tarangam

tarangam anedi sunna vadda praarambhamai, perugutundi ledhaa taggutundi, aapai okati ledhaa anthakante ekkuva saarlu sunnaki tirigi vachhe vaisaalyamtho kuudina tarangam lanty dolanamu. taramgaalanu "klupta dolanalu" anie pilustaaru. daani pulls sankhya mariyu dhisha aadhaaramgaa taramgaala vargeekarana sthaapinchabadindi. taramgaalu nirdishta lakshanaalatoo nindi untaayi, ivi signal prosessingku upayogapadataayi.
udaaharanaku, madhya c yokka frequency mariyu sekanulo sumaru padava vanthu swalpa vyavadhi kaligi undela oka taramgaanni srushtinchavachu. eee tarangam oka sraavyata recording nundi srushtinchabadina sankethamtho sanklishtamgaa unte, appudu phalita sanketam paatalo madhya sii note eppudu kanipinchindo nirnayinchadaaniki upayogapadutundi. ganitasaastraparamgaa, sankethamlo oka bhaagam okela unte tarangam sankethamtho sahasambandham kaligi untundi. aneka aacharanaatmaka taramgaala anuvartanaalaku paraspara sambandham pradhaanamainadi.
oka ganita saadhanamgaa, audeo signals mariyu chitraalato sahaa conny veetike parimitam kakunda aneka rakaala dayta nundi samacharanni sekarinchadaaniki taramgaalanu upayoginchavacchu. daetaanu puurtigaa vislaeshimchadaaniki taramgaala samiti avasaram. "paripuurakaramaina" taramgaalu antaraalu ledhaa ativyaapti lekunda oka sanketaanni kullipotayi, tadwara kullina prakriya ganitasaastraparamgaa tirogamanamgaa untundi. anduvalla, taranga-aadhaarita kudimpu/ottidi taggimpu algorithamlalo paripuurakaramaina taramgaala setlu upayogapadataayi, ikkada kaneesa nashtamtho asalu samacharanni tirigi pondadam manchidi.
adhikaarika paramgaa, eee praatinidhyam anedi chadarapu-integrable functionla hilbert space kosam puurti, orthonormal bays functionla samiti ledhaa vector space yokka athi puurti sett ledhaa frameku sambandhinchi chadarapu-integrable function yokka taranga shreni praatinidhyam. idhi pondikaina sthithula dwara saadhinchabadutundi.
shaastreeya bhouthika saastramlo, vivartana drugvishayaanni hygens-fresnell suutram dwara vivarinchabadindi, idhi vyaapti chendutunna tarangapraantamlooni prati binduvunu vyaktigata golaakaara taramgaala sekaranagaa pariganistundi. pondikaina muulam (lazer vantivi) nundi vachhe tarangam daani tarangadairghyaaniki parimaanamlo polchadagina cheelika/eparcharunu edurkonnappudu lakshana vampu namuunaa chaalaa spashtamgaa untundi. idhi tarangapraamtamlo (ledhaa, samanamga, prati tarangam) ververu podavula maargaala dwara namodu uparitalaaniki prayaaninchae ververu paayintla adanamgaa ledhaa jokyam kaaranamgaa untundi. bahula, daggari antaram gala terachaapalu (udhaa.zii., vivartana grating), vividha teevrata yokka sanklishta namuunaaku daariteeyavachchu.
vyutpatti.
wavelet" anae padaanni digital signal prosessing mariyu anveshana geophysicslo dasabdaluga upayogistunnaru. chinna tarangam" anie ardham vachhe samaanamaina french padam "ondelete" nuu 1980la praarambhamlo morlet mariyu grossman upayoginchaaru.
taranga siddhaantam.
taranga siddhaantam aneka vishayaalaku vartistundi. anni taramgaantara parivartanalu nirantara-samaya (analog) sankethaala kosam samaya-pounahpunya praatinidhya rupaluga pariganinchabadataayi mariyu anduvalla ivi swaramela vislaeshanhaku sambandhinchinavi. diadic (octave byaand) aakruteekarana yokka vivikta-samaya vadapotha byaankulanu upayoginchadam dwara vivikta-samaya (namuunaa) sanketam yokka vivikta taramgaantara parivartana (nirantaram) aaa sanketam yokka taramgaantara anchanaa. atuvanti vadapotha byaanku yokka gunakaalanu taramgaala naamakaranamlo shift mariyu scaling gunakaalu antaaru. eee filter byaankulu parimita prerana pratispandana (phir) ledhaa ananta prerana pratispandana (ii. ii. aarr) filterlanu kaligi undavacchu. nirantara taranga parivartana (sidabluty) nuu yerparuchukune taramgaalu forier vislaeshanha sambandhita namuunaa siddhaantam yokka anischiti suutraaniki lobadi untayih daanilo konni sanghatanalatho kuudina sanketam ichinatlayithe, aaa sanghatanaku khachitamaina samayam mariyu pounahpunya pratispandana sthaayini ekakaalamlo ketayinchalemu. samayam mariyu pounahpunya pratispandana sthaayi yokka anischitula yokka utpatti takkuva parimitini kaligi untundi. anduvalla, eee signal yokka nirantara taramgaantara parivartana yokka scalogram loe, atuvanti sanghatana kevalam oka binduvuku badulugaa, time-scale plain loe mottam praantaanni gurtistundi. alaage, anischiti suutram yokka itara roopaala sandarbhamlo vivikta taramgaala sthaavaraalanu pariganinchavacchu.
