Filtro IIR en MSP430

 

 

JLY^J^[^C ^KILCAÙ@JIC NK OCRKAJM

TRCIKYMOJKL^C NK YKÝMAKY

TRÍI^JIM ;. NJYKÝC NK GJA^RC JJR TMYMBMFMY

TRKYKL^ML6

N[AIK @[MNMA[TK @MRIÏM BKNCAAM YMAWMNCR YCRJM YMA@MNC TRCGKYCRM6

NRM. MNRJMLM NKA IMROKL ^KAAKV ML@[JMLC

OCRKAJM, OJIHCMIÍL =; NK KLKRC 242=

 

Icltkljnc JL^RCN[IIJÙL................ ............................. ............................. .............................. ............................. ............................. ................................................... .................................... 9 OMRIC ^KÙRJIC.............. ............................ ............................. ............................. .............................. ............................. ............................. ....................................9 .....................9 Jopuasc jlvmrjmltk.................... jlvmrjmltk................................... ............................. ............................. .............................. ............................. .............................. ............................ ............ > ............................. .............. .............................. ............................. ............................. ....................................... ..........................; ..;

TRC@RMOM NKYMRRCAAMNC NKYMRRCAAMNC.. Njskýc pcr oknjc nk Omtamb................ ............................. ............................. .............................. ............................. .............................................. ................................ ; Jopakokltmijùl nka gjatrc kl ka OYT>94................ ............................. ............................. .............................. ............................. ............................ ..............; ; RKY[A^MNCY................ .............................. ............................. ............................. ............................. ............................. .............................. ............................. ..........................: ............: ICLIA[YJCLKY................ ............................. ............................. .............................. ............................. ............................. ................................................. .................................. =2 Ymavmncr.............. ............................ ............................. ............................. .............................. ............................. ............................. ................................................ ................................. =2 Nuaik................ .............................. ............................. ............................. ............................. ............................. .............................. ............................. .................................... ......................=9 =9 BJBAJC@RMGÏM................ ............................. ............................. .............................. ............................. ............................. .................................................. ..................................... =9

 

JL^RCN[IIJÙL. Kl ks ksttm príi príitj tjim im nk nj njsk ským ýmrí rí y sk jo jopa pako kokl kltm tmrí rí ul gj gjat atrc rc nj nj`j `jttma (J (JJR JR)) kl ul ojircicltrcamncr OYT>94, utjajzmlnc ka oêtcnc nk jlvmrjmlzm ma jopuasc vjstc kl iamsk  pmrm njskýmrac y cbskrvmlnc su rkspukstm kspkrmnm kl Omtamb. Nk j`uma omlkrm cbt cbtklnr klnrko kocs cs ic ickg kgjjij ijkl klttks ks,, ic icll ka ma ma`c `crj rjttoc nk nksm smrr rrca caaamn mncc y ic icll am my myun unmm nk nkaa ojircicltrcamncr jopamltmrkocskaacs ickgjijkltks pmrm ka gjatrc nj`jtma y oknjmltk ul bmrrjnc nk grkiuklijms icoprcbmrkocs gulijclmojkltc nk kstk.

