
anantamaina prerana pratispandana

anantamaina prerana pratispandana (ii. ii. aarr) anedi aneka sarala samaya-parivartana vyavasthalaku vartinche oka lakshanam, idhi oka nirdishta binduvunu daati sarigga sunnaga maarani, conny niravadhikamgaa konasage prerana pratispandana suutram _ 1 kaligi undatam dwara vaeru cheyabadutundi. idhi parimita prerana pratispandana (phir) vyavasthaku viruddhamgaa untundi, dheenilo prerana pratispandana "konni parimita suutram _ 3 kosam suutram _ 2 vadda khachitamgaa sunna avutundi, tadwara parimita vyavadhi untundi. sarala samaya-vaividhya vyavasthalaku saadhaarana udaaharanalu chaalaa varaku electronic mariyu digital filterlu. eee lakshanamtho unna vyavasthalanu "ir systems" ledhaa "ir filters" anie pilustaaru.
aacharanalo, ir vyavasthala yokka prerana pratispandana kooda saadhaaranamgaa sunnaki cherukuntundi mariyu oka nirdishta binduvunu daati nirlakshyam cheyabadutundi. ayithe ir ledhaa phir pratispandanalanu penche bhouthika vyavasthalu bhinnamgaa untaayi, mariyu andulone vyatyaasam yokka praamukhyata untundi. udaaharanaku, resisterlu, kpaasitarlu mariyu/ledhaa inductorlatho (mariyu bahusha leanier amplifierlu) koodi unde analog electronic filterlu saadhaaranamgaa ir filterlu. marovaipu, tapp cheyabadina aalasya line aadhaaramgaa vivikta-samaya filterlu (saadhaaranamgaa digital filterlu) "etuvanti feedback upayoginchakundaa" tappanisarigaa phir filterlu. analog vadapotaloni kpaasitarlu (ledhaa inductorlu) "memory" kaligi untaayi mariyu vaati antargata sthithi prerananu anusarinchi puurtigaa sadalinchadu (quantum prabhavalu vismarinchabadina kpaasitarlu mariyu inductorla yokka shaastreeya namuunaanu oohinchi). conny taruvaati sandarbhamlo, oka prerana tapp cheyabadina aalasya rekha mugimpuku cherukunna tarvaata, vyavasthaku aaa prerana yokka tadupari ghnaapakasakti undadu mariyu daani prarambha sthithiki tirigi vachindi; aaa binduvuku minchina daani prerana pratispandana khachitamgaa sunna.
amalu mariyu roopakalpana.
daadaapu anni analog electronic filterlu ir ayinappatikee, digital filterlu ir ledhaa phir kaavacchu. vivikta-samaya vadapotha yokka sthalavignaanamlo pratispandana undatam (krinda chuupina block rekhaachitram vantivi) saadhaaranamgaa ir pratispandananu srushtistundi. ir vadapotha yokka z domine badilee functionlo aaa feedback nibandhanalanu vivarinche oka chinna-kaani denaminator untundi. marovaipu, phir filter yokka badilee function, krinda nundi pondina saadhaarana roopamlo vyakteekarinchabadinatlugaa oka numerator matrame kaligi untundi. suutram _ 5 (feedback nibandhanalu) thoo unna suutram _ 4 gunakaalu annee sunna mariyu vadapotaku parimita dhruvalu laevu.
ir analog electronic filterlaku sambandhinchina badilee vidhulu vistrutamgaa adhyayanam cheyabaddaayi mariyu vaati vyaapti mariyu dasha lakshanaala kosam optimize cheyabaddaayi. eee nirantara-samaya vadapotha vidhulu laplace domainlo vivarinchabaddaayi. biolineer transform, impulse invarians ledhaa pole-jeero matching methed vanti konni ganita paddhatula upayogam dwara, z domainlo vyaktaparichae badilee vidhulu kaligina vivikta-samaya filterla vishayamlo kaavalasina parishkaralanu badilee cheyavachu. eee vidhamgaa digital ir filterlu chebishev filter, butterworth filter mariyu elliptic filter vanti analog filterla kosam prasiddha parishkaralapai aadharapadi undavacchu, aaa parishkarala lakshanaalanu vaarasatvamgaa pondavacchu.
badilee function utpannam.
avtput signal input signalku elaa sambandhinchinado nirvachinche difference equation paramgaa digital filterlu tarachugaa vivarinchabadataayi mariyu amalu cheyabadataayih
ekkadah
vyatyaasam sameekaranam yokka marinta ghaneebhavinchina roopam emitante
idhi, punarvyavastheekarinchinappu, avtundi
vadapotha yokka badilee functionnu kanugonadaaniki, memu modata paina perkonna sameekaranam yokka prati vaipu yokka z-parivartananu teesukuntamu, ikkada memu pondadaaniki samaya-badilee lakshanaanni upayogistamuh
badilee functionnu ilaa nirvachistaamuh
chaalaa ir filter designlalo coefficient formula _ 17 anedi 1 anie parigananaloki teesukunte, ir filter badilee function marinta saampradaaya roopaanni teesukuntundihi
sthirathvam.