taramgaantara parivartanalu vistrutamgaa moodu vargaluga vibhajinchabaddaayih nirantara, vivikta mariyu bahula parishkara aadhaarita.
nirantara taramgaantara parivartanalu (nirantara maarpu mariyu sthaayi paaraamitulu).
nirantara taramgaantara parivartanalalo, parimita shakti yokka icchina sanketam frequency byaandla yokka nirantara kutumbam (ledhaa "lp" function space "l" 2 (r) yokka saaruupya upasthaanaalu) paie anchanaa veyabadutundi. udaaharanaku, anni saanukuula pounahpunyaala "f"> 0 kosam ["f", 2 "f"] roopamlo unna prati pounahpunya bandlo signalnu suuchimchavachchu. appudu, anni phalita pounahpunya bhagalapai tagina samaikyata dwara asalu signalnu punarnirminchavachhu.
frequency byaandlu ledhaa sub-byaandlu (sub-byaandlu) anedi scale 1 vadda subspace yokka scale versionlu. eee subspace chaalaa sandarbhaallo "l" 2 (r) loe oka utpatti function si, "mother wavelet" yokka shiftla dwara utpatti avutundi. scale vann frequency byaand [1,2] yokka udaaharanaki eee function
suutram _ 1
(saadhaaraneekarinchina) sink functiontho. aaa, mayer yokka, mariyu mother vevletlaku maroe rendu udaaharanalu
scale "a" ledhaa frequency byaand [1/"a", 2/"a"] yokka upa sthalam functionla dwara utpatti cheyabadutundi (konnisaarlu "chiled vevletlu" anie pilustaaru)
suutram _ 2
ikkada "a" anedi sanukoolamgaa untundi mariyu scalenu nirvachistundi mariyu "b" anedi edainaa vaastava sankhya mariyu shiftnu nirvachistundi. eee jatha ("a", "b") kudi ardha samatalamlo r + × r loe oka binduvunu nirvachistundi.
scale "a" yokka upasthaanampai "x" function yokka projection appudu roopaanni kaligi untundi
suutram _ 3
taranga gunakaalu" thoo"
suutram _ 4
x" signal vislaeshanha kosam, taramgaala gunakaalanu signal yokka scalogramga sameekarinchavachhu.
konni nirantara taramgaala jaabitaanu chudandi.
vivikta taramgaantara parivartanalu (vivikta maarpu mariyu sthaayi paaraamitulu, nirantaram).
anni taramgaala gunakaalanu upayoginchi oka sanketaanni vislaeshimchadam gananaparamgaa asadhyam, kabatti sambandhita taramgaala gunakaala nundi oka sanketaanni punarnirminchagalagadaniki eguva ardhabhagam yokka vivikta upasamitini enchukovadam saripotunda anie evarainaa aalochinchavachhu. atuvanti vyavasthalo okati konni nijamaina paaraamitulu "a"> 1 ", b"> 0 kosam affine vyavastha. haaph plain yokka sambandhita vivikta upasamiti anni paayintlanu ("am", "nb am") "m", "n" thoo z loe kaligi untundi. sambandhita "chiled vevletlu" ippudu ilaa ivvabaddaayi
suutram _ 5
suutram dwara parimita shakti yokka edainaa sanketam "x" punarnirmaanaaniki tagina sharatu
suutram _ 6
antey functionla suutram _ 7 anedi "l" 2 (r) yokka orthonormal praatipadikanu yerparustundi.
bahula parishkara aadhaarita vivikta taramgaantaraalu (nirantaram) parivartana chendutaayi.