OMRIC ^KÙRJIC. [l gjatrc ks ul prciksc icoputmijclma c ma`crjtoc oknjmltk ka iuma ulm skýma nj`jtma (skiuklijm nk oukstrms) ks trmlsgcromnm kl ulm sk`ulnm skiuklijm nk oukstrms c skýma nj`jtma nk smajnm. Acs gjatrcs sk utjajzml ouihc kl tcncs acs íobjtcs nka prciksmnc nk skýma, oís c oklcs ousjimaks, y scl ulm icopclkltk ksklijma kl tcnm imnklm nk icouljimijùl. Iclstjtuykl am  bmsk nka prciksmnc nk skýma, quk puknk mpajimrsk m skýmaks nk tcnc tjpc (scljncs, joí`klks, vïnkc, vjbrmijclks sïsojims, kti.). Tcnkocs nksirjbjr acs gjatrcs oknjmltk ulm kiumijùl quk rkamijclm ulm skýma nk kltrmnm icl ulm skýma nk smajnm kl ka ncojljc nj`jtma. Nk kstm omlkrm, am smajnm nka gjatrc sk kspkijgjim icoc ul rksuatmnc nk suoms, rkstms y ouatjpajimijclks nk oukstrms nk kltrmnm mitumaks y mltkrj mlt krjcrk crks. s. Nj Njih ihms ms ki kiumi umijc jclk lkss sk nkl nklco cojl jlml ml tê têilj iljimo imoklt kltkk kiumijclks  aj ajlkm lkmak akss kl njgkrklijms. Ajlkmaks sj`ljgjim quk, sj am kltrmnm nk ul gjatrc ks am suom nk ncs gulijclks ksimamnms, am smajnm nka gjatrc ks j`uma m am suom ksimamnm nk ams smajnms nka gjatrc pmrm imnm ulm nk njihms gulijclks. Acs gjatrcs icl rkspukstm jopuasjclma jlgjljtm (JJR) sk njstjl`ukl nk acs gjatrcs GJR pcr am  prksklijm nk ulm rkiursjvjnmn, am skýma nk smajnm nka gjatrc sk rkjlykitm m am kltrmnm nka oj ojso soc, c, icls iclstj tjtu tuyk ykln lncc ul ij ijri riuj ujtc tc rkiu rkiurs rsjv jvcc c ic icll  gkknbmie . Ks Kstk tk oêtc oêtcnc nc pk pkro rojt jtkk jopakokltmr gjatrcs icl rkspukstm oís icopakfm y icl oklcs nmtcs. Icoc jlykitmocs iclstmltkokltk klkr`ïm kl ka ijriujtc, am rkspukstm jopuasjclma tjklk ulm nurmijùl pctklijma jlgjljtm, y nk mhï ak vjklk ka lcobrk. Am kiumijùl tïpjim nk ul gjatrc JJR sk kxprksm nk am sj`ujkltk omlkrm6  O 

 L 

 y ( l )?

∝? b  x ( l −e ) −∝? m  y ( l− e ) e 

e 

e 

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Acs gjat Acs gjatrcs rcs JJR sc scll ouy ouy kgj kgjim imik ikss y puk puknk nkll prc prcpc pcrij rijcl clmr mr pklnj pklnjklt kltks ks nk ic icrt rtkk ouy ouy  prclulijmnms. Tcr ctrc c trc amnc, ma pcskkr imrmitkrïstjims nk rkmajokltmijùl (c ( c gkknbmie), tjklkl tklnklijm m kltrmr kl csijamijùl y kl rksclmlijm.

 

Jopuasc jlvmrjmltk. Kl ka oêtcnc bmsmnc kl am jlvmrjmlzm nka jopuasc, ka cbfktjvc nk njskýmr ul gjatrc JJR quk tkl`m rkspukstm ma jopuasc uljnmn h ( l ) quk skm am vkrsjùl oukstrkmnm nk am rkspukstm ma jopuasc nka gjatrc mlmaù`jic. Ks nkijr, h ( l ) ?h ( l^  ) , l ?4,=,2 , …

nclnk ^ ks ka jltkrvmac nk oukstrkc. ^comlnc kl iukltm quk ulm skýma icltjlum kl ka tjkopc  x m (t ) iuyc kspkitrc ks  X m ( G )  sk ouks ou kstr trkm km m ulm ulm gr grki kiuk ukli lijm jm  G s?= / ^   ouks oukstr trms ms pc pcrr sk sk`ul `ulnc nc,, ka kspki kspkitr trcc nk am skýma skýma oukstrk ouk strkmnm mnm ks am rkpktj rkpktjijù ijùll pkrjùnj pkrjùnjim im nka kspkitrc kspkitrc ksim ksimamn amncc  G s X m ( G )  nk pkrï pkrïcn cncc  G s. Kspkiïgjimokltk, am rkamijùl ks ∜

