx
¤
§tyx r t}tr v wrr xyq u
wq |
x w
y
xy
{tr suwx |wvxyr
yxâz â¢
0.2
0.4
0.6
0.8
−60
−40
−20
0
20
40
60
−60
−50
−40
−30
−20
−10
0
10
Ω/π
Ω/π
|Α(Ω,ϑ)|
/[dB]
ϑ/ο
t~
yx¦
§tyx r t}tr
v wrr xyq
x w
y
xytqr sx
vyx uxq x
yw|
wq |tqr xyxyxy uy
¡ß wq | ß
ÏÊ
× íØ
Ò Ú Ø
Ò Ø
× êØl
éëëÒ Ø
ììÛÓ×Ô×Õ l
ÛÜ×Ô
Ûì í
ÓÒ
í
ÛÓ×
vxy y
wq x
v wyt uq
xr{xxq u
wq |
uwx |
wvxyr
yxz u
wq |
x | wvxyr
yx wq |
wq |
x |
wvxyr
yxtq r xy
r sx
x wq u
wyx |yx ut |
w xyyyt u
wyytx |
r sx yx ut |
w xyyy sxyx t u |xqx | wu |t
xyxq x
xr{xxqr sx
x w
y
xy
r v
r
tq t~ u¡
wq |£wq |r sxut~q w tqr xyx ury
yw|ut |x sxyx
yxwqyx
wtqtq~tqr xyxyxq xwq |qt uxwu{xwuwq
|t uryr tqt
vux |qr sxut~q wtqr xyx urt u
x wu
yx |
pqr sxut
wr x |uxq wytzr sxut~q wtqr xyx urt uwrr sx
wyy wu
yw|ut |xz{stx
yw|
wq |tqr xyxyxy u t
vtq~x
y
ß wrwq p è ¢ß |z
yy
vr x |
q yyx
wr x |qt uxwr ß
|èsx
x w
y
xy u|y w{r sxty
tqv ru y
â£
uxq uy u
tq r sx
0
0.5
1
1.5
2
2.5
3
3.5
4
4.5
x 10
4
−10
−5
0
5
10
15
20
25
30
35
40
discrete time n
ensemble MSE / [dB]
fullband fixed aperture
subband fixed aperture
subband scaled aperture
fullband non−uniform spacing
t~
yx¬
ªx wyqtq~
y}x u
wq |
âÉ
uxq uy u
tqr sxqx ur x |
wyy wwux
sx
wq |
x w
y
xy yxvyx uxqru w r y w|tr tq w
r t
x |
wtq t
vx
xqrwr tq {sxyx q |x
vutr tq
r sx
yw|
wq |ut~q w t u wyytx |
r prt u xtr sxy wv
vtx | r â £
qt y
uv wx | wyy w xx
xqruz y
wr xyq wr t}x
r tt ux uw
tqv
rzwq |wvvtx uwrwv
|xw tqx â ¤¢ r x ws uxq uy ut~q w sx u
wq |
x w
y
xy u
uxï â¤s wqqxr xy
wqî u{tr s
ð â¢wq |vyrrvxxq~r s
⢢¬wus wy wr xyt ux |
tq
t~ sx
r x
vy w|t
xq utqr sxu
wq |
wux |
x w
y
xyt u usyr xqx |
wy |tq~
pq w wux uzr sx
t u
vxy wr x |
tq
tq wr tq
{tr s wq
ª« w~
ytr s
sxw|wvr tq
r sx
x w
y
xy uurwyruwr
âß{tr swur xv
utx
âß
£zwq |wr
â ßßßßr sx
ur xv
utx t uyx |
x |
w
w~qtr
|x
ß
ªx wyqtq~
y}x u|xvt r x | tq t~
¬
tq |t wr x r s wrr sx
r vxy y
u r sx
x | wvxyr
yx u
wq |
wux |
x w
y
xy tq s w}tq~ wur xy q}xy~xq x uvxx | wq |
{xy ur x w| urwr x xyyy sx wrr xy t u |
x r wq xq
s wq x | u
vvyx uutq tqr xyxyxy u wr { yx
xq tx uz
{sxyxr sxtq yx wux |uv wr t wyx u
r tqt u
xqxr
y
vyt utq~zr sxur x w|
urwr x« Ývxy y
wq xt ur sxuw
x
wu r sx
wq | w~ytr s
x
vtr tq~ w
uxq uy uz
{st s t us{x}xyyx wsx | wrwu
urwqr t w{xy
vx
tr
yr sxy wq wut u r sx s wy wr xyt ur t
r sx
x w
y
xy uz
v{xy
uvx r y w |xq utr tx u
§
r sx }wyt
u
ur x w|
urwr x
xyyy u
wyxvyx uxqr x |tq
t~É sx
wq |
x |wvxyr
yxs w}tq~ ⣠uxq uy u
x
st
trust~s
v{xy
wr
{xyyx
xq tx uz
r y wttq~¥
wu yx
xq tq yx wux u
sx u
wq |
x | wvxyr
yx usx
x s wu ut
twy §
s wy wr xyt ur t rr sx
wq |w