edainaa discretised wavelet transformlo, eguva sagam plaenlooni prati sarihaddu deerghachaturasraakaara praantaaniki parimita sankhyalo wavelet gunakaalu matrame untaayi. ayinappatikee, prati gunakam oka samagrata yokka moolyaankanam avasaram. pratyeka paristhitulalo scale cheyabadina mariyu marchabadina taramgaalu bahula parishkara vislaeshanhanu roopondinchinatlayithe eee sankhya sanklishtatanu nivaarinchavacchu. dheeni ardham, "l" 2 (r) loe "tandri tarangam" φ anae sahayaka function undaali, mariyu "a" anedi oka puurnaamkam. oka vilakshanhamaina empika "a" = 2 mariyu "b" = 1. tandri mariyu talli taramgaala yokka atyanta prasiddha jatha dabechis 4-tapp taramgaalu. prati orthonormal vivikta taramgaala aadharaanni bahula parishkara vislaeshanhatoe anubandhinchalemani gamaninchandi; udaaharanaku, journ taramgaala vislaeshanha yea bahula parishkara vislaeshanhanu angeekarinchadu.
talli mariyu tandri taramgaala nundi okaru upasthaanaalanu nirmistaaru
suutram _ 8
suutram _ 9
father wavelet formula _ 10 time domine lakshanaalanu unchutundi, ayithe mother wavelets formula _ 11 frequency domine lakshanaalanu unchutundi.
veeti nundi kramam avasaram
suutram _ 12
l2" yokka bahula parishkara vislaeshanhanu yerparustundi mariyu upasthaanaala suutram _ 13 anedi paina perkonna kramam yokka orthogonal "thedaalu", antey, "Wm" anedi upasthaanamlo "v" m "−1 lopala" vm "yokka orthogonal puurakam,
suutram _ 14
sampling siddhaantaaniki saaruupyatagaa, 2 "m" sampling dhooramtho kuudina sthalam "vm" anedi frequency bays byaandnu 0 nundi 1/2 "m"-1 varaku cover chestundi. orthogonal complimentga, "wm" sumaruga byaandnu cover chestundi [1/2 "m" −1⁄2 "m"].
aaa cherikalu mariyu orthogonality sambandhaala nundi, mukhyamgaa suutram _ 15, gurtimpulanu santruptipariche krama suutram _ 16 mariyu suutram _ 17 unikini anusaristundi.
suutram _ 18 kabatti suutram _ 19 mariyu
suutram _ 20 kabatti suutram _ 21
modati jatha yokka rendava gurtimpu tandri tarangam φ kosam oka merugudala sameekaranam. rendu jatala gurtimpulu vegavantamaina taramgaala parivartana yokka algorithanku aadharam.
bahula parishkara vislaeshanha nundi "l" 2 sthalam yokka orthogonal kullipovadaanni ilaa pondutundi
suutram _ 22
edainaa signal ledhaa function formula _ 23 kosam idhi sambandhita sub spacela yokka basis functionlalo praatinidhyaanni istundi
suutram _ 24
gunakaalu ekkada unnaayi
suutram _ 25 mariyu
suutram _ 26
samaya-kaarana taramgaalu.
taatkaalika sankethaalanu nija samayamlo proses cheyadaaniki, tarangam filterlu bhavishyattu nundi signal viluvalanu access cheyakapovadam mariyu kaneesa taatkaalika japyalanu pondadam chaalaa avasaram. samaya-kaarana taramgaala praatinidhyaalanu suu mariyu lindeberg abhivruddhi chesaaru, taruvaati paddhatiloo ghnaapakasakti-samarthavanthamaina samaya-punaraavruta amalu kooda untundi.
talli tarangam.
aacharanaatmaka anuvartanaala kosam, mariyu samarthatha kaaranaala kosam, mother (prototype) wavelet (functionlu) gaa compact saportto nirantaram differentiable functionlanu ishtapadataaru. ayithe, vislaeshanhaatmaka avasaralanu (nirantaram unna doublutylo) santrupti parachadaniki mariyu saadhaaranamgaa saiddhaantika kaaranaala valla, space formula _ 27 yokka upa pradaesam nundi wavelet functionlanu enchukuntaaru, idhi lebsgu kolavagala functionla sthalam, ivi puurtigaa integrable mariyu square integrable anae ardhamlo untaayi.
suutram _ 28 mariyu suutram _ 29
eee pradaesamloe undatam valla sunna sagatu mariyu chadarapu pramaanam yokka paristhitulanu roopondinchagalarani nirdhaaristundih
suutram _ 30 anedi sunna sagatu kosam sharatu, mariyu
suutram _ 31 anedi chadarapu pramaanam okadaaniki sharatu.
nirantara taramgaantara parivartanaku "si" oka tarangaphalakam kavalante (khachitamaina prakatana kosam akkada chudandi), mother tarangaphalakam sthiramaina viloma parivartananu pondadaaniki aamodayogyamaina pramaanaanni (vadulugaa cheppalante, oka rakamaina sagam-bhedatmakata) santrupti parachali.
