
filter design

oru koottam aavasyakathakal niravettunna oru signal prosessing filter roopakalppana cheiyunna prakriyayaan filter design, avayil chilath vairudhyamullathaayirikkam. oro aavasyangalum upayogapradamaakkunnathin mathiyaya alavil niravettunna filterinte saakshaathkaaram kandethuka ennathaanu uddeshyam.
filter design prakriya oro aavasyavum kuraykkenda oru error functionilekku sambhavana cheiyunna opttimaiseshan prashnamaayi visheshippikkaam. design prakriyayude chila bhagangal automated aakam, ennaal saadhaaranayaayi oru nalla phalam labhikkunnathin parichayasambannanaaya oru electrical enchineeyar aavasyamaanu.
digital filterukalude roopakalppana vanjanaaparamaaya sankeernamaaya vishayamaan. filterukal eluppathil manassilakkukayum kanakkaakkukayum cheyyaamenkilum avayude roopakalppanayudeyum nadappaakkalinteyum praayogika velluvilikal praadhaanyamarhikkunnavu koodaathe avaa vipulamaaya gaveshana vishayavumaanu.
saadhaarana design aavasyakathakal.
design prakriyayil pariganikkunna saadhaarana aavasyakathakal ivayaanu
freekwansi function.
aavashyamaaya aavruthi prathikaranamaanu oru pradhana paaraameettar.
prathyekichum, prathikarana vakrathinte kuthaneyum sankeernathayum filter kramatthinum saadhyathayeyum nirnnayikkunna gadakamaanu.
oru phastt-oordar recursive filterinu orotta freekwansi-dependent ghadakam maathrame undaakoo. ithinartham aavruthi prathikaranatthinte charivu oru ashtakathinu 6 db aayi parimithappedutthiyirikku ennaanu. pala aavasyangalkkum ithu paryaapthamalla. uyarnna charivukal nedaan uyarnna oordar filterukal aavasyamaanu.
aavasyamulla freekwansi functionumaayi bandhappett, oro freekwensik, thathfalamaayundaakunna freekwansi function aavasyamullathu ekadeshamaayi kanakkaakkunnath ethra pradhaanamaanennu vivarikkunna oru "waiting" function undayirikkaam. bharam koodumbol, adutha ekadesha kanakk kooduthal pradhaanamaan.
freekwansi functionte saadhaarana udaaharanagal ivayaanu
aavegaparamaaya prathikaranam.
filterinte freekwansi function athinte impulse prathikaranavum thammil nerittulla oru anuroopamunda aadyathethu randaamathethinte forrier parivarthanamaanu. athinartham freekwansi functionile eathu aavasyakathayum impulse prathikaranatthil oru aavasyakathayaanu, thirichum.
ennirunnaalum, chila aaplikkeshanukalil ithu filterinte impulse prathikaranamayirikkaam, matellaa aavashyakathakalum kanakkileduthu abhyarthicha impulse prathikaranatthinu kazhiyunnathra aduthu oru ekadesha kanakk nirmmikkaan design prakriya lakshyamidunnu.
chila sandarbhangalil parasparam swathanthramaayi thiranjedukkunna filterinte freekwansi function impulse prathikaranavum pariganikkunnath prasakthamaayekkaam. udaaharanathinu, filterinte oru prathyeka freekwansi function "thathfalamaayundaakunna filterinu signal domainil kazhiyunnathra cheria phalapradamaaya veethiyum undaayirikkanamennu namukk aavashyamaayi vannekkaam. eee function aavasyamulla freekwansi functionumaayi yaathoru bandhavumillengilum filterinte aavasyamulla impulse prathikaranamaayi valare idungiya function pariganikkunnathiloode randaamathe avastha saakshaathkarikkaanaakum. eee rund vairudhyamulla design lakshyangalum kazhiyunnathra niravettaan sramikkunna oru filter saakshaathkarikkuka ennathaanu design prakriyayude lakshyam. oru udaaharanam uyarnna resolutionulla oodiyoyaanu, athil sthiramaaya avastha signalukalkkulla (sinasoyidukalude koottam) aavruthi prathikaranam (vyapthiyum ghattavum) praadhamika filter aavasyakathayaanu, athesamayam aniyanthrithamaaya aavega prathikaranam shanikamaaya signalukalude samayam vyaapikkunnath moolam apratheekshithamaya adhapathanathinu kaaranamaayekkam.