xtrwut~sr{xy§
wr{xyyx
xq tx u st uyyx uvq |urr sx|tyx r t}tr
v wrr xyqtq t~¡z{sxyxr sx wy~xy
x w
{t |r s wr{xy
yx
xq tx uw{ u
yxut~q wv{xyrv wuur sy
~sr sx
uur x
ur sx
x w
{t |r s q wyy{ ur{wy |ur sxst~sxy
yx
xq tx uz
xrr xyyx u
r tqt u
uxy}x | sxvyvux |
wvvyws~t}x uwwtyrw}x
tq}wyt wqr§|
xr
|t¥xyxqrwvxyr
yx
utx u sx
rw}xur y
r
yxt u x wy
}t ut
x tq
t~
Éz {sxyx {xy tqr xyxyxq x u
vvyx uutq
wq xuxxqwrr sx
{xyyx
xq tx u{tr stqx ws
rw}x
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
−15
−10
−5
0
5
10
15
20
normalised angular frequency Ω/π
PSD / [dB]
fullband fixed aperture
subband fixed aperture
subband scaled aperture
fullband non−uniform spacing
t~
yxÉ § yx ut |
wxyyywrur x w|urwr x
t~
ß us{ u r sx ~ wtq yx uvq ux r sx
x w
y
xy y
yw|ut |x st u
~
yx tq |t wr x u r s wr r sx
ß
|q ur y wtqr r{wy |u
yw|ut |x
t u
x |
wq | r s wr
r sxytvvx
r sx
x w
y
xy~ wtqt u wty
u
w|x uvtr x
r sxu
wq |x |~x u wq |r sx
tqr x~y wr tq }wyt
uwvxy
r
yx u{tr stqr sx
x w
y
xy st uwust~st~sru
r s wr
vx wî utq r sx
§
r sxu
wq |
wvvywsx u
tq t~
É
wyx qr |
xr|t uryr tq x¥x ru wrr sx rw}x
wy~tq u
rwyxwyx u
ru{q}xy~xq xwrr sx
wq |x |~x u
tq |t}t |
w u
wq |u w
ux |
{tqv
r v{xyrr sx
w|wvr t}xw~ytr s
¬
Ï o
ÓÙë Ø
Û í
y
r sx
uxq wyt
tq
x £
{tr s â £wq |
â ¡z
â Éz
ï
â ¤z ð â ¢z wq |
â ¢¢¬
y
r sx
vyvux |
usx
xzr sx wyt utq~
v
rwr tq w
vx
tr tx u wyx ~t}xq tq t~ sx
x w
y
xy
yx
tyx u wq x
r y w ¢ uxq uy u tqv
ru wq | sxq x ¢
yx
wq wut ur xy
wqîvxy wr tq u
v wyx |rr sxu
wq |
x | wvxyr
yx wy str x r
yx r x r s wr r sx
v
rw
r tq w
vx
tr r sxu
wq | usx
x utq ~xqxy wt u
ut~qtwqr{xyr s wqr sx
wq | wvvyws yr sx
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
−0.2
−0.15
−0.1
−0.05
0
0.05
normalised angular frequency
Ω
/
π
gain from broadside / [dB]
t~
yx ß wtq yx uvq ux r sx
x w
y
xy r
{wy |
yw|ut |x yxvyx uxqr tq~ r sx|t uryr tq t
vux |q
r sxut~q w
0
10
20
30
40
50
60
70
80
90
100
10
1
10
2
10
3
10
4
10
5
10
6
fullband adaptive temporal dimension
computational complx (MACs)
fullband fixed aperture
subband fixed aperture
subband scaled aperture
fullband non−uniform spacing
t~
yx
v
rwr tq w
vx
tr tx u
wq |
x |
wvxyr
yxz u
wq |
x | wvxyr
yx wq | u
wq | uwx |
wvxyr
yx
ut
wr tq utqx £ z{sxyx wq |w
wq |qx ur x |
wyy w
x w
y
xy
r tt utq~ w
âÉuxq uyut~q wu
vy}t |x |wut
twyur x w|
urwr xvxy y
wq xtqr xy
u
tqr xyxyxq xu
vvyx uutqztr wq
xqr x |r s wr r sx
v
rwr tq w
vx
tr|t¥xy u
y |xy u
w~qtr
|x
ooÐll
x
s w}x vyvux | w u
wq |
wux | uwx | wvxyr
yx
x w
y
xy{st s s wu r sx w
ttr
r
wtqrwtq
wvvy
t
wr x
q urwqr yx u
r tq wyuu
w {t |x yx