vivikta taramgaala parivartana kosam, taramgaala shreni anedi "l" 2 (r) loe unna gurtimpuku praatinidhyam vahinchaalane sharatu kaneesam avasaram. vivikta doubluty yokka chaalaa nirmaanaalu multy solution vislaeshanhanu upayogistaayi, idhi scaling function dwara taramgaanni nirvachistundi. eee scaling function anedi functional equationku parishkaram.
chaalaa sandarbhaallo si nii ekkuva sankhyalo "m" adrushyamayye kshanaalatoo nirantara functionga parimitam cheyadam upayogakaramgaa untundi, i.ii. anni puurnaamkaalu "m" <"m" kosam"
suutram _ 32
mother vevletnu "a" kaarakamtho scale (ledhaa vistarinchabadindi) chesi, "b" kaarakamtho anuvadinchi (ledhaa maarchabadindi) ivvadaaniki (morlet yokka asalu suutreekarana kinda):
suutram _ 33
nirantara Wt kosam, jatha ("a", "b") puurti sagam-plain r + × r loe maarutuu untundi; vivikta Wt kosam eee jatha daani vivikta upasamitilo maarutuu untundi, dheenini "affine group" anie kooda pilustaaru.
eee vidhulanu tarachugaa (nirantara) parivartana yokka aadhara vidhulu anie tappugaa suuchistaaru. vaastavaaniki, nirantara forier parivartanalo vale, nirantara taramgaantara parivartanalo etuvanti aadharam ledhu. samaya-pounahpunya vivarana suukshmamgaa bhinnamaina suutreekarananu upayogistundi (delprat tarvaata).
parimiti
forier parivartana (nirantara-samayam) thoo poolikalu.
taramgaantara parivartananu tarachugaa forier parivartanatho poolchutaaru, dheenilo sankethaalu sinusoidla mottamgaa suuchimchabadataayi. vaastavaaniki, forier parivartananu mother tarangam yokka empikatho nirantara tarangam parivartana yokka pratyeka sandarbhamgaa chudavachu.
suutram _ 36.
saadhaaranamgaa pradhana vyatyaasam emitante, taramgaalu samayam mariyu pounahpunyam rendintiloonuu sthaanikeekarinchabadathaayi, ayithe praamaanika forier parivartana pounahpunyamlo matrame sthaanikeekarinchabadutundi. swalpakaalika forier transform (stft) anedi wavelet transformnu pooli untundi, dheenilo idhi samayam mariyu frequencini kooda sthaanikeekaristundi, conny frequency/time resolution trade-afto samasyalu unnaayi.
mukhyamgaa, deerghachaturasraakaara kitikee praantaanni oohisthe, oohisthe konchem bhinnamaina kernaltho kuudina parivartanagaa bhaavinchavachchu.
suutram _ 37
ikkada suutram _ _ tarachugaa suutram _ _ vraayavacchu, ikkada suutram _ 40 mariyu "u" varusaga windoing function yokka podavu mariyu taatkaalika offsetnu suuchistaayi. parseval siddhaantaanni upayoginchi, tarangam yokka saktini ilaa nirvachinchavacchu
suutram _ 41
dheeni nundi, vindo yokka taatkaalika maddatu yokka square samayam dwara offset "u" dwara ivvabadutundi
suutram _ 42
mariyu frequency formula _ 43 paie panichese vindo yokka spectral maddatu yokka square
suutram _ 44
time domainlo deerghachaturasraakaara vindoonu guninchadam anedi frequency domainlo formula _ 45 functiontho convolutionku anugunamgaa untundi, phalitamgaa chinna/sthaanikeekarinchina taatkaalika vindola kosam nakilee ringing kalakhandalu erpadataayi. nirantara-samaya forier parivartanatho, suutram _ 46 mariyu eee convolution forier pradaesamloe delta functiontho untundi, phalitamgaa signal suutram _ 47 yokka nijamaina forier parivartanaku daariteestundi. vindo function gassian vanti konni itara appodising filter kaavacchu. windoing function empika nijamaina forier parivartanaku sambandhinchi ujjaayimpu lopaanni prabhaavitam chestundi.
icchina resolution sell yokka time-bandwidth utpattini stftho minchakapovachhu. anni stft aadhaarita muulakaalu anni taatkaalika shiftulu ledhaa offsetlaku ekareeti varnapata mariyu taatkaalika maddatunu nirvahistaayi, tadwara takkuva mariyu adhika pounahpunyaalaku samaana spashtatanu saadhistaayi. spashtata puurtigaa namuunaa vedalpu dwara nirnayinchabadutundi.