badilee function oka vyavastha parimita-input, parimita-avtput (baibo) sthiramgaa undaa ledhaa anie nirnayinchadaaniki anumatistundi. nirdishtamgaa cheppalante, baibo sthirathva pramaanaaniki vyavastha yokka aarosi unit sarkilnu kaligi undaali. udaaharanaku, oka kaaryakaarana vyavastha kosam, badilee function yokka anni dhruvalu okati kante takkuva sampoorna viluvanu kaligi undaali. maroe maatalo cheppalante, anni stambhaalu suutram _ 19-plain loe oka unit sarkillo undaali.
dhruvalu suutram _ 19 yokka viluvalugaa nirvachinchabaddaayi, ivi suutram _ 21 yokka denaminatornu 0kii samanamga chestaih
spashtamgaa, suutram _ 23 ayithe, dhruvalu suutram _ 19-plain yokka muulam vadda laevu. idhi anni stambhaalu muulam vadda unna phir vadapotaku viruddhamgaa untundi, anduvalla idhi ellappuduu sthiramgaa untundi.
konnisaarlu ir filterlaku phir filterla kante praadhaanyata ivvabadutundi, endukante ir filter adhe kramamlo unna phir filter kante chaalaa padunaina parivartana praantam roll-aafnu saadhinchagaladu.
udaaharana.
vivikta-samaya vadapotha yokka badilee function suutram _ 21 nuu ilaa ivvanivvandih
suutram _ 27 dwara paalinchabadutundi, suutram _ 28 thoo oka vaastava sankhya. suutram _ 21 sthiramgaa untundi mariyu suutram _ 27 vadda oka dhruvamtho kaaranamavutundi. samaya-domine prerana pratispandananu ilaa chuupavachchuh
ikkada suutram _ 32 anedi unit step function. anni suutraalaku _ 33 anedi sunna kaanidi anie chudavachu, tadwara oka prerana pratispandana anantamgaa konasaagutundi.
prayojanaalu mariyu aprayojanaalu.
phir filterla kante digital ir filterlu kaligi unna pradhana prayojanam emitante, passband, stapband, repill mariyu/ledhaa roll-off paramgaa oka vivarananu teerchadaaniki, amalulo vaati saamarthyam. atuvanti specificationla samitini adhe avasaralanu teerchagala pharr filterku avasaramaina daanikante takkuva kramamlo (paina perkonna suutramloe "q") ir filtertho saadhinchavachchu. signal processorlo amalu cheyabadithe, idhi prati dasaku takkuva sankhyalo gananalanu suuchistumdi; ganana podupu tarachugaa chaalaa pedda amsam.
marovaipu, phir filterlanu roopondinchadam sulabham, udaaharanaku, oka nirdishta frequency pratispandana avasaraniki saripoyela. idhi mukhyamgaa avasaram saadhaarana kesulalo okati kanappudu (hye-paas, loe-paas, naach modalainavi) vartistundi.) ivi analog filterla kosam adhyayanam cheyabaddaayi mariyu optimize cheyabaddaayi. phir filterlanu kooda sulabhamgaa leanier faze (sthiramaina group delay verses frequency) gaa tayaaru cheyavachu-idhi ir filterlanu upayoginchi sulabhamgaa kalusukoleni lakshanam, aapai kevalam oka ujjaayimpugaa (udaaharanaku besel filtertho). digital ir filterlaku sambandhinchina maroka samasya emitante, parimaanaatmakatatoo kalipi feedback vyavastha kaaranamgaa, nishkriyamgaa unnappudu parimiti chakra pravartanaku sambhaavyata.
roopakalpana paddhatulu.
preranalo antaraayam.
impulse invarians anedi nirantara-samaya filterla nundi vivikta-samaya ananta-prerana-pratispandana (ii. ii. aarr) filterlanu roopondinchadaaniki oka saanketikata, dheenilo nirantara-samaya vyavastha yokka prerana pratispandananu vivikta-samaya vyavastha yokka prerana pratispandananu utpatti cheyadaaniki namoonaga teesukuntaaru. 
ess-plain nundi jedd-plain varaku mapping yokka rendu praathamika avasaralanu teerchadaaniki saadhaaranamgaa upayoginche paddhatullo impulse invarians okati. analog filter maadirigaane namuunaa samayamlo adhe avtput viluvanu kaligi unna t (z) nuu parishkarinchadam dwara idhi pondabadutundi, mariyu inputlu pulslo unnappudu matrame idhi vartistundi.
eee paddhati dwara utpatti cheyabadina digital filter yokka anni inputlu chaalaa khachitamaina pulls inputlu minaha sumaru viluvalu anie gamaninchandi. idhi saralamaina ir filter design paddhati. idhi takkuva pounahpunyaala vadda atyanta khachitamainadi, kabatti idhi saadhaaranamgaa takkuva-paas filterlalo upayoginchabadutundi.
