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Un système de modules avancé pour SIGNAL

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(1)Un système de modules avancé pour SIGNAL David Nowak, Jean-Pierre Talpin, Thierry Gautier. To cite this version: David Nowak, Jean-Pierre Talpin, Thierry Gautier. Un système de modules avancé pour SIGNAL. [Rapport de recherche] RR-3176, INRIA. 1997. �inria-00073513�. HAL Id: inria-00073513 https://hal.inria.fr/inria-00073513 Submitted on 24 May 2006. HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés..

(2) INSTITUT NATIONAL DE RECHERCHE EN INFORMATIQUE ET EN AUTOMATIQUE. Un syst`eme de modules avanc´e pour. . David Nowak, Jean-Pierre Talpin, Thierry Gautier. N ˚ 3176 Juin 1997 ` THEME 1. ISSN 0249-6399. apport de recherche.

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(214) ' µ³tQ}¸{³²´iYk.n q _En§_ q `a_g­³—™i±º _ q `a_Dn§k q _En q il}8g¯ †nh †›l_ {._ Y | r }‰nh ™_D}¿n

(215) —™i%| r }‰n q iY †}‰n§_

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(217)  3’  ¶^_Dg q_] Œl—†_g {8_

(218) nxoGy‹ilŒz_K{³²¾k8}8_¨_¥m˜y q _ghgh r }g¦k q g¯ ™Œl}‹ilk˜mg r }‰n q _f ghk8`°_f _gu_}ª‹Œ8µ µ   .  / 0 U   Y +  ( .  /K 0 U   Y + K ( .   Y + W(   Y + W ' (    Y + W J] R W ' ( . ·  / g¦k8®.g¦k8`ay.nh r };0. Á³Á È  3R.   Y +  (   Y +  W (   Y + W [ P R P  ( . b à  Y  W(   Y  W ' (   Y  W  a `  ’È Ã W ' ( +. +. +.  Y + W( Y

(219) '   Y + W( ' 8 :9 ( !   <    <      !  C ?>   ; !;$ Q <    $  D< C ;   ;. Ož Ÿ  _DghnK— ²¾_}‰›¿ q¦r }8}._`a_}‰nE{._anxoGy‹iYŒz_lµ1š²¾_g¯nk8}¸_D}8g¦_D`®.—†_±¬¿k. | r }¿nh ™_D}‰n¨n r k8g

(220) —†_g gh †Œz}‹¶·ili k˜m%q_] _DŒYnO—™_—™_D{8g _ r y=  _ f q iY n§_D

(221) :k ! q g < ›¿ ™g¯ ™g¯®˜ ™Œl—™_D}.gd †ª8il_ghg ¬¿r k8|D ¥_E_f g {‹iYi»] }8—†gu_k k.q }nx_oG}‰yœ›¿_l µ qhr }8}8_D`a_}‰nK{8_nxoGy‹iYŒz_  ­ gh_ Qghnu—2² ilr k.}¸g¦ghyœ ¼_{8k._

(222) n

(223) nxnxoGoGyœyœ__ q ' —2µ ² _Åm.y q _ghgh r } W»y‹i q _DnK¬¿k8_ _Dghn¨k8}¸g r k.g v nxoGyœ_{._ ' ­^iY— rzq gW  _g¯nO—Õi»º r }8|¥n¦ r }¬Gk˜ XiYg¦g r |D †_ i» ] | [ il¬¿k8_| r }8g¯nÇil}‰n§_Kg r }nxoGyœ_`» †}. †`iI— µ cedHfceg.

