A Nested WidebandAdaptiveArray Using Multirate Filter Banks Choo

0 downloads 0 Views 977KB Size Report
the SSA operates well across octave boundaries and ad- ... To overcome the octave barrier, the used of ... former which will be simulated and compared to stan-.
     

              % '(    !" #  $ && ()**+,-./> 0-),1 2313/4. ; < 5 6 5 0 0 )): ) :3. )*7+ 4)+78 9. 4),-.1 = ; 5 5 0JJ),8KLMNO9)+PLQR 0 /*7NJNNS 0), 9ABC BDE8 >F348 9.-3,.3 ,-?341-0@ ) 9)+G03:H/*7 TUVWXYZ [Y\]^_`T[abaI cdce bW[bf\g ahi`T[abacdce bW[bf\ ˆ‰yv ru‡ ˆy‰‰‚rw}xuxqu‰y ‰ˆ‰ˆu€|t¥wq|uz jklmnjom ~y‰ vu {st ‚ s |yw{ rsxt y t q €  uxru xyxqr uvw‚t q ~ wq| wvxyr yx € ‡ € pqu‚wrstx|uwvxyr vwvxyz€yx{xƒ„„…† |xyt}x|xw‡w ˆ‰y~xqxyw t u x| u wq| wux| €  rsx wu w ~xqxywtuwrt‰q ‰ˆ ¢zɟŽ ˆ‰y  ‹ xyzx x v w yt ‡ ‡ Š ‰{tqt~z{xyx}t  pqrsxˆ‰ x {rsx u wq| wux| y‰w| €   st ‰  ~xqxyw t u x| ut | x x ‚wq‚x x y ƒŒ„†Ž u ury ‚r yx t u   € € ˆ‰y „x‚Ž „x‚Ž wq| xw q ~ wvvy‰w‚s t q ¡ t q  Ž   ‡ ‡ ˆ‰y ˆ‰y  uxˆ y‰w| wq| xw t q ~ {sxyx qxwy ‚‰qurwqr  €uvwrt€w yxu‰ €rt‰q ‰}xy w‡{t|‡x ywq~x ‰ˆ ˆyx‘€xq‚txu tu ry‰|€‚xu rsx vy‰v‰ux| u€wq| u‚wx| wvxyr€yx xw‡ ˆ‰y|wy|u‚sx  x ut‡‰q‚ wrx|€ut‰wq|quwyx|yw{qt xy {st‡‚xuts {tq „x‚Ž£Ž ‚‰‡vwyx| qr‰„x‚Ž¤Ž urwq ‡ € sx „„… ˆ‰y |xut y x|Ž ~xqxyw t u x| xw xy |x‚‰ v‰uxu  ‡ ‡ ‡ y‰w|wq|ut ~qwt qr‰u|yw{t ‚swyx~y‰ ‰‚rw}x €wq|uz{st €vx|t{tqrr‰s pq ‰€y q‰rwrt‰qz {x €ux ‰{xy‚wux wq| €vvxy‚wux ‰| Ž ’‹ ˆy‰ t q rxy}w u q ~ t q v ru uxqu‰yu € ‡ ˆw‚x ‚swyw‚rxyu r‰ |xq‰rx }x‚r‰y wq| ‡wrytŠ ‘€wqrtrtxuz ˆ‰y ‰ ‰‚rw}x ‰‚rw}x  wtq}wyt{t|wxyqr wvxyr yx {xy wq|uz wq €   Ž ‹ yxuvx‚rt } x yxu‰€rt‰q tu w‚y‰uu‰‚rw}x w‚stx}x|Ž “x‰|x€q|wyt rswrw| ‡‰qurywrx ‰vxywrxu{x rsx|trt‰„„… x uwq|  Ê lškkj—™ kjl˙ kËjÌ͘n̖—Î ˆy‰  ‹ qw ‚wq xqx”r wqt q ‚yxwuxvxyˆ‰y wq‚xwq|  ‡ ‡ yx|wq|€ˆ‚x|€ ‚‰wq|‡v|‰xЇtrwt‹q{sxq kˆ‰y ÒÓÔÕÖÔ×Õ kØÔÙÚÓÒÙÛ×Ü tq~ uryr‰€‚rut‡€yxuŽtwy u€wq| ÝÊϕŠx‡vÐoÌÑ xw‡‚‰ˆ‰y‡‡vwyx| ˆ‰y  ‹ w yt w y‰w| wq| xw xyz {x sxyx    ‡ ‡   ‹ rt t u x w t q xwy ‚‰qurywt q x| t q t }wyt w €ƒª«Þ† wvvy‰w‚s žßŸz {st‚s ‚wq‡ x‡xà‚t €‡ xqr‹ tq‚x‡ • –—mn˜™šom–˜— ’y‰w| ˆ‰y ˆ ‰y   ‹ wq| xw t q ~ ut q ~ w t q xwy qt ‰ˆ w vy‰~xqxyw ‰  vƒŒ„† x‡xqrx|žžŸŽ‹sx‡xwquª«Þ t u x| ut | x x ‚wq‚x x y   ‡ ‡ € € ‡  ˆyx‘   uvw‚x| wyyw‹ yxu r u t q w xq‚‹ |xvxq|xqr uvwrt w ˆ‰y ‰vrt  x t u t q ~ wyyw‹ € € á‡â wy~ ‡tq‡ãáänååá ‰ ‰   ‹ yxu‰ rt qz ut q ‚x rsx w rxy t u vy‰v‰yrt qw yx w rx| r‰ ˆ‰y  {xt ~ sru ‚wq x w rx| wu €  ‡€ u wvxyr wq| rsx{trsˆyx‘”Š€x|xq‚‹wvxyr‰ˆ €rsxyxzrsx rwy xà‚t u€æx‚rxqrur‰wq|oäánååâtuÚ zrsx{sxyx‚‰}wytáwq‚x‚‰qrwt‡qwrytu rsxŠ ‰ˆ”rsxrxy ‰‚‰ ~xr‰rsutrsx~qwŽwyyw‹› €yxwyyw‹ œxq‚x ˆ‰y wq  ‰ ˆyx‘ ‰y|xy  uvwrt w yxu‰ rt q |x‚yxwuxu {t r s xq‚‹Ž pq r‰ sx o uxy}x| wyyw‹ |wrwŽ ‚‰qurywt q r wryt wq| rsx € € ‡ Š rsx }wytxxqwrt‰‡qw|xtq r‰uvwrtt‡wtr yxu‰ tqtxwyqrxyxur‚‰qurywt qtq~ }x‚r‰y qqruzu~tq~€‚s‰qr‰wu €rt‰qz yx‚‰q~ ‰ˆ‡‡utxq|w Úw tut‡~v‰ux  rsx‚‰qurywt rtr‰t‡‰quwqtr sw}x rsx vy‰‚xuut ~ qw u ‰ ‰ˆ ‰ˆ vyxuxy}wrt q qw t vt ‡ ŸŽ‹‰uvw‚x| ‰‚rw}x ‰}xy‚‰ ‰‚rw}x  x rsx wyyt x yz rsx ž ”‚ |tyx‚rt‰q ‰‰ˆq rsx‰ˆ wyyt|wrw}w‰qr‰ƒ§ç…†Žrsx wyyw‹ ‡  ‡ w‡uuvx‚tw vy‰æx‚rt Ÿ ‰ˆ ux| qx‘ w uxqu‰y wyyw‹u  z ¡ z t v   Œ„ qˆy‰vxyˆ‰y €‡xqrwrt‰€q ‰ˆ €swy‡‰qt‚ qxurtq~ ury€‚r€yx ¢z £Ÿ wq| ‡ xw rsx€sxq‚‰qurywt x|wu~€‰ytuvw‚xz{sxyx urwq|wy| qx| €‡q‚‰qurywt ‰q ‰ rx‚sqt ‘ x wux| wvvy‰ t wrt q ~ rsx t | xw ‚‰qrt q u ‰vrt ‰  t u wrt q r s u u ‚s wu rsx x wur xwq u‘ wyxu €  ‡ € € Š ‡ ‡ € € wvxyr’wux|‰qwswy ‰y yx‚‰‹x|Ž ƒª«„†x |xv €yx ¤Ÿ sw}x‡‰qtxxq‚wu€‹~~xurx|Ž €yut}x xwur u‘€wyx ƒèª„† w~‰ytrs‡u ž Ÿ qxurx|wyyw‹{t r swu‚w t q ~t q ‚wq Ÿz ÊÏÊ l ÖÖ ™Øê í u  ¢ z£z¦ €yxˆ‰y|t|tu‚¥€xyxqr‰‚rw}xˆyx‘ €xq‚‹t}xqrxy}w rstwvxyr uy‰w|vwvxy uuxu w ~xqxyt ‚ w|wvrt u wq| wux| € €yxŽ  §x „ wq|é wux|Ô×Õ xw ˆ‰yÓÙëÓìÛ ÛÓ×tyxu”rxy wqîur‰|x ˆ‰y wq| xw xy sw}t q ~ u‚w x | wvxyr   ‡ ‡ t q ~yx‘ €‡v‰uxrsx y‰w| ‡wq|uxqu‰yut ‡ ~€qwu ‹ ‡xwqu‰ˆwqw   ‚‰‘€‡xq‚‹v‰utqwq|u ~ y‰w|ƒ¨u€wq|uxqu‰yut ~ qw u t q r‰|x‚t wrx|ˆyx ‡ ‚‰  wq|u©†t u w|}wqrw~x‰ ut q rxy u‰ˆ € ‡ ‹ut‚wqu ”xrxy‰vxywrx| xq‚‹ wq|uz{st ‚ s wqîutqwrr‰ïwq ð|t¥rtxyxqrˆyx‘ €  ‰ ‰ ‹wq|w||t  ‹ yx|tq‚yxwut ‚t€ q~rsx‚‰ v rwrt qw‚‰ v x t r r t qw ‡ € ‡ Š ‰  xu {xy uw v t q ~ ywrx | x ‡ ‡ € ‰ˆ ª«„ q ~rsx ‚‰q}xy~xq‚x uvxx| r‹vx w|wvrt } x œ‰{x}xyzˆ‰y r‰ rsxt y yx| ‚x| wq|{t | rsŽ ‚yt r t ‚ w |x‚t  €  twutq~t‡trursxvxyˆ‰y‡wq‚x {x ¬ŸŽ ­€yrsxyz‚wqtqxrstxŠu vvwvxy |txwu‚‡€uuˆ‰ys‰{ ‡tq~rsxw~u‰yt€rswq|‡u wvvy‰w‚s ‰ wrt qzð âïzuvx‚ryww ‡ ‰trx| r‰ ‰ˆ wq‹ vy‰‚xuutq~ tq rsx u€wq| |‰‡wtqz{st‚s ‚wq x ~ tqrxy|xutu€~qtqwq|~ u€‚‰yyxwq|wrt‰wux| qu xŠwv~t‰‚ r‰ w‚‚‰‹ €rwîtqru q{sxq Ä»²»·¯® µÅ°±°Æ² ³´µ¶µ´½µ³·²·ÇDz¸¹¹ »È ´µº»¼ º°µ´¸½° º°» ¾¿ À´Á² ôµ¹´µ·º» ‡trt‹rt~tqwrx| 