 X ( g  ) )? G s

 X  U ( g   − −e ) G   _  ∝ ? ?− − m

e 

s

∜

Nclnk g ? G / G s  ks am grkiuklijm lcromajzmnm. Yj am grkiuklijm nk oukstrkc  G sks oklcr quk ncs vkiks am grkiuklijm oís matm icltkljnm kl  X m ( G ) sk prcnuik majmsjl`. Kxprksmnc kl ka icltkxtc nka oukstrc nk am rkspukstm ma jopuasc nk ul gjatrc mlmaù`jic icl am rkspukstm kl grkiuklijm  H m ( g   )), ka gjatrc nj`jtma icl am rkspukstm ma jopuasc h ( l )≭ hm (l^ ) tjklk am rkspukstm kl grkiuklijm ∜

 H   (( g  ) ) ? G s

 X   U ( g − e ) G  _  ∝ ? ?− − m

e 

s

∜

C, ac kqujvmakltk, ∜

 H   (( ϊ ) ? G s

 H   U( ϊ −2 τe ) G   _  ∝ ? ?− − m

e 

s

∜

C  H   (( Ϊ ^ )?

∜

2 τe   H  U( Ϊ −  )   ∝ ^  _ ^  ? ?− −

 =

m

e 

∜

Ka gjatrc nj`jtma icl am rkspukstm kl grkiuklijm  H ( ϊ ) tjklk am rkspukstm kl grkiuklijm nka gjatrc mlmaù`jic icrrkspclnjkltk sj ka jltkrimac nk oukstrkc ^ sk skakiijclm skakiijclm pmrm quk skm ac sugjijkltkokltk pkqukýc pmrm jopknjr pcr icopaktc c ma oklcs pmrm ojljojzmr acs kgkitcs nk majmsjl` . Tcr ac quk ka oêtcnc bmsmnc kl am jlvmrjmlzm nka jopuasc ks jlmprcpjmnc pmrm njskýmr njs kýmr gjatrc gjatrcss pmsm pmsm-ma -matcs tcs y rkihmzm rkihmzm-bml -bmlnm nm nkb nkbjnc jnc ma maj majmsj msjl` l` quk rksuatm nka prciksc nk oukstrkc. Mnkoís, sj tklkocs kl iukltm acs prctctjpcs mlmaù`jics, acs gjatrcs Ihkbyshkv JJ y acs Kaïptjics prkskltmríl pkcr icopcrtmojkltc nkbjnc ma rjzmnc kl am bmlnm lc pmsmltk.

 

TRC@RMOM NKYMRRCAAMNC. Njskýc pcr oknjc nk Omtamb. Yk njskýc ul gjatrc pmsm-bmfms, icl ulm grkiuklijm nk icrtk nk am bmlnm nk pmsc ;4 Hz, y ulm grkiuklijm nk oukstrkc nk 2;7 Hz. Icl ka ma`crjtoc nksmrrcaamnc pmrm kstk tjpc nk gjatrc, sk cbtjk cbt jklk lkll acs acs >= ic ickgj kgjij ijkl kltk tkss nk nkaa gj gjat atrc rc qu qukk skríl skríl ut utja jajz jzmn mncs cs kl am prc`rm prc`rmom omij ijùl ùl nka ojircicltrcamncr. Kstm `rígjim skrvjrí nk rkgkrklijm pmrm smbkr sj ka gjatrc jopakokltmnc gulijclm icrrkitmokltk.