dheeniki viruddhamgaa, taramgaantara parivartana yokka bahula parishkara lakshanaalu takkuva pounahpunyaalaku pedda taatkaalika maddatunu andistaayi, adhe samayamlo taramgaantara parivartana yokka scaling lakshanaala dwara adhika pounahpunyaala kosam chinna taatkaalika vedalpulanu nirvahistaayi. eee lakshanam sampradaaya samaya-pounahpunya vislaeshanhanu samaya-sthaayi vislaeshanhagaa vistaristundi. 
vivikta taramgaantara parivartana gananaparamgaa takkuva sanklishtamgaa untundi, vegavantamaina forier parivartana kosam o ("n" logg "n") thoo poliste o ("n") samayam padutundi. eee ganana prayojanam parivartanaku swaabhaavikamainadi kaadu, conny frequency yokka lagarithmic vibhajana empikanu pratibimbistumdi, idhi fft (vegavantamaina forier parivartana) yokka samaana antara frequency vibhaagaalaku viruddhamgaa untundi, idhi dft (vivikta forier parivartana) vale adhe basis functionlanu upayogistundi. vadapotha parimaanaaniki signal parimaanamtho sambandham lenappudu matrame eee sanklishtata vartistundani gamaninchadam kooda mukhyam. shannon tarangam vanti compact maddatu laeni taramgaaniki o ("n" 2) avasaram. (udaaharanaku, lagarithmic forier transform kooda o ("n") sanklishtatatoe untundi, conny asalu signalnu samayanusaaramgaa lagarithamikga sample cheyali, idhi konni rakaala sankethaalaku matrame upayogapadutundi.)
tarangam yokka nirvachanam.
oka tarangam (ledhaa tarangam kutumbam) nuu vividha margallo nirvachinchavacchuh
scaling filter.
oka orthogonal tarangam puurtigaa scaling vadapotha dwara nirvachinchabadutundi-2 "n" podavu mariyu mottam 1 yokka takkuva-paas parimita prerana pratispandana (phir) vadapotha. biorthogonal taramgaalalo, pratyeka kullina mariyu punarnirmaana vadapotalu nirvachinchabaddaayi.
orthogonal tharamgaalatho vislaeshanha kosam hye paas vadapotha takkuva paas yokka quadrature mirror vadapotagaa lekkinchabadutundi mariyu punarnirmaana vadapotalu kullina vadapotalaku samayam viruddhamgaa untaayi.
daabecheelu mariyu simlet taramgaalanu scaling vadapotha dwara nirvachinchavacchu.
scaling function.
taramgaalu taramgaala function si ("t") (i dwara nirvachinchabadataayi.ii. time domainlo mother wavelet) mariyu scaling function φ ("t") (father wavelet anie kooda pilustaaru).
wavelet function anedi byaand-paas filter mariyu scaling, idhi prati sthaayiki daani bandwidthnu sagaaniki taggistundi. idhi mottam varnapataanni cover cheyadaaniki, anantamaina sthaayilu avasaramavutaayani samasyanu srushtistundi. scaling function transform yokka atyalpa sthaayini filter chestundi mariyu mottam spectrum cover cheyabadindani nirdhaaristundi. vivaranaatmaka vivarana kosam chudandi.
compact maddatu unna tarangam kosam, φ ("t") nii podavulo parimitamainadigaa pariganinchavacchu mariyu idhi scaling vadapotha "g" kuu samanam.
mair taramgaalanu scaling functionla dwara nirvachinchavacchu.
taramgaala function.
tarangam anedi tarangam function si ("t") gaa matrame samaya domine praatinidhyaanni kaligi untundi.
udaaharanaku, mexican topi taramgaalanu taramgaala function dwara nirvachinchavacchu. konni nirantara taramgaala jaabitaanu chudandi.
charitra.
20va sataabdam praarambhamlo harr yokka panitho praarambhinchi, taramgaala abhivruddhini aneka pratyeka aalochanaa vidhaanaalatho anusandhaaninchavacchu. dennis gabar taruvaata chesina pani valla gabar anuvulu (1946) labhinchaayi, ivi taramgaala maadirigaane nirminchabaddaayi mariyu ilanti prayojanaalaku vartimpajeyabaddaayi.
appati nundi taranga siddhaantaaniki gananeeyamaina sahakaram sahakaram zweig nirantara taranga parivartana (sidabluty) nuu kanugonadam (modata dheenini coclear parivartana anie pilustaaru mariyu dhwaniki chevi yokka praticharyanu adhyayanam chestunnappudu kanugonabadindi), pierry goupillad, grossman mariyu morlet yokka suutreekarana ippudu sidabluty (1982) anie piluvabadedi, zaan-olov stromberg yokka vivikta taramgaalapai (1983), leey gall-tabatabai (elgity) 5/3 taps leanier faze (1988) thoo orthogonal kaani filter byaank, ingrid doubechies yokka compact saportto orthogonal taramgaalu (1988), mallat yokka orthogonal kaani multy resolution framework (1989), almistox binquins, delphiol yokka kotta taramgaala vibhajana (1991), delphiol yokka kotta taramgaala vibhajana (1990), delfall yokka kotta taramgaala vibhajana (1993), delfall yokka kotta taramgaala vibhajana (1990), delfall yokka kotta taramgaala vibhajana ( ( mutyamu.