h0[n] v[n]

N

N

g0[n]

h1[n]

N

N

g1[n]

hK- 1[n]

N

N

gK-1[n]

A

GSC

x1[n]

A

GSC

A

GSC

v[n]

­twq|~€u‹qrsxut yx ž „€u ”wq|rxy |x‚‰ wqîuއv‰utrt‰q ‹ ‡xwq ‰ˆ wqw‹utu analysis filter bank

x0[n]

e[n] S

synthesis filter bank

20log10|Hk(ejΩ)|

0 −20

xM −1[n]

­twvxyr~€yxyxŽ¡ „€wq| w|wvrt}x xw‡ˆ‰y‡xy {trs ”Šx| €

−40

|Α(Ω,ϑ)| /[dB]

−60

10 −80

­tð ~➢ ­trxy wqî ‚swyw‚rxytrsurt‚ ⢢¬‚‰xà‚t ˆ‰y ï ⠞¤xwq| €yx  wux|‰qwvy‰r‰r‹vx{t qruŽ ytwq|uz rs‡u tŽžx¡ŽŸŽ|x‚t… ‡utwrx‡vxy‹ wvvy‰w‚s tu ðr‰ ‰}xyuw ‡¢Ÿvz x{stu€‚s ˆw‚r‰y ‰ˆ ï w  ž ‹xu€vy‰‚xuux| ‚wqxà‚t vvyxuu wtwtqut|xvxq|xqr q~tq u€wq|uwq|vxy ‡tr Ž ‹ u€„ wq|uwq|xqrr‰|x‚‰ ‰ ‹uxutu v‰ut r t qutqwyx­t~vxyˆ‰y ‡ ‡x|urtq‹~ wqw Ž ”ytxruxy€‰ˆwqîu ‰ˆ u ‚s wu us‰{q ‚‰qut w žz €  Ÿ ” ‹ wqw ut u r xyu  z â wq| |x‚ ߃ž†ï žz tuw‡‡wrtv‰tqq~‹‹wwˆw‚r‰y ðŽ‰ˆ ð„‹qrsxut u{x| tu‹w‚stwvvy‰vyt x}x| w‹rx €tvq ˆw‚r‰y ˆ‰ ‰   ŸŽ ­‰y ‰ ” ‰}xyuw ” rxyv‰ w rt q r xyu  v x | r xy wqîu ‡  s ð ïzŸ ‚wq{st‚sx wyxxà‚t‚‰qut |xyx| sxyxz rsx ”tƒç„­’u† ‹ r‡vxyux‡xqrx| {tŸ rwq| x qr |xut ~ qx| wq| ‰qpqrsx‰€‡y {‰yîz ‰|€wrt{x‰qx‰ˆ‡vw‰ut‹qrsx~x ~xqvy‰ wux| ‰ ”  r‰r‹vx {vwuu r xyŽ  ­‰ ˆ‰y ‰| xyw t u x| |t u ‚yxrx yt x y rywquˆ‰y ƒŒ§­† € ‡ ‡ € ~ q w‚‚‰y|t q ~ r‰ˆ‰ywrt‰žqz{st x‰ˆz rsxwq~srˆ‰y{wy||xut w~qt r |x ‚swyw‚rxyt u rt ‚ ¤ŸŽƒ …u‚†swqw|x‡Štwr‡uvwŸurywt ‡ç„­’ €{trs ï ⠞¤ wq|u q~rsrsx‰ˆ yxu⢢¬ ‚‰xà‚t x qru t u  ~tqwð}âxqu wyxž¢tq €‚‰­tut‡~qŽ~v ŽxwŠ”}wr‰rxxy€x|zxrswr r t q ~ u wq| ut ~ € yxw }w€€x| wyyw‹ ˆ‰y wq| rswr ï   ‡âwt¬qut€ ut€~~wrx}xyut qwu rsx ‰us‰{q wq|u wyx ‚‰ v x ‚‰q ‡ Š  qu‰ˆrsxyx q ~ wq|uz{st ‚ swyxrsxyx 戉yx  yx|€q|wqr wq| ‚wq x ‰‡trrx| ˆy‰‡ vy‰‚xuutq~Ž ØÒ ÊϏsx lé‰ ÖÖÔ×Õ kØÔÙÚÓÒÙ ‚î |twq~yw~ ”‡Šx|‰ˆwvxyrw urwq|wy| u wq| xw €  ‡tq ˆ‰y­t~‡Ž¡xy¬vy‰‚xuut yx wyyw‹ |wrw t u us‰{q € zž¦y‰w|ŸŽ sxwq|wyyw‹ut wqw‹utu~焭’uz w€xxwq|uŽ | jz|x‚‰ ‡q “t v‰uxrsx qw u t q r‰u r st xw‚s |xvxq|xqr y‰w|wq| sx xwxw‡‡ˆ‰yˆ‰y‡‡xyzxy sxyx xuŠ€x‡wq|z vwytwq‹ wtqŒ„z tu ‰vxywrx|Ž 0

0.2

0.4

0.6

0.8

1

1.2

normalized frequency Ω/π

1.4

1.6

 



 





 



 

 



   

 







1.8

2

0 −10 −20 −30 −40 −50 −60 0.8 0.6 0.4 0.2

−20

0

−40

−60

­twvxyr~€yx€yxŽ¢ §tyx‚rt}tr‹ vwrrxyq ‰ˆ xw‡ˆ‰y‡xy {trs ”Šx| u ‰ˆwyx‚‰qury €‚rx|ˆu 焭’ € wq||xq‰rx| xw‡ ˆ‰y‰wu€rv‡lŽ€xyruˆ‰y ‰€rv‡€rsxr ‹wut‡xwqu ‰ˆ w u‹qrsxut sxwvxyr ‰q tu yx‚t ‰qw r‰   ‹ uvwrt w yxu‰ rt v y‰‚w vy‰v‰yrt € ‰rs yxwq|rsxˆyx‘ xq‚‹‰ˆrsxt vt q ~t q ~{w}x € ˆ‰y‡tq~ ury€‡‚r€yx tq ­t~Ž¡z …u u€€rt‚szˆ‰yrsx ˆ‰yv‰‰y‡Ž yxu‰ xw  ‡ ‰{xy}tr‹ˆyx‘vwrrxyq  wr rsx xq €  ‹ ‚txƒuŽ st† zu €yx‚‰y|t x¥x‚r‰q ttuqu ~txq‚‰ qrsx|t‚€wrx|qrxyx| rsx |t y x‚rt  ˆ‰y xw xy› u ~wt q t q |xvxq  ‡ ‡   |xq‚‹‰ˆrsxq‰y w t u x|wq~ w yˆyx‘ xq‚‹ wq|w§ç… ‡ € € ‰qurywrxuw ˆ‰y ztq ­t~Ž¢z{st ‚ s|x xw xy› u ~wt q yx ‡  ‡ ‡  ‰ uv‰quxwuwˆ q‚rt q‰ˆˆyx‘ xq‚‹wq|§ç…Ž‰‰}xy‚‰ x € € ‡ rsttqry‰|uz rsx€‚x|Žu€wq| wux| u‚wx| wvxyr€yx xw‡ˆ‰y‡xy tu kjl˙ Î˗ËnjЖl˙ lojÐ˙ j ËnmšnËlškkj—™ kËjÌ͘nÌËn sxu x€yx|wvxyr €wq|wyyw‹wux|u‚w €qyxxw‚sƒ„„…†wvvy‰w‚s €vy‰uxu Ž ‰‚rw}xz w~yxuut |t¥xyxqr wvxyr {t r st tŽ x }x‹ ‰{xyˆyx‘€xq‚‹‰‚rw}xuwyxvy‰‚xuux| ‹vy‰ 60

40

20

ϑ/ο

   