kaaryakaaranathvam.
nadappakkaan kazhiyunnathinu, eathu samayathe aasrayikkunna filter (thalsamayam pravartthikkunnu) kaaryakaaranamaayirikkanam filter prathikaranam nilavilullathum kazhinjathumaaya inputtukale maathram aasrayichirikkunnu. avasana ghattam vare eee aavasyakatha upekshikkuka ennathaanu oru saadhaarana sameepanam. thathfalamaayundaakunna filter kaaryakaaranamallengil, uchithamaaya samayaparidhi (allengil kaalathamasam) avatharippichu athu kaaryakaaranamaakkam. filter oru valia sisttathinte bhaagamaanenkil (saadhaaranayaayi ithu) itharathilulla kaalathamasam muzhuvan systethinteyum pravartthanatthe baadikkunnathinaal shradhaapoorvvam avatharippikkendathundu.
thalsamayam pravartthikkaattha filterukal (udha.jii. imej prosessinginu) kaaranam allathathaayirikkaam. ithu iii.jii. seero delay recursive filterukalude roopakalppana anuvadikkunnu, avide oru kaaryakaarana filterinte group delay athinte hermissian noonn-kaaryakaarana filter raddaakkunnu.
sthiratha.
oro parimithamaaya inputt signal parimithamaaya filter prathikaranam nalkunnuvennu oru sthirathayulla filter urappu nalkunnu. eee aavasyakatha niravettaattha oru filter chila saahacharyangalil upayogashoonyamo doshakaramo aayirikkam. chila design sameepanagalkk sthiratha urappakkaan kazhiyum, udaaharanathinu phir filter polulla pheed-forwade sarcuteukal maathram upayogikkunnathiloode. maruvashathu, feedback sarkyoottukale adisthaanamaakkiyulla filterukalkku mattu gunangalundu, athinaal eee klaas filterukalil asthiramaaya filterukal ulppedunnundengilum avaykku munganana nalkaam. eee saahacharyathil, asthiratha ozhivakkaan filterukal shradhaapoorvvam roopakalppana cheyyanam.
pradesham.
chila prayogangalil praadeshika prathibhasangalaayi visheshippikkaan kazhiyunna gadakangal adangiyirikkunna signalukalumaayi naam edapedanam, udaaharanathinu pulsukal allengil gattangal, avaykku oru nischitha samayadairkhyamundu. oru signalil oru philttar prayogikkunnathinte anantharafalamaayi, avabodhajanyamaaya padangalil, praadeshika prathibhaasangalude dairkhyam filterinte veethiyiloode vipuleekarikkunnu ennathaanu. filterinte impulse prathikarana pravartthanatthinte veethi kazhiyunnathra hrasvamaayi nilanirthendathu chilappol pradhaanamaanennu ithu soochippikkunnu.
forrier parivartthanatthinte anishchithathva bandham anusarichu, filterinte impulse prathikarana pravartthanatthinte veethiyum athinte freekwansi pravartthanatthinte veethiyum oru nischitha sthiraankathe kaviyanam. ithinartham filterinte lokkeshanile eathu aavasyavum athinte freekwansi functionte veethiyil oru boundine soochippikkunnu ennaanu. thathfalamaayi, filterinte impulse prathikarana pravartthanatthinte pradeshatheyum athinte freekwansi pravartthanatheyum sambandhicha aavasyakathakal oresamayam niravettaan kazhinjekkilla. parasparavirudhamaaya aavashyakathakalude oru saadhaarana udaaharanamaanithu.
