
upsampling

digital signal prosessinglo, upsampling, vistarana mariyu interpolation anevi bahula-raetu digital signal prosessing vyavasthalo resampling prakriyatho anubandhinchabadina padaalu. "upsampling" anedi "vistarana" kii paryaayapadamgaa undavacchu ledhaa idhi "vistarana" mariyu vadapotha ("interpolation") yokka mottam prakriyanu vivarinchavacchu. signal" ledhaa itara nirantara function yokka namuunaala shrenipai upsampling chesinappudu, idhi adhika retutho (ledhaa chaayaachitram vishayamlo vale saandrata) signalnu sample cheyadam dwara pondina kramam yokka ujjaayimpunu utpatti chestundi. udaaharanaku, sekanuku 44,100 namuunaala vadda compact disk audeo 5/4 kaarakamtho upsample cheyabadithe, phalitamgaa namuunaa-raetu 55,125 avutundi.
oka puurnaanka karakam dwara upsampling.
oka puurnaanka karakam "l" dwara raetu perugudalanu 2-dasala prakriyagaa vivarinchavacchu, marinta samarthavanthamaina samaanamaina amalutho
eee applicationlo, filternu interpolation filter anie pilustaaru, mariyu daani roopakalpana krinda charchinchabadindi. interpolation filter oka phir rakam ayinappudu, daani saamarthyaanni meruguparachavacchu, endukante sunnalu daani dott utpatti gananalaku aemee dohadam cheyavu. dayta stream mariyu gananalu rendinti nundi vaatini tolaginchadam sulabhamaina vishayam. prati avtput namuunaa kosam multirate interpolating phir filter dwara chese ganana oka chukka utpattih
ikkada "h" [] kramam anedi interpolation filter yokka prerana pratispandana, mariyu "k" anedi "k" yokka atipedda viluva, dheeniki "h" ["j" + "kl"] sunna kaanidi. l" = 2 vishayamlo, "h" [] nuu haaph-byaand filterga roopondinchavacchu, ikkada daadaapu sagam gunakaalu sunnaga untaayi mariyu chukkala utpattullo cherchaalsina avasaram ledhu. l" yokka viramalalo teesukunna prerana pratispandana gunakaalu oka anugunyatanu yerparustaayi, mariyu atuvanti anugunyatalu (dasalu anie pilustaaru) kalisi gunakam cheyabadataayi. prerana pratispandana yokka prati "l" dasalu "x" [] dayta stream yokka adhe varusa viluvalanu filter chestaayi mariyu "l" varusa avtput viluvalalo okadaanni utpatti chestaayi. konni bahula-processor nirmaanaalalo, eee chukka utpattulu ekakaalamlo nirvahinchabadataayi, eee sandarbhamlo dheenini polyphace filter antaaru.
paripuurnata kosam, prati dasha yokka saadhyamayye, conny asambhavamaina amalu "h" [] shreni yokka kaapeelo itara dasala gunakaalanu sunnaalatoe bharti cheyadam, mariyu suutram _ 4 kramaanni asalu input raetu kante l retlu vaegamgaa proses cheyadam anie ippudu memu prastaavinchaamu. appudu prati "l" avutputlalo "l-1" sunna avutundi. kaavalasina "y" [] kramam anedi dasala mottam, ikkada prati mottam yokka "l-1" padaalu oke vidhamgaa sunnaga untaayi.  oka dasha yokka upayogakaramaina avutputla madhya "l-1" sunnalanu lekkinchadam mariyu vaatini mottamlo jodinchadam anedi samarthavantamgaa ksheenata. idhi vaatini assalu lekkinchakapovadam lantidhe phalitam. aaa samaanatvaanni "rendava goppa gurtimpu" anie pilustaaru. idhi konnisaarlu polyphace paddhati yokka utpannaalalo upayoginchabadutundi.
interpolation filter design.
suutram _ 5 anedi edainaa function yokka forier transform, suutram _ 6, dheeni namuunaalu kontha viramamlo, suutram _ 7 suutram _ 8 kramaniki samanam. appudu suutram _ 8 kramam yokka vivikta-samaya forier parivartana (dtft) suutram _ 10 yokka aavartana sankalanam yokka forier shreni praatinidhyam.
suutram _ 11 sekanla unitlanu kaligi unnappudu, suutram _ 12 heartz (Hz) unitlanu kaligi untundi. namuunaa suutram _ 13 retlu vaegamgaa (virama suutram _ 14 vadda) suutram _ 15 yokka karakam dwara aavartanaanni penchutundi.
idhi interpolation yokka kaavalasina phalitam kooda. eee rendu pampineelaku oka udaaharana chitram 2 yokka modati mariyu moodava graphlalo chithreekarinchabadindi.
adanapu namuunaalanu sunnalu choppinchinappudu, avi forier shreni yokka sunna-viluva padaalanu tolaginchi namuunaa-viramanni suutram _ 16kii taggistaayi, dheenini ilaa vraayavachuhu
idhi formula _ 18 viluvatho sambandham lekunda formula _ 13 nirnayinche adhika dayta-raetu vadda amalu cheyabadina digital filter yokka dtft aavartanaaniki samanam. rendava graph loe paas filter mariyu formula _ 20 nuu varnistundi, phalitamgaa kaavalasina varnapata pampinhee (moodava graph) jarugutundi. vadapotha yokka bandwidth anedi asalu suutram _ 8 kramam yokka nikevist frequency.  Hz unitlalo aaa viluva suutram _ 22 ayithe filter design applicationlaku saadhaaranamgaa saadhaaraneekarinchina unitlu avasaram. (chitram 2, pattika chudandi) 
pakshika karakam dwara upsampling.
l"/"m" anedi upsampling karakanni suuchistumdi, ikkada "l"> "m".
upsampling kuu dayta retunu penchina tarvaata loe paas filter avasaram, mariyu down sampling kuu decimation kii mundu loe paas filter avasaram. anduvalla, rendu operationlanu rendu cutoff frequencielalo takkuva unna oke filter dwara saadhinchavachchu. l"> "m" kesu kosam, interpolation filter cutoff, formula _ 23 "intermediate sample kii saikils", takkuva frequency.