~yxuut }€rtx‰‹qt{tu ‡|xywtqwyyw‹uŽ pq‡|‰t‰‚rw}xr‰‰‚rw}x q~ u‰z w ‚‰qurwqr¢zÉuvwrt w ŸŽ “x yxu‰ rwt q x|ˆy‰ wq xŠw ‡vx tq „x‚Ž ¡Žžz wq| ~xqxywtux rsx‚‰‡‡uryxq‚x ‚r€ €yx{trtsq „x‚Ž¡Ž Ë Ï• ÔÙë Ø …qx €‚r€yxˆ‰ywqwyyw‹‰vxy Šw‡vx ‰ˆrsxvy‰v‰ux|ury  ⡉‚rw}xu €rttutq~  â¢uxq wrtu‰yuvxy q~‰}xywywq~x‰ˆ Ž£Ž sxux ‰‚rw}x ‰‚rw}xu tu vy‰}t |x|t q ­t~wq| ‚wq ï ‹ } x| uv t r rt q ~ w y‰w| ut ~ qw t q r‰ ⬠€qtx yxu‰   §tu‚wy|t § ‚‰t‡u v‰qxqr q€~xq‚‹rsx‰‚rw}x tq ˆyx‘ utq€uˆ‰y€wq|‡wq|u€ßzwq|uŽ rsxžz {st‰{xur ‚‰qrwt q x| x ust€~sxurwq|uˆyx‘€ xq‚‹ wq| ‰‚rw}x ¡ s‰| rsx ‰‚rw}x ux‚‰q| wq| rsx uvwqu urt€‰qzwq|u ¢r‰ ¦Ž pq ‰y|xyr‰ xqswq‚x uvwrtw yxu‰€ ‰qx ˆy‰­t‡~rsxŽ £z wyyw‹~‰xuwvxyrr‰€rsxyx tuqx|‰Šr€‰x{xy| {sxq ŸŽ ‰qx strsx~sxyu€rsx‰‚rw}x  É pq ž‰vxywrxu ‰q rsx ‰{ Œ„ ˆ‰y wq| xw xy  ‡ ‡ xursxwq| wq|vy‰‚xuu‰yu |yw{u trut qvwq|€r ˆy‰‡¡ ‰vxywrx rsx wy~xur‰q wvxyr €yxŽŠr Œ„ rsx qx stut~sxyx ˆ‰y‰‚rw}xz {t~sxurrs rsx‰‚rw}xyx‡wtwq| qtq~‚‰}xyt ¢ vy‰‚xuu‰yu yxuv‰q  rsx st q ~ ¢ u wq|uŽ € sxwvxyr €yxutxˆ‰yrsxrsyxx‰‚rw}x wq|uwyx  â¡z  ⤠wq|  ⠞  yxuvx‚rt}x‹z{trs  xtq~ rsx |tu rwq‚x xr{xxqw ww|æw‚xqr uxqu‰yuuwrt uurˆ‹t{w}x q~rsxxq~rsŽ ‚ytrxytw r‰ ˆ‰y  w}‰tsx| uvwrt t w ut q ~ rsx u w x ‡ wyyw‹u‚wqu€‚sx yxwu€ux|us‰{qwq|tqx­tvwyr ~Ž £ ‰ˆtu €t‚uxwz‰ˆutqqxurx| x‚‰q‰ ‚x uxqu‰yu ‡ ux}xywu €wyyw‹uzu€‚swursxuxqu‰yut~qwu   Ÿz   Ÿ wq|   Ÿ tq rsx w‰}x xŠw‡vx z {st‚s yx‘€tyxu w r‰rw ‰ˆv‰utrt  â ¬ qxurx| wyyw‹‡xwx‡tqxqruŽ pˆˆ‰yrsxux uxqu‰y ‰  ‹ qu{xyxx ryw‚rx|ˆy‰ xwy qt uvw‚x| € ‡ Š xˆ‰yx rsttr {‰qqt€q~Ž| ‚‰qrwtq   ⠞¡ u€‚s xx‡xqru wyyw‹z ÏÊ w ÎØ~xqxyw רÒÔtuwrtÛìԉíqÛÓ׉ˆ rsx w‰}x xŠw‡vxz tr ‚wq x …uus‰{q r‰ x |x‚‰‡v‰ux| tqr‰ rswr rsx uxqu‰y ïut~â qwu qxx|  ƒž† tq ‰y|xy r‰ uxr €v w u€wq| xw‡ ‡ u€‚s wq|u ˆ‰y€wqttu‡ˆwrt‰yxy{st  ‰‚rw}xuŽ ­€yrsxyzrsx~xqxy ‚wqyxu‰ } x ‰quˆ‰y   wq|   ‚wq x us‰{qr‰ ‰x‹   â   ƒ ž†ƒ   ž† ƒ † wq|  â ƒ † ƒ  ž†  ‰| ƒ«† ƒ¡† ‡    {sxyx ! tu rsx "‰‰y ‰vxywr‰y wq| ‡‰| yxvyxuxqrursx “t‰ˆ r‰‚rw}xu ‰| ‰ ‰  qŽ s ƒ †wq| ƒ¡†z{x‚wq|xut ~ qwq ‡„„…€ˆ‰y wq‹‰vxywrt  q xy wq| uxqu‰y x x €‡ ‡xqru  vxy ‰‚rw}xŽ ‰rx rswr rsx ï urwrx| tq ƒž† tu rsx ‰ˆ u€#wq|u yx‘ t y x| r‰ yxu‰ } x rsx ‡|xuttqty‡x|€‡q€‡q€‡xy xy‰ˆ ‰‚rw}xu € ‰ ‹t  x v q ~ wq t q rx~xy r t ‡ ‡€  ï  vrxyx‡‰ˆrst u t u vxy t u ut x wq| w‹sw}x w|}wqrw~xut q ‡  ‡ ‰ˆ w~‰yt}x rws‡~‰ytt‚ r‚‰s‡‡ŽvxŠtr‹ wq| ‚‰q}xy~xq‚x uvxx| ‰ˆ wquw|wvrt

x0 [ n]



















7

d

x1 [ n]





GSC

A

GSC

A

d

x2 [ n]

GSC GSC

S

4

e [ n]

A GSC

d

x4 [ n]

5

A

d

x3 [ n]

6

A

GSC

3

2

2d

x5 [ n]

GSC A

1

2d

x6 [ n]

A

4d

x7 [ n]

A

­twvxyr~€yxyxŽ£ „€wq| w|wvrt}x xw‡ˆ‰y‡xy {trs u‚wx| € $ o˜Ì šmjm–˜—jÐ o˜Ì ÐË%–m& $ ϕ ÍéÖÔ×Õ oÔìØì …ˆ|yt}€xq wq|” ˆ‰y ‰ ‹t x|wvxyr yx xw xyx v q ~wŒ„ €  ‡ ‡ ‡ Š ª«„† ‹  w q‰y w t u x| x wur xwq u‘ wyx ƒ ‡ yx‘€tyxu‡w ‚‰‡v€rwrt‰‡qw ‚‰‡€vxŠtr‹ ‰ˆ ƒ w†  ~‰yt r s ‰vxywrt ‰ ˆ‰y ‰   w‚‚€‡€ w rx ƒ«…† qu t r u ‚ît q ~ ‡€‡wrytrtvŠ‹wq|‘  ˆ‰yt t x u‚xqr}x‚r‰ywq|¡   ¡  r uw|wv €s yxvyxuxqrtq~ rsx rx‡v‰yw |t‡xqut‰q rt}xtŽxvwyrz {t r Ž rsx xurwvr‰|xw‹ tqx xq~rs ‰ˆ rsx xw‡ˆ‰y‡xyŽ stu w‚‚y € '()*+,- ⠃ †  ¡  ¡ ƒ¢† pˆut~{xqw€r‰ux|‰vxywrx w qxurx|w ˆwyyw‹wq| €rttux w w}wtwx uxqu‰y € wq| Œ„z '(),. ,- ⠃  †  ¡   ¡  ƒ£† {‰€| yxu€rz{trs   w‚‚‰y|tq~ r‰ ƒ¡†Ž $ ÏÊ léÖÖÔ×Õ oÔìØì ­‰y焭’wqw w u€‹wq|utu ‰yu‹qrsxut |x‚‰‡v‰utur”t‰rqzxy wqwqîtxà‚tu wuu‰‚t xqr ‡w‰|rx|{t €wrx|rs / â 0 ƒ¢ï‰~ ï  ¢ï  †z {trs ‰ˆ rsx vy‰r‰r‹vx ”rxy ž£ŸŽ sxyxˆ‰yxxtwq~”Šrsxx| 'x(q~rs 























 

 