computational sankeernnatha.
filter prathikaranam kanakkakkaan aavashyamaaya pravartthanangalude ennam (kootticherkalukalum gunanagalum) kazhiyunnathra kuravaayirikkanam ennathaanu eathoru roopakalppanayileyum pothuvaaya aagraham. chila prayogangalil, eee aagraham karsanamaaya oru aavasyakathayaanu, udaaharanathinu parimithamaaya computational vibhavangal, parimithamaaya oorjja vibhavangal allengil parimithamaaya samayam enniva kaaranam. thalsamaya aaplikkeshanukalil avasana paridhi saadhaaranamaanu.
oru filterinu vyathyasthamaaya computational sankeernnatha undaakunnathin niravadhi vazhikalundu. udaaharanathinu, oru filterinte kramam pravartthanangalude ennathinu erekkure aanupaathikamaanu. ithinartham oru loow oordar filter thiranjedukkunnathiloode kanakkukoottal samayam kuraykkaan kazhiyum ennaanu.
vyathirikthamaya filterukalkku computational sankeernnatha filter gunakangalude ennathinu erekkure aanupaathikamaanu. filterinu niravadhi gunakangal undengil, udaaharanathinu tomography daatta polulla bahumukha signalukalude kaaryatthil, poojyathinu aduthullava neekkam cheythukondu gunakangalude ennam kuraykkunnathu prasakthamayirikkum. multirate filterukalil, inputt signal daunsaambil cheythirikkunna bandwidth paridhikal prayojanappeduthunnathi gunakangalude ennam (udha.jii. athinte nirnaayaka aavruthiyilekku), filteringinu sesham upsample cheythu.
computational sankeernathayumaayi bandhapetta mattoru prashnam verthirikkalaan, athaayath, rando athiladhikamo lalithamaaya filterukalude konvalyooshanaayi oru filter engane ezhuthaam. prathyekichum, eee prashnam bahumukha filterukalkku praadhaanyamullathaanu, udha.jii.imej prosessingil upayogikkunna 2dii filter. eee saahacharyathil, filterine thirashcheena dishayil oru 1 dii filterinteyum lamba dishayil oru 1 dii filterinteyum konvalyooshanaayi verthirikkaan kazhiyumenkil computational sankeernathayil ganyamaaya kuravu labikkum. filter design prakriyayude phalam, udha.jii.verthirikkaavunna filteraayi allengil verthirikkaavunna filterukalude oru koottamaayi aavasyamulla chila filterukale kanakkaakkuka.
mattu parigananakal.
filter engane nadappaakkanamenn theerumaanikkendathundu
analog filterukal.
leanier analog filterukalude roopakalppana mikkavarum leanier filter vibhaagathil ulkkollunnu.
digital filterukal.
oru yoonit impulsinode avaa engane prathikarikkunnu ennathine aashrayich digital filterukale rund adisthaana roopangalil onnaayi tharamthirickunnu
sample nirakk.
sample nirakk chila baahya niyanthranangalaal nischayichittillenkil, anuyojyamaaya sample nirakk thiranjedukkunnathu oru pradhana design theerumaanamaanu. uyarnna nirakkin computational vibhavangalude kaaryatthil kooduthal aavashyamaayi varum, ennaal aanti-eliasing filterukalude kaaryatthil kuravaanu. sisttathile mattu signalukalumaayulla edapedalum adikkalum oru prasnamaakaam.
aanti-eliasing.
eathoru digital filter roopakalppanaykkum, aliasingh efakttukal vishakalanam cheyyukayum ozhivaakkukayum cheiyunnathu nirnaayakamaan. palappozhum, inputtilum aouttputtilum analog aanti-eliasing filterukal cherthaanu ithu cheiyunnathu, angane naikvist freakwensick mukalilulla freekwansi gadakangalonnum ozhivaakkunnu. sankeernnatha (i.iii.atharam filterukalude steepness) aavashyamaaya signal-tuu-noys anupaathatheyum sample nirakkum signalinte ettavum uyarnna aavruthiyum thammilulla anupaathatheyum aasrayichirikkunnu.