Gjatrc atrc pmsm-bmfm njskýc njskýc pcr oknjc nk Omtamb.  Gj`urm =. Gj

 

Jopakokltmijùl nka gjatrc kl ka OYT>94. M icltjlumijùl, sk oukstrm ka iùnj`c pmrm am jopakokltmijùl nka gjatrc kl am OYT>94. Trjokrc nkiamrmocs ulms gulijclks pmrm jljijmajzmr ka MNI, ka tjookr, iclgj`urmijùl nk acs  pukrtcs y am iclgj`urmijùl nka rkacf, nkspuês vjklk am nkiamrmijùl nk acs ickgjijkltks `klkrmncs kl Omtamb, ul mrrk`ac nclnk sk `umrnml acs vmacrks nk kltrmnm mltkrjcrks, am vmrjmbak vmacrSkltrmnm nclnk sk `umrnm ka vmacr akïnc pcr ka MNI, vmacrSsmajnm nclnk sk `umrnm ka rksuatmnc nk am iclvcauijùl nka gjatrc y ams vmrjmbaks nk tjpc ihmr quk lcs  pkrojtjrí klvjmr am vmrjmbak mltkrjcr ma NMI.

 

Kl am sj`ujkltk pmrtk sk rkmajzm am iclvcauijùl nk omlkrm lc rkiursjvm nk acs ickgjijkltks nka gjatrc njskýmnc y nk acs vmacrks nk am skýma nk kltrmnm `klkrmnm. Kl ul ijiac jlgjljtc ks nclnk sk rkmajzm am iclvcauijùl nka gjatrc y ka klvïc ma NMI. Trjokrc sk mpm`m ka IT[, nk kstm gcrom, ka prciksc sk rkmajzm imnm 2;7 Hz. Ka gjatrc iclstm nk am iclvcauijùl mpajimlnc am gùrouam nka gjatrc vjstc mltkrjcrokltk y ul rk`jstrc nk icrrjojkltc  pmrm ocvkr acs vmacrks v macrks mltkrjcrks. Ma gjlma, scac ks ka iùnj`c pmrm klvjmr ak nmtc ma NMI. Am vmrjmbak vmacrSsmajnm sk pmrtk kl ncs pcrquk scac sk puknkl klvjmr pmquktks nk 8 bjts ma NMI y rkicrnkocs quk omlkfmocs =4 bjts.

Ka iùnj`c nksmrrcaamnc guk kl bmsk ma iùnj`c nksmrrcaamnc pmrm ka oukstrkc nk skýmaks, tcomlnc icoc vmrjmltk am grkiuklijm nk oukstrkc kspkijgjimnm pmrm ka tjpc nk gjatrc.

 

Ka iùnj`c icopaktc nk oukstrm m icltjlumijùl6

 

RKY[A^MNCY. Icl ka sj`u Icl sj`ujk jklt ltkk ij ijri riuj ujtc tc,, sk rk rkma majz jzmr mrcl cl am amss pru prukbm kbmss ic icrrk rrkspc spcln lnjk jklt ltks, ks, ocnj ocnjgj gjiml imlnc nc  prjlijpmaokltk am grkiuklijm nk am skýma, msï icoc am gcrom nk am skýma nk kltrmnm.

 Gj`urm 2. Ijriujtc utjajzmnc. Ijriujtc utjajzmnc.

 

 Gj`urm 9. Kspkijgjimijclks Kspkijgjimijclks nka `klkrmncr nk skýmaks. skýmaks.

 Gj`urm >. Gulijclmojkltc Gulijclmojkltc nka gjatrc icl ulm skýma sklcjnma nk ; Hz.

 

 Gj`urm ;.Gulijclmojkltc gjatrc icl ulm skýma skýma sklcjnma nk :.; Hz. ;.Gulijclmojkltc nka gjatrc

 Gj`urm 7. Gulijclmojkltc Gulijclmojkltc nka gjatrc gjatrc icl ulm skýma skýma sklcjnma nk =4 Hz.

 

 Gj`urm 0. Gulijclmojkltc gjatrc icl ulm skýma skýma sklcjnma nk 24 Hz. Gulijclmojkltc nka gjatrc

 Gj`urm 8. Gulijclmojkltc Gulijclmojkltc nka gjatrc gjatrc icl ulm skýma skýma iumnrmnm nk ; Hz. Hz.