‡ˆ‰y‡‡xy‰ˆ ‚wƒ€uxu ž†”xŠrywrxy ‚‰wqîuˆ‰y ‡v€rw ‰|x‚‰qw‡€v‰ut rtwvxyr ‚‰yx‡urv€t‰xqŠwq| trwq|‹tquxwrsxˆ‰y €Ž ¡Žux‘€‰xqr‡v‹€yx‚‰qury €uw}t‚rt‰qq~u‰ˆwytut~ux ­t ‰ qwtq rsxu w‚‚‰y|t q ~ r‰ ~ rwrt qw u€wqwq|wvvy‰ |‰‡Šwtt‡qwrx|€xr‰ wqrt‡ðxurt‡us‰yrxy xu‰{xyrx‡€v|wrx ‹ ywrx wq| ð v‰yw |tï‡vwyw xqut‰xq yx‘yxw€ttuywrtx|‰ˆ‰yqu sw}x wq‹ r‰xw‡xˆ‰y‰vxywrx| xyz w r s‰ ~s q‰{ ‡ ¬ŸŽ€ sxyxz rsx|xq‰rx| ‚‰ur‰ˆwu w”wvvy‰Šx|wvxyr tŠ ‡wrx€‹yxu€wq| xw‡ˆ‰y‡xy‚wq x ïð ð ð '.()*+,- â ƒ †  ¡   ƒ  ž† ! '(/ ƒ¤† ­‰yrsxvy‰v‰ux|„„… ˆ‰y‡xyzrsxq€‡‡vwyx|r‰rsx xy‰ˆw‚rt}x xwu‡q‰r‚swq~x|‚‰ uxqu‰yut ~ qw u vxy‰‚rw}xt ””Šrx|xy wvxyr ~sxyw‚‚‰y|t q€‡xyq~‰ˆr‰wqw­t~‹Žut£zu €swuyx u‚sxr‰ ‡xxzt‡€vrxw‡stxqrx| wqîu yxu€rtq~ tq '.(),. ,- â ƒ †  ¡   ƒ   ž† ! '(/ ðï ð 𠃦† «…u vxy ˆ€ wq| uw‡vtq~ vxyt‰|Ž l–ÌšÐjm–˜—l j—™ nËlšÐml ˆ‰‰{twq|q~z{xxw‡wuuxuu pq„„…rsxy‰w| wq|tq ‚‰rxy‡‡vwyx rsxrsx vy‰v‰ux| ˆ‰y ‰ˆ xy u w‚st xqzt}x|q ‡ ‰ ‹vwrrxyqwq|t |trxyyx‚rt } t r r u‰‚rw}x t q }wyt w qryxu‰ rt €  wq| ‚‰q}xy~xq‚xzwq| ‰ˆ ‰ u t q rxyˆxyxq‚x u vvyxuut q ‡ € ‰ˆ ‚‰q‡~vrsxtxŠtry‹tqr‰v€‰rsxy ˆ€uxqu‰yu tu‚sx q rxy‡‡xuu |yw{t wq| wq|{trsu€w ”wq| ˆy‰ ru ‡ Šx| wvxyr€yxŽ ϕ "™x ÛÒt Øêttrí‹Û ‰ˆÛí rsxԄ„… ííØÒ×xw ˆ‰y xy ˆ‰y }wyt‰ u uxq sx ‡ ‡ €  u‰y­t~Žx¤x‡Š‹xqrrsxq€‡ xyu  wq| ‰‚rw}xu  tu t €urywrx| tq ‰ˆâž¤u x w v x  ⠞žwq|  â¢zyx‘€tytq~ ‡ Š ‰ ï ‰ut~‡qtvwyt w|x‚‰ v‰ut r t qt q r‰ q~rsxt‡ ‡|tyx‚rt}tr‹ vwrrxyq {trs€­t~wq|uŽ Ž ” us‰{q ¢z w ‚wqr  vy‰}x xqrt q wt q rwt q t q ~‰‚rw}x t q }wyt w qrwq|rsxyxˆ‰yx ‡ ‡  tq}wytwqr yxu‰€rt‰q w‚y‰uu w {t|x uvx‚ ryqxwy€‡sxˆyx‘‚wq„„…€xq‚‹ x q‰rx|Ž ˆ‰y‡xyq {t ursr‰{wy|u ”rxyu tqt‚‰yv‰ xw w|wvrt } x ‡    ywrx| xqw x u r‰ urxxy t q rxyˆxyxyu t  € € ‡  ‰ ‰ ‰î  qwrt q‰~rsx wyyw‹ˆy‰ |t y x‚rt qu‰rsxy rswq rsx |t ‡  ‰|x ‰qurywrxrst ‹ yx‚rt qŽ u x¥x‚rz{xwvv r{‰ y‰w| ‡  qrxyˆxyxyut xu‰ˆ wq|t ‡vtq~t}qx~‰qr‰rsxwyyw‹ˆy‰ ‡‰ˆwq~tqrxyxur ‹  ¡ß wq| yxuvx‚rt z {st x rsx ut ~ qw žß txu wr ry‰w|ut |xŽ sx ut‡€wrt‰q €rttuxu  â ¡ ‰‚ rw}xu{t s  ➞uxqu‰yuvxy ‰‚rw}x wq| u€ux‘€xqr‹ sxwux|”‰qrxyw vy‰r‰r‹vx ‰qxu wqîu wyx rsx ‚swyw‚rxyt u x| ‰ˆ  tvxyïq ­t‡â~trŽž¤Žrt zq~w|x‚t x q~rs  â ¢¢¬  ‡wrt‰qˆw‚r‰y‰ˆð ➢Ž …ˆrxyw|wvrw ­t~wq| ަtt€qurywrxursx ‹vwrrxyqt rt‚xuuˆ‰qzrsx |t y x‚rt } t r q u ‚ €  st ‰ˆ   q t q ~ rsx r{‰ y‰w| rxyˆxyxyuŽ u € €   ­t‹ ~rsxŽ ¤z‘{sxyx ‰q tutu wvv ‚‰qrywuru {t r s q‰ w|wvrwrt t x | wq| u ux‘ xqr t x u‚xqr xw vwrrxyq q‰r uxr € €wq‹ uvx‚t”‚€tqrxyˆxyxyuށ ‡ r‰ u€vvyxuu 



 

