saidhaanthikamaaya adisthaanam.
design prashnatthinte bhagangal freekwansi domainil vivarichirikkunna chila aavasyakathakal time domainil prakadippikkappedumbol iva vairudhyamundaakniyekam vasthuthayumayi bandhappettirikkunnu. udaaharanathinu, ekapaksheeyamaaya impulse prathikaranavum ekapaksheeyamaaya freekwansi function ulla oru filter nedaan kazhiyilla. samayavum aavruthi domain thammilulla bandhathe soochippikkunna mattu efakttukal ivayaanu
anishchithathvathinte thathwam.
gabor paridhi prasthaavichathupole, oru anishchithathva thathwam, freekwansi functionte veethiyum impulse prathikaranatthinte veethiyum oru prathyeka sthiraankathekkaal cheruthakaan kazhiyilla. oru prathyeka aavruthi veethiyumaayi poruthappedunna oru prathyeka aavruthi function abhyarthikkukayaanenkil, signal domainile filterinte ettavum kuranja veethi sajjamaakkumennaan ithu soochippikkunnathu. thirichum, prathikaranatthinte paramavadhi veethi nalkukayaanengil, ithu aavruthiyile saadhyamaaya ettavum cheria veethi nirnnayikkunnu.
filter design prakriya upayogapradamaaya oru vittuveezhcha kandethaan shramichekkaavunna parasparavirudhamaaya aavashyakathakalude oru saadhaarana udaaharanamaanithu.
vyathiyana vipuleekarana sidhaantham.
formula _ 1 inputt signalinte vyathiyaanamaayirikkatte, formula _ 2 filterinte vyathiyaanamaayirikkatte. filter prathikaranatthinte vyathyasam, formula _ 3, pinneedu nalkunnu
ithinartham formula _ 7 aanu, koodaathe pulsukal allengil filter prathikaranatthile gattangal polulla vividha savisheshathakalude praadeshikavalkkaranam signal domainile filter veethi kondu parimithappedutthiyirikku ennaanu. krithyamaaya oru praadeshikavalkkaranam abhyarthikkukayaanenkil, signal domainil cheria veethiyulla oru filter aavasyamaanu, anishchithathva thathwathiloode, freekwansi domainile athinte veethi aniyanthrithamaayi cheruthakaan kazhiyilla.
asymptotic perumattavum vichedanam.
f (t)" oru functionayirikkatte, formula _ 8 athinte forrier parivarthanamaayirikkatte.
f"-nte aadya derivativinu oordar formula _ 9 undengil, "f"-nuu formula _ 10 pole oru asymptotic shayamundennu parayunna oru sidhaanthamundu.
eee sidhaanthathinte anantharafalamaayi, oru filterinte aavruthi pravartthanam athinte aavega prathikaranatthinu vegathil kshayikkaan anuvadikkunnathinu kazhiyunnathra sugamamayirikkanam, athuvazhi oru cheria veethiyum.
reethishaasthram.
remace exchange algorithathe adisthaanamaakkiyulla paarkk-mcclellan filter design algorithamaanu phir filterukal roopakalppana cheiyunnathinulla oru saadhaarana reethi. ivide upayokthaav aavasyamulla oru aavruthi prathikaranam, eee prathikaranatthil ninnulla pisakukalkkulla waiting function, filter oordar "n" enniva vyakthamaakkunnu. algoritam pinneedu idealil ninnulla paramavadhi vyathiyaanam kuraykkunna "n" gunakangalude koottam kandethunnu. avabodhapoorvvam, ningalkk "n" gunakangal maathrame upayogikkaan kazhiyoo ennathinaal ningalkk aavasyamulla prathikaranatthilekku athicheraan kazhiyunnathra aduthulla filter ithu kandethunnu. eee reethi praayogikamaayi valare eluppamaanu, kuranjathu oru vaachakathil aavasyamulla filter "n" umm eduthu opttimal coffificientukal nalkunna oru prograam ulppedunnu. eee reethiyil roopakalppana cheytha filterukalude oru poraayma avayil passbandle (kall) niravadhi cheria tharamgangal adangiyirikkunnu ennathaanu, kaaranam atharam oru filter peak error kuraykkunnu.