xq
y wq~x
y yx u
r tq xq
qr xyx |
x | wvxyr
yx
x w
y
xy u wr
{ yx
xq tx u wq
x
}xy
x
|y w{tq~ uxq uy
tqv
ru
y
w qx ur x | wyy wz
u
s r s wr
{xyrw}x uyyx uvq |rwq wyy w tq yx wux |wvxy
r
yx x s w}x us{q r s wr r sx q ur y wtqr t u
x |
wyuu r sx rw}x
wq |
wy~tq uz wq | q t
tr x |
r sxr xy
wqîu|t uryr tq
q r tqz{st s wq
xîxvr
wuu
wwu qx x uuwy
|x ut~q
||tr tq wz
r sx
usx
xtqsxytrur sx {
v
rwr tq w
vx
tr~xqxy w
u
wq |
wvvywsx ux
s w}x
v wyx |
}wyt
u
yw|
wq |
x w
y
tq~ t
vx
xqrwr tq tq
r s r sx
wq | wq | u
wq | |
wtqz
{sxyx
r sx |x uqru
¥xywq |x~y w|wr tq{tr s
yx uvx r r r sx « Ý vxy y
wq x{sxq
v wyx | r w
wq |usx
xx
vtr tq~r sxxqr tyxuxq uywyy w|wrw
w
xtrwrw
sst~sxyur
nËÍËnËoËl
§
qqz ¨
vr t
w
yx
xq
§
wtq
|wv
r t}x
qr xqq w
yx uutq~
~ytr s
y
yw|
wq |
Ýq}tyq
xqruz©
z
$¢
¡¢
¡ £z
ɬ¦
§x u wq | §xqx |t rz ¨yw|
wq |wy
y w|x ut~q
utq~r sxwu
vrr t r sxy
qx
w
uv wx | wyy wuz©
z
¦ ¡¡z ɬ¬
p ust
wy
z ¨sxy
qx
w
uv wx |wyy wuz©
z ¤ ¤É
¦ß zɤ
¢ xxy
wqqz ¨
ux
ur xxytq~|t~trw
t yvsqx
wyy wz©
tq
z
yqrz çqrz
wq w|wz
ÉÉz£z¡ £¬
¡ £¬¢
£
s
z ¨yx
xq
tq |xvxq |xqr
x w
y
xy
{tr s {yx uvq uxxyyyz© tq
z
§xr ytrz
«t st~ wqzÉÉ £z£z ÉÉ £
Éɬ
¤
§wy |zè xqqx |zwq |ètt w
uqz
¨sxy wq | |x ut~q
yw|
wq | uxq uy wyy wu
{tr s yx
xq tq}wyt wqr wy
x|
x w
v wrr xyq uz©
!
z" # z ß ¡
ß¡¢z
ÉÉ £
¦ ª
Þwq
yxx uz $
!!
z
t
xzx{ %yîz ßß
¬ xt uuz è
r x{wyrz «
s w
xyrz
p
y
|xyz wq |
« ¥
wqz ¨ q
Ýàtxqr
sx
x
yyw|
wq |
|wvr t}xx w
y
tq~z©tq
&
!
! z
«q
r xyxz z
ÉÉÉzz¢ ɤ
£ßß
É
xt uuzè r x{wyrzwq | ªt
z ¨
yw|
wq |w|wvr t}x
x w
y
xytqu
wq |u{tr suwx |
wvxyr
yxz© tq
&
!
!
z«qr xyxz z
ßß z z ɬ
¡ß
ß çªyurzpppz ¨ q ~ytr s
y ªtqx wy q
ur y wtqx | |wvr t}x yy wyx uutq~z©
' z ¬zÉ ¤
É¡ £zɦ
ª
ytàr s wq |
t
z ¨
q r xyq wr t}x
vvywsrªtqx wyq ur y wtqx | |wvr t}xx w
y
tq~z©
z z
¦
¡¢z
ɬ
t |y{wq |§r x wyq uz
(
&
)
zyxqr t xwzÝq~x{|t¥uzx{%yîz
ɬ£
¡ ttyx
wq |
«Þxrr xytz
¨
|wvr t}xtr xytq~
tq
wq |u{tr sytr t ww
vtq~ q wut uzÝ
vxy
t
xqruwq | vvt wr tq u r
ur t Ýs wq x
wr tqz©
z$ ¬zvv
¬¤
¬¦£zÉÉ
¢ xxy
wqqz ¨
q wut u
wq ||x ut~q
r ty wr x
uur x
u
y wq xwr tq w
ur t w
x sx uz©
tq
z
x{%yîz* z
ɬ¬z£z vv
£ ¦ß
£ ¦¡
£
xt uu ¨ q wut u wq | wur p
vx
xqrwr tq
ç}xy uw
vx | «|
wr x | tr xy wqî u© pq
«styr xy
wq | p
y
|xyzx |try uz+
'
!
)
&
,
zs wvr xy ¡zv w~x u ¤¡
¦¢ç
y |
*qt}xy utryx uuz
«wyr xqx îzxt uuzwq |èr x{wyrz ¨§x
ut~q x wy xyx r èx q ur y
r tq ç}xy uw
vx |
tr xywqî u y
wq | |wvr t}xtr xy uz©
!
z$ ¬zvv ߬
߬¤zÉÉÉ
¦ x
wq |
wys wq~
y
æ
xq
è
ur«t
yvsqx yy wu
*utq~
wq |
|wvr t}xtr xy u
,
!
&
)
z ¢ É
¦
£z
x
ßß
¬ § è «y~ wq { u
vrr t q}xy~xq x
ª«
ur t Ýs wq xxy u
)
'
z ¡
¤