|Α(Ω,ϑ)| /[dB] 10 0 −10 −20 −30 −40 −50 −60 0.8 0.6

Ω/π

0.4 0.2

0

−40

−20

−60

yx‚rt€}yxtr‹vwrrxyq {t­t~rs€yxu‚w¤ x|§twvxyr ⠞žz ‰ˆâ¢Žu€wq| xw‡ˆ‰y‡xy 60

20

40

ϑ/ο

|Α(Ω,ϑ)| /[dB] 10 0 −10 −20 −30 −40 −50 −60 0.8 0.6 0.4

Ω/π

0.2

0

−40

−20

−60

ϑ/ο

­tvyxuxq‚x ‰ˆ „„… ˆ‰y ~€yx ¦ ‰ˆ§tyy‰w| x‚rt}trwq|‹ vwrrxyq xw  ‡ tqrxyˆxyxyuˆy‰‡ ¡ß ‡wq|xytžßq rsxŽ ÏÊ í–×ÛÓ×íØÒÚØÒØ×êØ léëëÒØììÛÓ×Ô×Õ lÛÜ×Ô ™ÛìíÓÒ …wvxyrvxyˆ‰yyxz‡uwq‚xwq|‚‰‡”vwytx|u‰qwvxyrxr{xxq u wq| u‚w x | € ˆ ”  yx wq| wq| x| €€yx tq€rxy‡ ‰ˆ rsxŠ ‡xwq u‘€€wyx| yxut€|€w xyy‰yŠ tu wvxyr ˆ ‚wyytx| ‰€xr{xxq rŽ sxrsxyxut|xw€‡wˆ‰yxyy‰y‡xy sxyx t u |x”qx| wu |t  Ÿ ­t ˆxyxq‚x ‰ rv r  t q ~ uŽ ¡ € € ‰ˆ tqrxyxur wq|q‰t ˆy‰‡ y‰w|ut wq| £wq‹yx wq| ‡rsxwtquttq~qw~ tqrxyˆxyxq‚x |xŽ sxyx  ˆ‰yx u x wu{x wu wq‹ |tur‰yrtut‰‡qt€‡wv‰ux|‰qrsx ut~qw‰ˆ tqrxyxurt u ‡xwutu wrrsx €yx|Ž ‰ pqrsx rx|u‚xqwyt zrsx ut ~ qw‰ˆ t q rxyxur  u y‰w|ut | xz {st x y‰w| wq| t q rxyˆxyxyu t vt q ~x    ‡ ˆ‰ywyyw‹› „pè ‰ˆ ‹ wr wq ¢ß |’z‚‰yy vrx| q‚‰yyx  ß € y „ 莏sxtq rsxxw‡”ˆ‰yŠ€x|‡wvxyr wtqrx|v‡€ruq‰tˆy‰ux‡wržßâ|’£ uxqu‰yu xyu|yw{rsxt €yx ‚wuxz 60

20

40



















40

20 fullband fixed aperture subband fixed aperture subband scaled aperture fullband non−uniform spacing

35

10

25

PSD / [dB]

ensemble MSE / [dB]

30

fullband fixed aperture subband fixed aperture subband scaled aperture fullband non−uniform spacing

15

20 15 10 5

5

0

−5

0

−10

−5

0

0.5

1

1.5

2

2.5

3

3.5

4

 





0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

­t~€yx É „§ ‰ˆ yxut|€w xyy‰y wr urxw|‹ urwrxŽ

4

x 10





−15

4.5

­t~€yx ¬ ªxwyqtq~ ‚€y}xuŽ wq|sx ˆ  âÉwq|uxqu‰yu tq rsxxy qxurx| wyyw‹w‚wuxŽryw|trt‰qw ˆ‰y xw yxvyxuxqru € wtq t‡vx‡‡xqrwrt‡‰q {sxyx q‰ |x‚‰‡v‰utrt‰q rt‰ˆ‡rsxx |‰‡y‰w| x| ‰€wyyw‹ rŽ pr xtuxxt‡rxqruz sxy wv‰y vwrtxxyqwrt | r‰ }x‹â€wq|rt£tu€xuutqt~wqwˆ‰y ‡tu‹‚wyytuvw‚x|  tqv€rz wq| wvvtxu w rwv sx u€rs |xwq|w‹ txwqx‡‰ˆˆ‰y‡xyu⠀¤¢uxïr‰ xw‚s uxqu‰y ut~qwŽ ➤‚swqqx” r xy wqîu{t  ux| ðtq ­t➢~Ž Žwq|vy‰r‰r‹vx x q~rs ⢢¬wu‚swyw‚rxyt sxrx ‰ v‰yw|t xqut q‰ˆrsxu wq| wux| ‡ ‡ €  Ž ˆ‰y ‹  xw xy t u us‰yrxqx| w‚‚‰y|t q ~ pq w ‚wuxuz Œ„‡ tu ‡‰vxywrx| tq ‚‰‡tqwrt‰q {trs wq ª«„ wrsx~‰ ‰q ‰ˆâßrsx£zwq| ytrâßs‡ {tž rŸŽs wsxurxvw|wvrt xw‡ˆ‰ywr ‡xyuâ ßßßßrsx urwyru wr  ‰ˆ ut  x urxvªxwyqt €‚x| |xvt ‹ w‚rx|‡w~qttq r­t€|x~Ž ¬‰ˆtqžßŽ|t‚wrx rswr rsx utx qtu~ yx|‚€y}xu „„… ‰ ” rvxyˆ‰y u rsx x| wvxyr yx u wq| wux| € ‡ € €  Š ˆ‰y ˆwurxy xw xy t q sw}t q ~ ‚‰q}xy~xq‚x uvxx| ‰{xy‡ urxw|‹ ‡ urwrx xyy‰yŽ sx wrrxy tu |€x r‰ wq wq|xq ‰q ‰ˆ tqwrxyˆxyxyu ‰ ˆyx‘  swq‚x| u€vvyxuut wr { xq‚t x uz € ‰ ‰ˆ „ yxu‰ {sxyxrsxt q ‚yxwux|uvwrt rt qt u xqx”rŽ y € ‡wq‚xt u rsxuw€‡x vytwu ursxtq~ˆ‹€zrsxurxw|‹ urwrx«„Ývxyˆ‰y   wq| wyxw‚sx| ~‰ytrs‡ wrxŠvw ‰u€trtqurwqrt ~ w w ‹ ‰{xyuxqu‰yuz {st ‚ s t u s‰{x}xy vx‰Štr‹Žˆ yrsxy wqw‹utu rsx ‚swyw‚rxyturt‚ ‰ˆ rsx xw‚‰‡ ˆ‰yurxw|‹ v‰{xy uvx‚ryw |xqutrtxu qƒ­t„§†~ŽÉމˆsxˆ rsx €}wytwq|‰‡€u ‡xyuz€urwrxxyy‰yuwyxvyxuxqrx|t ”wrŠx|wvxyr q ~  â£uxqu‰yuxŠsttrust~sv‰{xy €yxsw}t ‰ ˆyx‘ ‰¥ ˆyx‘   {xy xq‚t x uzrywt t q ~ wu xq‚‹ t q ‚yxwuxuŽ € € sx ”  u wq| x| wvxyr yx u‚sx x swu ut t w €urt‚ r‰rsxˆ Š € wq|€ wxtr‡wut~sr‹‡‰{xyy „§„§ ‚swyw‚rxyt ‹ wr‰{xyˆyx‘ uŽ strsxu ‚‰yyxuv‰q|ur‰rsx|t y x‚rt } t r €~xq‚t¡z x{sxyx ­t ‰   vwrrxyq t q w y~xy xw {t | rs wr {xy  ‡ €~srsx ˆyx‘ ‰ ‰yxut  xq‚t x uw {u ~ qwv‰{xyr‰vwuursy‰ € ‡ u‹urx€‡xq‚tŽ …uxuz rsxxrrxyyxu‰ r‰{wy|u rsx st ~ sxy xw‡{t€|rtrs‰qtqwyy‰{u sxvy‰v‰ux| ˆyx‘ ‰ u uxy}x|Ž tq}wytwqr „§|€xr‰ „„…wvvy‰w‚s~t ‰‚rw}x  ‹ } xuwˆwt y ‰‚rw}x utxuŽ sx ury€‚r€yxu€vvyxuut tu ‚xwy‰q‹ ­twr~Ž€rsxÉzyx {sxyx ‰ xx uxxq  }t|t‚wqu¥txyxqr tqwvxyr {xy t q rxyˆxyxq‚x ‰{xyˆyx‘€xq‚txu{trstq xw‚s‰‚rw}xŽ discrete time n