(224) @ž Ÿ0¡^¢¼£ b pr Qqq _}q r }.g±—™_6|jilg{8k ^]· R ( p¼r k q nxo˜yœ_ q W ^]¼  R Á³Á W ' y‹3i R q {‹il}.g  ­Q «—uº iYk.n ` œ }¿R;n à _ ­ iY¬¿— k8rz_q g Wr _}g¯ndily.{8y._K—† †nx¬¿oGk8y;_K_ —Õ i ­œq_¥_D] ndŒl¬¿—†_¨k8{._ _¨W5'@ghk8_D®8ghndghk8{.`a_¨y.nxoGn¦ yœr _ }³µ È  µ ,G 2W5'@_ghnu{8_¨nxo˜yœ_   Ž  R P à P Á R  à  +QGÈ    HÁ ÆzG‘j‘j’¼‘ eO_y q _} r }8gO— ²¾_¥m˜_`ay.—†_ (  

(225)  

(226)   " !#$.  .

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(230)  ? O '

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(232) _Dn O g k.gX—Õi | }‰n iY †}‰n§_

(233) ' D_ n ^J iiY— rlq gu—†_nxoGyœ_ X '

(234)

(235) ' µ;tN}.g¦k. «n§_Y­7^J _¥f nÇil}‰ndily8y.—« ™¬¿k©_ f i] k8} ®— rzrGq rg¦¬¿—¥_fk8__ }@­ ^r J±} D_ _gh}n il{=y8_f y˜{8—†k˜ † †¬¿nXk=¬G_ f k.i»]_ —2 ²¾_U}‰n¦ † _ qÁ³Á bdÈ « —³0o%R i»_¥nk8—™}8iu_

(236) | _ r q¦}‰q n _q k iYq ™}‰{8n¦_d_=nx{8oG_¥yœ›G_l †_µ;}‰1=n _ |¥Á@ ·Á} Èr  k80gOR iY`

(237) _D] }8'_ µ i»] †}‰¶·n qhi±r {8Œ_k˜f }© q _ f _Kq iY†— _—« ™g g¦iY} n¦r r nh } r }8| gOr }8{8g¯_ ™g¯C n§_  i]  $ ¬¿ k‹ < iY}¿nh †< ª8 _ q _Dk8n }˜{³ †›l² < _ +q gh _D—«—™_D `a< _ }‰< n  n µ r k.n¦_gu—†_gu›li q ™il®.—†_g —†q †iY® —«q ™gG_D_Kg

(238) f g¦}³_ ² q ili y8y‹{˜i †n q iY † g¦Gg§iY  }¿

(239) Kn  y8il gd{‹ il!#}. gd_D—n ²¾_gh}‰_ ›¿q ia qhr } }8r }8n˜__Df `aX_µ }‰n{._nxoGy‹ilŒz_  µ ' }nxoGyœ_ ŒX_f }©_ f v wp i q | [ _¥ilm˜¬¿_k8`a_y.—†ilv_ly8] ­ vyœ—†_¨_D— q gh| /2[ |¥_º¤f µ ` ª‹i Œ8{8µ _

(240) ˆnx0Çr o˜­ yœ—†_‡_¨{8gh|_ [ P_f J±` q g¦i _ q {.i _( nx oGyœ _ ' {8 kX y q¦r |' _(

(241) q g¦gh

(242) k8g '{ ] µ r «[n‡_D¹ n q _ ™›l}8i g¯q nÇ ™ilil}.®.|D—†_¨ ¥_lf ¬¿­@k‹|YiY² _D}¿ghnhn †ª=i _f _¨{. _DnO_—™¬¿_Dk³gO²¾¬Gk8k8}8il_E}‰} n¦ «ª‹k.|j›ziY_¥n¦—†_—†_k q ›Ygši g r Õil}‰®˜nu—™_¨ghk8{8y8_y nxq oG ™`•yœ_E_Df g_µ g¯n

(243) iYnhn ™®8k©_f _ i | il¬¿k8_. /   Y +  W ( 0 - pn npn "      "   Y +  /W4   ! W5" 0L( 8 :9 +( ! !# ?>   .  !. . . Ož Ÿ ˆ. HHJILK5MONQPQR. X. . '    '      !;$Q  Q  . .   ' 1 Y  /  0 ' Z Z.