jpeg 2000 pramaanaanni 1997 nundi 2000 varaku touradz ibrahimi (taruvaata jpeg adhyakshudu) adhyakshatana ummadi photographic nipunula brundam (jpeg) kamitee abhivruddhi chesindi. asalu jpeg formatt upayoginche dicti algorithanku viruddhamgaa, jpeg 2000 badulugaa vivikta taramgaantara parivartana (didabluty) algorithamlanu upayogistundi. idhi daani lassie compression algorithm kosam cdf 9/7 wavelet transform transform ingrid doubechies abhivruddhi chesindi) mariyu lii gall-tabatabai (elgity) 5/3 discreet-time filter byaank (deediyar lae gall mariyu allie zhe abhivruddhi chesindi. chesindi tabatabai) daani nashtarahita kudimpu algorithm kosam. chalana jpeg 2000 podigimputoe kuudina jpeg 2000 saanketikata saanketikata digital cinema kosam veediyo coding pramaanamgaa empika cheyabadindi.
taramgaalu marutayi.
tarangam anedi icchina function ledhaa nirantara-samaya sanketaanni vividha sthaayi bhagaluga vibhajinchadaaniki upayoginche ganita function. saadhaaranamgaa prati scale bhaagaaniki frequency paridhini ketayinchavacchu. prati scale bhaganni daani scaleku saripoye resolutiontho adhyayanam cheyavachu. taramgaala parivartana anedi taramgaala dwara oka function yokka praatinidhyam. taramgaalu parimita-podavu ledhaa vaegamgaa ksheenistunna dolana taranga roopam ("mother tarangam" anie pilustaaru) yokka scale mariyu anuvaada kaapeelu ("dotter taramgaalu" anie pilustaaru). discontinuitylu mariyu padunaina sikharaalanu kaligi unna vidhulanu suuchimchadaaniki mariyu parimita, naan-periodic mariyu/ledhaa naan-stationary sankethaalanu khachitamgaa punarnirminchadaaniki mariyu punarnirminchadaaniki saampradaaya forier transformla kante wavelet transformlaku prayojanaalu unnaayi.
taramgaantara parivartanalu vivikta taramgaantara parivartanalu (dwts) mariyu nirantara taramgaantara parivartanalu (cwts) gaa vargeekarinchabaddaayi. dwt mariyu cwt rendoo nirantara-samaya (analog) parivartanalu anie gamaninchandi. avi nirantara-samaya (analog) sankethaalanu suuchimchadaaniki upayoginchavacchu. cwts saadhyamayye prati sthaayi mariyu anuvaadampai panicheestaayi, ayithe dwts oka nirdishta upasamiti sthaayi mariyu anuvaada viluvalu ledhaa praatinidhya gridnu upayogistaayi.
ververu anuvartanaalaku saripoye pedda sankhyalo taramgaantara parivartanalu unnaayi. puurti jabita kosam taranga-sambandhita parivartanala jaabitaanu chudandi, conny saadhaaranamainavi krinda ivvabaddaayi
saadhaaraneekarinchina parivartanalu.
aneka saadhaaraneekarinchina parivartanalu unnaayi, veetilo taramgaantara parivartana oka pratyeka sandarbham. udaaharanaku, yosef joseph heisenberg samuuhamlooki sthaayini pravesapettaadu, idhi samayam, sthaayi mariyu pounahpunyam yokka vidhi ayina nirantara parivartana sthalaaniki daariteesindi. sidabluty anedi phalitamgaa vachhe vachhe time-scale-frequency valume dwara dvimiteeya mukka.
saadhaaraneekarinchina parivartanaku maroka udaaharana chirplet parivartana, dheenilo sidabluty kooda chirplet parivartana dwara dvi-miteeya mukka.
saadhaaraneekarinchina parivartanalaku oka mukhyamaina anuvartana praantam adhika pounahpunya spashtata keelakamaina vyavasthalanu kaligi untundi. udaaharanaku, darkfield electron optical transforms pratyaksha mariyu paraspara sthalam madhya madhyantara anuvu clustering yokka harmonic vislaeshanhaloo vistrutamgaa upayoginchabaddaayi, i.ii. spatikaalu mariyu sphatika lopaala adhyayanamlo. ippudu transmission electron microscopelu anni rakaala nanostructurelo anhu aavartanampai picometer-scale samaachaaramtho digital chitraalanu andinchagala saamarthyaanni kaligi unnanduna, adhika frequency resolutiontho (brushletlu mariyu rijletlu vantivi) intermediate transformla kosam namuunaa gurtimpu mariyu strain/metrology applicationla paridhi vaegamgaa perugutondi.