normalised angular frequency Ω/π

1

‰ˆ „„… rsx xw žßˆy‰‡us‰{uy‰w|utrsx|xŽ~wtqstyxuv‰qux  ‡ ˆ‰yß |’­t‡~xyŽ‚‰qurywt ”~ u yx t q |t ‚ wrxu rswr rsx € ˆ ”   qr r‰{wy|u y‰w|ut | x t u x | wq| rswr  € ˆ‰y ˆwt  ‹  rsxrsx ytu€vvxwq|‰ˆ rsxx|~xu xw xy ~wt q t u y u w |xuvt  wq|‡ rsx‡ tqrx~ywrt‰q ‰ˆ }wyt‡ ‰€u wvxyrx rvxwîu wu‰ st~st~tqsru­trswr €yxu {ttqrstrsxq rsx„§xw‰ˆ‡rsxˆ‰y‡u€xyŽ wq|stuwvvy‰w‚sxu Ž ~ É ‰q x¥x‚ru wr rsx ‰‚rw}x wyx€r q‰rwyxwyxu |€x €r‰r |t‰ˆuur‰yrt‰{‚‰q}xy~xq‚xwrrsx wy~t q u ‡ wq|x|~xu‰ˆ v‰{xy r‰ rsx ‰ ‹  tw|wvrt q|t}t|}€xwwu~€ wq|u ‚w ux| { t q v r €  € ‰ytrs‡ ž¬ŸŽ Ï­‰y rsxoÓÙë Ø Ûí u‚xqwyt‰ tq „x‚Ž £Ž  {trs  â £â wq|¢¢¬ ˆ‰yârsx¡z   â Éz ï ⠞¤z ð ⠞¢z wq| vy‰v‰ux| ~ ‚‰‡„„…v€rwrtxw‰qw‡ˆ‰y‚‰‡‡xy ­trsx~Ž wytžžŽtquvtqsx vyx‘xŠ€ttrytxuxu wqwyx„„…x~tŠrywu‚sx }xq¢‡tqxzuxqu‰yu wq| sxq‚x € ¢ ‡wq|‰yx €‡ruvwyx|r‰rsxu ” ‰ ‹ wqw ut u r xy wqî‰vxywrt qu‚‰  ”rtЉx|qw wvxyr rrsxx‚r€uyxŽ€wq|‰rxu‚sxrswr‡xursxtq ~xqxyw ‚‰‡v€rwtu €yxxŠtrwy‚st ‰ˆ ‹ ‚‰ v ‡ ut~qt”‚wqr‹ ‰{xy rswq rsx ˆ€ wq| wvvy‰w‚sŽ ­‰y rsx 



 



0.05

gain from broadside / [dB]

−10

0

−0.05

−0.1

−0.15

−0.2 0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

­t{wy|~€yx y‰w|ut Œwt|xqyxvyxuxqrt ‰ˆq~ rsxrsx|t„„…ur‰yrt‰xwq‡t ˆ‰yv‰ux| yxuv‰qux žß ‡xy r‰‰q  ‡ rsx ut~qw ‰ˆ tqrxyxurŽ normalised angular frequency Ω/π

6

computational complx (MACs)

fullband fixed aperture subband fixed aperture subband scaled aperture fullband non−uniform spacing

5

10



4

10

3

10



   

   

2

10



1

10

¡Ÿ …Žpust‡wy€z ¨sx‰y‹‰ˆz€•qx‘ƒ¤†€w¤Éž‹uvw‚x|wyyw‹uz ¦ß zžÉ¤ Ž © ¢Ÿ “Žwyyw‹zx©xyt‡q wqqz ¨…uxˆurxxytq~|tz~t‰y‰qr‰z rw ‡t‚y‰vs‰qx çqrŽz wqw|wz žÉɞz£z¡£¬ž ¡£¬¢Ž £Ÿ {tŽrss‰‰{€zyxuv‰qux ¨­yx‘€xyy‰yz xq‚‹©tqt|xvxq|xqr xw‡ˆ‰y‡xyz q §xry‰trz«t‚st~wqz žÉÉ£z£z ÉÉ£  ÉɬŽ Ž“t twwyyw‹u uxqu‰y ¤Ÿ §Ž’Ž“wy|z莅Ž xqqx|‹zwq| èŽ u‰qz ‡ ‰ˆ ¨sx‰y‹ wq| |xut ~ q y‰w| wq| {trs ˆyx‘€xq‚‹ tq}wytwqr ˆwy”xz | ƒ †z xw‡žß ¡ vwrrxyquz © žß¡¢z žÉÉ£Ž yxxuz ¦Ÿ œŽx‹zªŽ x{Þwq ‰yîz ßß Ž z “t “Ž Ž „rx{wyrz «Ž „‚sw ¬Ÿ „Žy‰“xt u uz èŽ xyrz pŽ  “Ž œ‰¥ «Ž xyz wq| wq|…|wvrt‡}wqzx’xw‡¨…qˆ‰y‡Ýà‚t „‚sx€‡|xˆ‰y’y‰w| tqz ~z«‰q©xqrtq  rxyx‹z …z žÉÉÉz žz¢É¤ £ßߎ “xtuuz èŽ}x“ށxw„rx{wyrz “Ž wq|u{t ªt€z ¨…rsu‚w ÉŸ „Žwq|w|wvrt wq|q u€ y‰w|x| ˆ‰y xyt ‡ ‡ wvxyr€yxzz «‰qrxyx‹z © tq …z  ßß z z ž É¬ ž¡ß Ž çŽ ªŽqx|­y‰urz…|wvrtpppz}x¨…q…yyw‹…~‰yty‰‚xuut žßŸ urywt rs‡ ˆ‰yq~zªt© qxwy‹ ‰q z ƒ¬†zÉ ¤ É¡£zžÉ¦ Ž Ž Œytàrs wq| “Ž t‡qzx|…|wvrt Ž‹ ‰qurywt žžŸ ªŽ…vvy‰w‚sr‰ªt ¨…q …}rx’xw xyqwrt‡}x q xwy ˆ‰yžÉ¬ Ž‡tq~z© z ƒž†z  ¦ ¡¢z ž Ÿ ’Ž“t|zy‰{wq|„ާބrxwyquz žÉ¬£Ž yxqrt‚xœwzÝq~x{‰‰|t¥uz x{ ‰yîz  ‰tyx wq|rs yt«ŽÞxrrxy ž¡Ÿ …ŽŒt tz v¨…|wvrt }x ‹­tuturzÝxytŠqvxy~ tq …qw „t €xqruwq|u{t r t ‚ w„w t q ~ ‡  ݂s‰ wq‚x ‡wrt‰qz©wq| …vvt‚wrt‰qu r‰ …‚‰€z urt$ ‚ƒ¬†zvvŽ ž¬¤  ž¬¦£z žÉÉ Ž ž¢Ÿ “Žu‹urx‡xuxˆ‰yy‡wqqz ‡€r©tywrxtq wrtz ‰‹qx{ut‰ˆu wq|w‚‰‰yîz€|xuturt„…z ‚wq‚x¨…qw ‚~wq ‰ˆx‚s‰xuz žÉ¬¬z£zvvŽ  £¦ß  £¦¡Ž “xtuuŽvx¨…qw ­wurrxy p’wqîu©Ž ‰ ‰ˆ ‹ ž£Ÿ „Žç}xyuw ut u wq| v x xqrwrt q ‡ ‡ ­t Ž «‰| ŒŽ  | w rx| pq «‚“st‡yrxy wq| pŽ € Ž y‰€z|‚swvrxy xyzx|tr‰yuz ¡zvw~xu  ¤¡  ¦¢ŽçŠˆ‰y| qt}xyutr‹ yxuuz«wy‚s  ßß Ž      