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(245)  .   !;< . .    < $. r q r ] i Y 8 } u g 2 — ² Å _ ˜ m  _ a ` . y † — l _ 7^J_g¯nš †}8ghn§il}8|D Å_E ­ f 8 { D _ ˜ k 6 m º ™ D g @ µ ^ ¶ D _ u g Y › i ™ l i . ® † —  _  g D _ f § n l i ‰ } d n } ˜ k z › D _ « — † —  _ g i | [ il¬¿k8_K ™}8g¯nÇil}.|D ™iYn¦ r }³­8 «—·}³²½oi y8ilgO{³² _ q¦q _k q {8_

(246) nxoGy;_Yµ  Ž   R  P à P Á R #   

(247) U  ?  1  <DA C - <  " =   Y   L< Y +? 1  "A -   7" 1 Y     "  ' 1 Y <"  

(248) < ' ' npnpn npnpn  Ž  R P à P Á R    !;   C    $   #  '  <) ;  

(249) #  < !#$    &1 Y  &1 Y   &1 Y  '     3     ’ R  IÁ Æz˜‘‘j’‘ ¶^_Dg q_] Œl—†_g {8_

(250) nxoGy‹ilŒz_K{³²¾k8}6y q¦r |_Dg¦g¦k.gug r }‰n q _f ghk8`°_f _gu_}ª‹Œ8µ^b ˜µ 3. &. . . !. . . . . !. . . !. ,.  . . /   Y +  K ( 0 - pn npn "   Y + W(      "   Y + ) K  2   3;K " V( U W   Y + ) *   Y + ) * '    K 5(  2   !;K " ( "  Y + ) *   Y + ) *

(251) * '   Y + ) &* 1 K    !;K "  4 (  Y + ) * ^]  0 R

(252)   Y + ) *   Y + ) * ^]   R    Y + ) * ^]  &6 @0 R

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(256) nxo˜yœ_lµ ɗ^yœ_k˜nug¯ ™`ay.—†_`a_D}¿nE_D¹ n q _¨®. ™_D}nxoGy©_Yf µ ' }8__f ¬¿k‹iYnh r } _g¯n ®. ™_D}nxoGy©_Df _g¯ ( ] Œ‰ilk8| [ _6{8_—2² r y©_ f q iIn§_k q (VU g r }‰n±{‹iY}8g —2²¾_}‰›¿ qhr }8}8_D` _D}‰n%{8_ Z —™_Dgg¯ ™Œl}‹ilk˜m i¸  nxoGy‹ilŒz_ / 2µ _Yµ ɗ™g r }‰n%_Df n˜_Kf {=_f |¥—Õi q _f g=0\_¥n Z —™_KnxoGy;_{8_—2²¾_¥m˜y q _Dg¦g¯ r } W i ] { q¦r †n¦_{8_¨— ² r y©_ f q iYn¦_k q ( U _g¯n6_f ŒziY—ilk6nxoGyœ_{8k } v k.y.—™_¥n {8_Kgh †Œz}‹ilk˜m i ] Œ‰iYk8| [ _K{8_2( U µ ). ). $. +. +. +. . . ?>. cedHfceg. . '.

(257) @ž Ÿ0¡^¢¼£. bH‚ ' }8_O| r `ay r gh «n¦ r }{8_Oy q¦r |_Dg¦g¦k.g©_Dghn©®. ™_D} nxoGy©_Df _ug¯ ‹—™_Dg©y q¦r |_ghg¦k8g | r ` y r gG_f g g r }‰n ®. ™_D}¶ rznxoGq guy©_Df{.g_µ —™i{©_Df |D—™i q iYnh r }{³²¾k8} y qhr |D_ghg¦k8gš— r |jiY—2­ |_y q¦r |_ghg¦k8gš_ghnunxoGy=_f y8k˜ ™gug r } ™q {8iY_D—« ™}‰gGn¦_Qf «ª‹{8|jkKiYy n¦_q¦rk |q _D g¦gh_k8g¯gn=µIi¶·s¤i\r Œk._n˜f }©_ f _ fid] q iI—2²—†_D †g§}‰iY›Gnh q¦r r } }8}8T_W `a / _D }¿n\Y {8_ ;nx0 o˜_y8g¯iln