fractional wavelet transform (efordabluty) anedi fractional forier transform domainlalo classical wavelet transform yokka saadhaaraneekarana. eee parivartana samayam mariyu pakshika-domine samacharanni ekakaalamlo andinchagaladu mariyu samaya-pakshika-frequency plainloo sankethaalanu suuchistumdi.
applications.
saadhaaranamgaa, signal ippatike sample cheyabadi unte dayta compression kosam dwt kii oka ujjaayimpu upayoginchabadutundi, mariyu signal vislaeshanha kosam cwt. anduvalla, didabluty ujjaayimpu saadhaaranamgaa injaneering mariyu computer sainslo mariyu sidabluty shaastreeya parisoedhanaloo upayoginchabadutundi.
konni itara parivartanala maadirigaane, daetaanu maarchadaaniki taramgaala parivartanalanu upayoginchavacchu, taruvaata roopaantaram chendina daetaanu encode cheyavachu, phalitamgaa samarthavanthamaina kudimpu vastundi. udaaharanaku, jpeg 2000 anedi biorthogonal taramgaalanu upayoginche chitra sampeedana pramaanam. dheeni ardham frame atigaa unnappatikee, idhi oka "biginchina frame" (vector space yokka framela rakalanu chudandi), mariyu adhe frame functionlu (sanklishta taramgaala vishayamlo samyogam minaha) vislaeshanha mariyu samslaeshanha rendintikee upayoginchabadataayi, antey.ii., munduku mariyu viloma parivartana rendintiloonuu. vivaraala kosam taramgaala kudimpu chudandi.
taramgaala gunakam parimiti aadhaaramgaa daetaanu sunnitamgaa/denoise cheyadaaniki sambandhita upayogam, dheenini taramgaala sankocham anie kooda pilustaaru. avaanchita frequency bhagalaku anugunamgaa unde taramgaala gunakaalanu anukuulamgaa parimitaparachadam dwara sunnitatvam mariyu/ledhaa denoising karyakalapalanu nirvahinchavacchu.
communication anuvartanaala kosam taramgaala parivartanalu kooda upayoginchadam prarambhamayyayi. wavelet off dm anedi hechdi-plc (panasonic abhivruddhi chesina power line communications technology) loe upayoginche praathamika modulation pathakam, mariyu ieee 1901 pramaanamloo cherchabadina aichhika modlalo okati. saampradaaya fft dm kante dm yokka tarangam lothaina sthaayilanu saadhinchagaladu, mariyu dm yokka taramgaaniki rakshana viramam avasaram ledhu (idhi saadhaaranamgaa fft dm vyavasthalalo gananeeyamaina ovarheadnu suuchistumdi).
oka sanketam yokka praatinidhyamgaa.
tarachugaa, sankethaalanu sinusoidla mottamgaa suuchimchavachchu. ayithe, aakasmika viraamtho kuudina nirantaram kaani sanketaanni pariganinchandi; eee sanketaanni ippatikee sinusoidla mottamgaa suuchimchavachchu, conny anantamaina sankhya avasaram, idhi gibbs drugvishayam anie piluvabade pariseelana. appudu, dheeniki anantamaina sankhyalo forier gunakaalu avasaram, idhi kudimpu vanti aneka anuvartanaalaku aacharanaatmakamainadi kaadu. eee sankethaalanu vaati samaya-sthaanikeekarinchina pravartana kaaranamgaa nilipivethatho vivarinchadaaniki taramgaalu marinta upayogakaramgaa untaayi (forier mariyu taramgaala parivartanalu rendoo frequency-sthaanikeekarinchabaddaayi, conny taramgaalu adanapu samaya-sthaanikeekarinche lakshanaanni kaligi untaayi). eee kaaranamgaa, aacharanalo aneka rakaala sankethaalu forier domainlo naan-spurse kaavacchu, conny wavelet domainlo chaalaa takkuvagaa untaayi. idhi signal punarnirmaanamlo, mukhyamgaa iteevala prajaadarana pondina compressed sensing rangamlo upayogapadutundi. (swalpakaalika forier transform (stft) kooda samayam mariyu frequencylo sthaanikeekarinchabadindani gamaninchandi, ayithe frequency-time resolution trade-offlo tarachugaa samasyalu untaayi. multy solution vislaeshanha kaaranamgaa taramgaalu merugaina sanketha praatinidhyaalu.)