10

0

10

20

30

40

50

60

70

80

90

100

­twvxyr~€yx€yxzžž u‰€‡wq|v€rwrt” ‰x|qw‚‰wvxyr‡v€yxxŠtwq|  r t x u‰ˆˆ wq|” x| €  Š u wq| u‚w € x| Š wvxyr€yxŽ utwyyw‹  z{sxyx„„…wq|wˆ ‡€wrtxw‰qut‡ˆ‰yq ‡„x‚Ž£Ž € wq|qxurx|  xy rt t u t q ~ w   âÉ uxqu‰y ut~qwu € vy‰}t |x| w utu‡€vvyxuut twy urxw|‹ ‡wq‚xrswrtqrsxrxy‡‚‰u‡‰ˆ rurwrx‚wq vxyˆ‰y ‰ tvq€rxyˆxyxq‚x qzt x q‰rx|  rwrt‰qw ‚‰‡vxŠtr‹ |t¥xyu ‹   ‰y|xyu ‰ˆ ‡w~qtr€|xŽ o˜—oКl–˜—l “xxw‡sw}x vy‰v‰ux| w u wq| wux| u‚w x | wvxyr yx €  € ˆ‰y  ‹ xy {st ‚ s swu rsx w t t r r‰ wt q rwt q wvvy‰ w‚y‰uu w‡{t|x ˆyx‘€xq‚‹Š ‰ tywq~xŽ yxu‰ rt q ‡wrx‹ ‡‚‰qurwqr € ‰‰y ‰ ” ‹ yxu‰ rt q xq‚‰ qrxyx| x| wvxyr yx € €  € Š ˆ‰y ‰ ˆyx‘ ‰}xy‚‰  xw xyu wr { xq‚t x u ‚wq x x |yw{t‡q~‡uxqu‰y tqv€ru ˆy‰€‡ w qxurx| wyyw‹z u€‚s‡ rswr‹ ‰{xyyxŽ ‰‚rw}xu ‰ˆ tqq‚yxwux| ‚‰yyxuv‰q|r‰ wq wyyw‹ wvxy “x ˆ  rw‚y‰uu sw}x us‰{q rswr rsx ‚‰qurywt r t u € rsx ‰‚rw}x wq| ‡wy~tquz wq| ‰q‹ t‡t€rx|” x|‹ rsxwu u‡”wrxy wuwqî› u |tur‰yrt‹‰|xut q ˆ€~q‚rtqŽ ‰qz {st‚s ‚wq x îxvr qx‚xuuwy‹ …||t ‰ rt‚‰‰qw‡v‹xzrsx„„…u‚sx xt q sxyt r ursx {‚‰ v ‡ ‡ € “x ‰ ‰ˆ ‹ rwrt qw t r ~xqxyw u wq| wvvy‰w‚sxuŽ € Š ‰ ˆ‰y sw}x ‚‰ vwyx| }wyt u y‰w| wq| xw t q ~ t v x ‡ €    ‡ ‡ ‡ ‰ ‰rs ˆ  xqrwrt q t q rsx wq| wq| u wq| |‰ wt q ‡{sxyx‹ rsx „„… |‰xu q‰r€ u€¥xy wq‹ |x~yw|wrt € ‰q‡{trsz r‰u‚sxrsx‡x«„ÝxŠv‰vxyˆ‰y ‚‰‡vwyx| r‰ w ‡rsxwq‚xxqrt{sxq ˆyxuvx‚r w€xtwq| t r t q ~ y x uxqu‰y wyyw‹ |wrw r wr w ‡€‚s st~sxy ‚‰urŽ nËÍËn˗oËl §‰‡wtq …|wv ‰vrt‡qw~…­yx‘~‰yt€xq‚‹ žŸ rt§Ž}x…qrxqqw €qqz ¨„€y‰‚xuut ‡ ˆ‰y’y‰w|  ’wq| r s  Ýq}t © z • $ƒ¢†y‰q‡¡¢žxqruz¡£žzžÉ¬¦Ž Ž œŽ §‰~qxu€utwq|q~rsxwu‹ ­Ž §Ž ’xqx|t  Ÿ yw‹|xut ‚ rz ¨’y‰w| wq| wy     ‹ vr‰rt ‚ rsx‰y‹‰ˆ qx‘ w ‡ € € uvw‚x| wyyw‹uz© z ƒž†  ¦ ¡¡z žÉ¬¬Ž fullband adaptive temporal dimension







     





    



     ! "#





$!!   

%



 &!       ! 

!

 &!       

 ' 



 







    







 (  & )  %



     





   



    &  , *

%

*

 + '! ) 

„Ž “xtuuz wq| èŽ “Ž „rx{wyrz ¨§x ž¤Ÿ «Žut~qœwyrxqx‚îz ‰ˆ xwy xyˆx‚r èx‚‰qury€‚rt‰q ç}xyuw‡vx| ­trxy ’wqîuˆ‰y „€wq| …|wvrtz}$x ­tƒ¬†zrxyuzvvŽ© žß¬ž žß¬¤z žÉÉɎ ž¦Ÿ “ŽœŽ wq| ’Ž­wyswq~ æxq‹Ž è‰}x€­turr«txyuސ ‚y‰vs‰qxx‰…yyw‹u utq~ „€’‰y‰ wq|€…|wvrt z ž¢Éƒž† ž¦  £z­xŽ  ßß Ž  …u‹ „ ‰ ‰q}xy~xq‚x ‰ˆ ž¬Ÿ §Žª«„莅‚‰«‰y~wqŽ { vr‰rt ‚ ‡ wq‚x  urt ‚ ݂s‰ x yuŽ € z  ƒ¡† ž ¤ ž¡¤z«wy‚s žÉÉ£Ž 

    ! 

 



*    ,  !     & )          ) '                 

Suggest Documents