(258) Œz_f _ Œ‰iY —†_ i i ]S;_ |D n˜_O f {8k»nxo˜ yœ _ " ŒX7_f 1}©Y _ f v r·k ]     !Y  " _Dghn

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(260) Y {. _ q ¸_Dq n Y ¬Gk˜ Q}8_»r g 2r  }¿ q nK y8ilgd—† †® r q _g  j npnpn  q —{‹²¾k8il}8}g {8_gO­Y_¥`an_` ®j q npnp_Dn gd q ilk—Õiu` º _ r ™`a}.g _Dn¦| k r }‰_\n¦n †_}‰il}.nughk8 «n¦}8 «_

(261) ›z_ ›Y{8i q_ ™il®.—†_K_Dgh{8n _ _D †}‰ n§ _ 2il k˜!m | " }‰¿n µ iI ™}‰n§_DgQ{ }‰n  Ž  R P à P Á R TW  /   Y   02U  2   " 71Y  j npnpn  q  < #  

(262) ## <    ( "   Y    

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(265) nxo˜y8ilŒz_K_g¯nu †}‰›li ™il}‰nšiYk| k gu{8_

(266) —2² _Åm _f |k˜n¦ }³µ ` / Ž  0"R ( P à P Á / R 0    Y `  < 7  

(267) #@ < !#$    K   ` / `0    Y  K K 

(268) }} r n§\_ `

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(271) #    !  C  ;   + 

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(277) nxoGy‹ilŒl_ghk. †›Yil}‰n¦_ (   Y  L (   Y  (   Y  K (   Y  L [ b P R P à (   Y K (VU L [ b P R P à . +. +. +. +. HHJILK5MONQPQR. +. +. . U.

(278) b.      

(279)  . d}6i»—™i»n q il}.gh «n¦ r }6ghk. «›liY}¿n¦_.   !;< . .    < $. (. K V( U L [ b P R P à V beV7d V h V7i V d Xh K ( U L [ b P R P à   Y +  K /  0 ¿­;{ r }8|  +  ( µ 3 ² r^k ] r . . . y‹i qu[ oGy r nq [³_] g¦_Y­ }yœ_k.n q _`ay.—™il|D_ q r ¦ q q q {‹il}8g —™i»y _Dk.›z_{8_

(280) nxo˜y8ilŒz_l­8—†_g ||Dk _}8|D_gš{._ y‹i  µ €.µO{‹il}8g —†_K|jilgO{8_

(281) —™ia| r `ay r gh «n¦ r } {8_Ky qhr |D_ghg¦k8gD­ r } iE—™i»n q li }.gh «n¦ r }7( * V V7Z 2V X. p i qO[ oGy r n [³_D] g¦_. * ' ' * ' V4V7Z VX * ' ' ' ` *

(282) * ' V#Z &V V Z X * ' '

(283) * ' ' ' . +. ` '. ­ r }6i»{ r }8|

(284) —™iay q _k˜›z_{._KnxoGy‹iYŒz_ ( .  Y. . ) *

(285) * '  Y. . ) *  Y + ) * '   Y + ) *

(286) * '   Y + ) * ''   Y +. pq i q —2² [ oGy q r n [³_] g¦_O{³²½ †}8q {8k8|¥n¦ r } r }i r qh_Dq n ) * ' ' ' q µ d}»yœ_k.nN{ q r }8| _D` y˜—Õil|D_ {8il}8g©—™iy _k˜›z_

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