ICLIA[YJCLKY. Ymavmncr. Am jopakokltmijùl nk gjatrcs nj`jtmaks ks ouy jopcrtmltk kl am krm mituma, ym quk mhcrrml kspmijc y hmikl m acs sjstkoms oms kgjijkltks. M trkvks nk kstm príitjim pmsmocs pcr tcnc ka nksmrrcaac nk njskýc nk ul gjatrc GJR. Ka oêtcnc nk cbtklijùl nk acs ickgjijkltks ks ma`c rkmaokltk sklijaac y am jopakokltmijùl kl hmrnwmrk tmopcic ks icopajimnc, sjl kobmr`c, sk lctmrcl ma`ulcs nktmaaks. Tcr kfkopac, mulquk ka gjatrc guk njskýmnc pmrm ulm grkiuklijm nk icrtk nk =4 Hz, pkrc ka 04% nk am skýma lc sk cbtuvc m acs =4 Hz sjlc mprcxjomnmokltk

 

m acs :.; Hz. [lm omlkrm nk hmikr oms kgjijkltk ka prciksc ks usmr vmrjmbaks nk tjpc kltkrc, ym quk ka prciksc icl gactm gactmltks ltks rkqujkrk oís tjkopc nk prciksmo prciksmojkltc jkltc mulquk ksc qujtmrïm  prkijsjùl.

Nuaik. Tmrm ac`rmr jopakokltmr ul gjatrc nj`jtma tjpc GJR, guk lkiksmrjc hmikr prkvjmokltk ka njskýc y ka oêtcnc kopakmnc pmrm njskýmrac guk pcr am vkltmlm Hmlljl` pmrm ul gjatrc pmsm bmfms. Tmrm icoprcbmr y cbtklkr acs ickgjijkltks lkiksmrjcs, sk utjajzù ul ma`crjtoc nksmrrcaamnc nksmrrca amnc kl Omtamb. Ma rkmajzmr ams prukbms, ams grkiukl grkiuklijms ijms oklcrks m =4 Hz sk ac`rml cbskrvmr m am smajnm nka ojircicltrcamncr icl ijkrtm mtklumijùl m pmrtjr nk : Hz pcr ka hkihc nk am grkiuklijm nk icrtk lc sk kliuklt kliukltrm rm kl ka pultc kxmitc. Ctrc pultc m rksimtmr, ks quk, sj pcr oknjc nka `klkrmncr oktkocs ulm skýma iumnrmnm, am rkspukstm nka gjatrc ks icoc sj am skýma nk kltrmnm gukrm sklcjnma, kstc ks quk, pcr am lmturmakzm nka gjatrc, ka gjatrc scac nkfm  pmsmr am gulnmokltma y kajojlmlnc tcncs acs mroùljics quk icopclkl am skýma iumnrmnm. Tmrm gjlmajzmr, hmy quk hmikr hjlimpjê quk ks sklijaac jopakokltmr ul gjatrc, iumlnc sk tjklk su njskýc prkvjmokltk y usmlnc am iclvcauijùl lc rkiursjvm pmrm kl kstk imsc gjatrcs tjpc GJR.

BJBAJC@RMGÏM. Pjaajs F. ^copejls. Bjcoknjima nj`jtma sj`lma prciksjl`.Trkltjik Hmaa. Omy4, =::9. Mavmrkz I. Fksös. Jopakokltmijùl nk gjjatrcs nj`jtmaks tjpc GJR kl GT@M. Citubrk, 244; O. Omrtïlkz, A. @ùokz, M. F. Ykrrmlc, F. Wjaam, F. @ùokz. Njskýc nk gjatrcs GJR. 244: M. ^êaakz. Gjatrcs GJR6 Oêtcnc nk vkltmlm. 2424