idhi ippudu pedda sankhyalo anuvartanaala kosam taramgaantara parivartanalu enduku avalambinchabadutunnayo prerepistundi, tarachugaa sampradaaya forier parivartananu bharti chestundi. paramaanu gatisastram, gandaragolam siddhaantam, abb initio gananalu, khagola bhouthika shaastram, gurutvakarshana taranga taatkaalika dayta vislaeshanha, saandrata-maatrika sthaanikeekarana, bhookampa shaastram, optics, allakallolam mariyu quantum mechanics vanti bhouthika saastramlooni aneka rangaalu eee namuunaa maarpunu chushai. eee maarpu image prosessing, eejee, emg, egg vislaeshanhalu, medadu layalu, dna vislaeshanha, protein vislaeshanha, vaataavarana shaastram, maanava laingika pratispandana vislaeshanha, saadhaarana signal prosessing, prasangam gurtimpu, dhvanisaastram, kampana sankethaalu, computer graphics, multifractal vislaeshanha mariyu viralamaina codinglo kooda sambhavinchindi. computer drushti mariyu chitra prosessinglo, scale space praatinidhyam mariyu gassian utpanna operatorla bhavananu canonical bahula-sthaayi praatinidhyamgaa pariganistaaru.
taramgaala denoising.
manam sabdam chese signal suutraanni kolustaamu anukundam, ikkada suutram 49 signalnu suuchistumdi mariyu suutram 50 sabdaanni suuchistumdi. suutram _ 49 oka nirdishta taramgaala praatipadikana arudaina praatinidhyaanni kaligi undani mariyu suutram _ 52 anie anukundam.
suutram _ 53 yokka taramgaantara parivartana suutram _ 54 gaa undanivvandi, ikkada suutram _ 55 anedi signal bhaagam yokka taramgaantara parivartana mariyu suutram _ 56 anedi sabdam bhaagam yokka taramgaantara parivartana.
suutram _ 57 looni chaalaa muulakaalu 0 ledhaa 0 kii daggaragaa untaayi, mariyu suutram _ 58
suutram _ 59 orthogonal kabatti, anchanaa samasya iid gassian sabdamlo signal yokka recoveryki samanam. suutram _ 57 chaalaa takkuvagaa unnanduna, suutram _ 57 kosam gassian mishrama namuunaanu vartimpajeyadam oka paddhati.
oka puurva suutram _ 62 nuu oohinchandi, ikkada suutram _ 63 anedi "mukhyamaina" gunakaala yokka vaividhyam mariyu suutram _ 64 anedi "mukhyamaina" gunakaala vaividhyam.
appudu suutram _ 65, suutram _ 66 nuu sankocham karakam anie pilustaaru, idhi munupati vyatyaasaala suutram _ 63 mariyu suutram _ 64 paie aadharapadi untundi. sankocham parimiti kante sunnaki diguvana unna gunakaalanu amarchadam dwara, viloma parivartana vartimpajesina tarvaata, sparsity ooha kaaranamgaa oohinchinanta chinna mottamlo signal kolpotundi. pedda gunakaalu pradhanamgaa sparsity kaaranamgaa signalnu suuchistaayani bhaavistunnaaru, mariyu ganankaparamga chaalaa takkuva signal, ekkuva sabdam unnappatikee, atuvanti takkuva parimaana gunakaalalo soochinchabadutundani bhaavistunnaaru... anduvalla jeero-avt operation ekkuva sabdam tolagistundani mariyu ekkuva signal kaadani bhaavistunnaaru. saadhaaranamgaa, eee prakriyaloo paina perkonna parimiti gunakaalu savarinchabadavu. atuvanti attenuation dwara tolaginchabadutundani anchanaa vesina sabdam yokka ganaanka anchanaa aadhaaramgaa, taranga-aadhaarita denoising kosam konni algorithamlu pedda gunakaalanu kooda tagginchavachhu.
chivaraga, suutram _ 69 pondadaaniki viloma taramgaantara parivartananu vartinchandi.
bahulasthayi vaataavarana network.
agrawal mariyu itarulu. ververu samaya pramaanaalalo vaataavaranaanni sanklishta netvarklagaa nirminchadaaniki mariyu parisoedhinchadaaniki pratipaadita taramgaala aadhaarita adhunaatana sarala mariyu naan leanier paddhatulu. vividha samayaallo sst datasetlanu upayoginchi nirminchina vaataavarana netvarklu vaataavarana prakriyala yokka taramgaala aadhaarita bahula-sthaayi vislaeshanha vyavastha gatiseelatanu baga ardham chesukogala vaagdaanaanni kaligi undani, idhi prakriyalanu oke samaya sthaayilo vislaeshimchinappudu tappipovachhu.