laplace transform ledhaa z-transform kosam, transformation tarvaata avtput anedi inputnu sambandhita transformation function, t (s) ledhaa t (z) thoo guninchadam matrame. y (s) mariyu y (z) anevi varusaga input x (s) mariyu input x (z) yokka converted avtput.
unit preranapai laplace transform ledhaa z-transformnu vartimpajesetappudu, phalitam 1 avutundi. anduvalla, marpidi tarvaata avtput phalitaalu 
ippudu analog filter yokka avtput time domainlo inverse laplace transform matrame.
manam t kii badulugaa nt nii upayogiste, sampling samayamlo pulls nundi utpannamaina avtput y (nt) nuu pondavacchu. dheenini y (n) gaa kooda vyakteekarinchavachhu.
eee vivikta samaya sanketam t (z) pondadaaniki z-transformnu vartimpajeyavachu.
chivari sameekaranam ganitasaastraparamgaa vivaristundi, oka digital ir vadapotha anedi analog signal meeda z-transformnu nirvahinchadam, idhi laplace dwara namuunaa cheyabadi, t (s) gaa maarchabadutundi, idhi saadhaaranamgaa saralikrutam cheyabadutundi
suutramloe gunakam t kanipistundane vaastavam patla shraddha vahinchandi. endukante, unit pulls kosam laplace transform mariyu z-transform 1 ayinappatikee, pulls tappanisarigaa okela undadu. analog sankethaala kosam, pulls anantamaina viluvanu kaligi untundi, conny t = 0 vadda praantam 1, conny idhi vivikta-samaya pulls t = 0 vadda 1, kabatti gunakam t uniki avasaram.
adugu invarians.
impulse invariant kante step invarians merugaina design paddhati. digital filter namuunaanu sekarinchetappudu vividha sthiraamkaalatho input yokka aneka vibhaagaalanu kaligi untundi, idhi vivikta dasalato koodi untundi. step invariant ir filter anedi edisi kii adhe input step signal kante takkuva khachitamainadi. ayithe, idhi impulse invariant kante edainaa inputku merugaina ujjaayimpu.
t (z) mariyu t (s) rendoo dasala inputlu ayinappudu oke namuunaa viluvala samasyanu step invariant parishkaristundi. digital filterku input u (n), mariyu analog filterku input u (t). marchabadina avtput signalnu pondadaaniki eee rendu inputlapai z-transform mariyu laplace transformnu vartinchandi.
step input formula _ 45 paie z-transform cheyandi
z-transform formula _ 46 tarvaata avtput maarchabadindi
step input formula _ 47 paie laplace transform cheyandi
laplace transform formula _ 48 tarvaata avtput maarchabadindi
analog vadapotha yokka avtput y (t), idhi y (s) yokka inverse laplace transform. prati t sekanlaku namuunaa teesukunte, adhi y (n), idhi y (z) yokka viloma marpidi.eee sankethaalu digital vadapotha mariyu analog vadapotha kosam parishkarinchadaaniki upayoginchabadataayi mariyu namuunaa samayamlo adhe avutputnu kaligi untaayi.
eee krindi sameekaranam t (z) yokka parishkaranni suuchistumdi, idhi analog filterku sumaru suutram. 
dvipada parivartana.
dvimukha parivartana anedi conformal mapping yokka pratyeka kesu, tarachugaa nirantara-samaya domainloni leanier, time-invariant (lti) filter yokka badilee function formula _ 53nii (tarachugaa analog filter anie pilustaaru) badilee function formula _ 54kii maarchadaaniki upayogistaaru.
dwiparshwa parivartana anedi sahaja lagarithm function yokka modati-kramam ujjaayimpu, idhi "s"-plain kuu "z"-plain yokka khachitamaina mapping. laplace parivartananu vivikta-samaya sanketampai pradarsinchinappudu (vivikta-samaya kramam yokka prati moolakam tadanugunamgaa aalasyamaina unit preranaku jatacheyabadinappudu), phalitam khachitamgaa vivikta-samaya kramam yokka z parivartana pratyaamnaayam.
ikkada suutram _ 56 anedi dwiparshwa parivartana utpannamlo upayoginche trepazoidal niyamam yokka sankhya ekikarana dasha parimaanam; ledhaa, maroe maatalo cheppalante, namuunaa kaalam. paina perkonna dwiparshwa ujjaayimpunu suutram _ 57 kosam parishkarinchavacchu ledhaa suutram _ 58 kosam ilanti ujjaayimpunu nirvahinchavacchu.
eee mapping yokka vilomam (mariyu daani modati-kramam dwiparshwa ujjaayimpu)
eee sambandham edainaa analog filter yokka laplace badilee function ledhaa analog filter yokka digital infinite impulse response (ir) filter tii (jedd) loe upayoginchabadutundi.
dvipada parivartana tappanisarigaa eee modati arder ujjaayimpunu upayogistundi mariyu nirantara-samaya badilee function, suutram _ 60 loki pratyaamnaayam chestundi.
adhi
idhi analog filter yokka laplace badilee function nundi praarambhinchi, ir digital filternu lekkinchadaaniki upayoginchabadutundi. 