oru vyathiriktha phir filter kandethunnathinulla mattoru reethi nutson muthalaayavayil vivarichirikkunna "filter opttimaiseshan" aanu.ithu pishakinte squarinte integral athinte paramavadhi moolyathinu pakaram kuraykkunnu. athinte adisthaana roopathil eee sameepanathin filter formula _ 11-nte oru anuyojyamaaya freekwansi function oru freekwansi waiting function formula _ 12, filter kofishyantukal sthithicheyyunna signal domainil coordinate formula _ 13 ennivaykkoppam vyakthamaakkendathundu.
oru error function formula _ 14 ingane nirvachikkappedunnu
ivide formula _ 16 ennathu discreet filter formula _ 17 ennathu nirddishta kordinettukalil nirvachichirikkunna discreet-time forrier transformaanu. ivide upayogikkunna maanadandam aupachaarikamaayi formula _ 18 speysukalile saadhaarana maanadandamaanu. ithinartham formula _ 14 filterinte abhyarthicha freekwansi function, formula _ 20, realved filterinte yadhaartha freekwansi function, formula _ 21 enniva thammilulla vyathiyaanam alakkunnu. ennirunnaalum, error function kanakkaakkunnathin munbu vyathiyaanam waiting function formula _ 22 nuu vidheyamaan.
error function sthaapichukazhinjaal, opttimal filter nalkunnathu cofficient formula _ 16 aanu, ithu formula _ 14 kuraykkunnu. anubandha kuranja square prashnam pariharichukondu ithu cheyyaan kazhiyum. praayogikamaayi, formula _ 18 maanadandam freekwansi domainile vyathiriktha poyintukalkku anuyojyamaaya thukayiloode ekadeshamaayi kanakkaakkendathund. ennirunnaalum, upayogapradamaaya oru ekadesha kanakk labhikkunnathin eee pooyintukal signal domainile gunakangalude ennathekkaal ganyamaayi kooduthalaayirikkanam.
rund domainukalilum oresamayam opttimaiseshan.
signal domainil aavasyamulla filter impulse prathikaranavumayi bandhapetta oru adhika pishak padam anubandha waiting functionotoppam ulppeduthunnathinu munbathe reethi vipuleekarikkaam. anuyojyamaaya impulse prathikaranam anuyojyamaaya freekwansi functionil ninnu swathanthramaayi thiranjedukkaam, ithu praayogikamaayi phalapradamaaya veethi parimithappeduthunnathinum signal domainile thathfalamaayundaakunna filterinte ring efakttukal neekkam cheiyunnathinum upayogikkunnu. oru idungiya ideal filter impulse response function thiranjedutthaanu ithu cheiyunnathu, udha.jii., oru aavegavum uthbhavasthaanathuninnulla doorathinanusarichu vegathil valarunna bhaaranirnaya pravartthanavum, udha.jii., dooram chathurashra. opttimal filter ippozhum oru lalithamaaya kuranja square prashnam pariharichukondu kanakkakkaan kazhiyum, thathfalamaayundaakunna filter rund domainukalileyum anuyojyamaaya pravarthanangalkku poornnamaayum anuyojyamaaya oru "othutheerppu" aanu. rund waiting functionukalude aapekshika sakthiyaanu oru pradhana paaraameettar, ithu anuyojyamaaya functionumaayi thaarathamyappeduthumbol eathu domainil nalla phitt undaayirikkendathu pradhaanamaanennu nirnnayikkunnu.

