
shatkon namunakaran

ack bahuayami sanket m swatantra charr kaa ack kaary haye jahan sootra _ 1. vaastavik duniya key sanket, joe aam taur parr nirantar samay sanket hain, koo yeh sunishchit karane key liye discretise (namuna) kiya jaanaa chaahiye kii digital system kaa upayog sanketon koo sansaadhit karane key liye kiya jaa sakata haye. yeh vivechana kii iss prakriya key dauran haye jahan namuna chitran chitra mein aataa haye. halanki ack nirantar samay sanket kaa ack asatat pratinidhitva praapt karane key kaee tareeke hain, aavadhik namunakaran abb taka kii sabse saral yojana haye. saiddhaantik roop seey, kissy bhee bindu key sambandh mein namuna liya jaa sakata haye. lekin vyaavhaarik roop seey, namoone lene kaa kaary una binduon key ack samooh key sambandh mein kiya jaataa haye jinaki ack nishchit beejganitiya sanrachana hoti haye. aisee sanrachanaon koo jaali kahaa jaataa haye. ganitiya roop seey, ack sootra _ 2-ayami sanket key namoone lene kii prakriya koo iss prakaar likhaa jaa sakata haih
jahan sootra _ 4 nirantar domen m-ayami sadish (m-d) haye jiska namuna liya jaa rhaa haye, sootra _ 5 ack namoone key soochkaankon key anuroop ack m-ayami purnank sadish haye, aur "v" ack sootra _ 6 namuna matricks haye.
prerana.
bahuayami namunakaran sanketon koo sansaadhit karane key liye digital tarikon koo dekhane kaa avsar pradaan kartaa haye. digital domen mein sanketon koo sansaadhit karane key kuchh laabhon mein prograam karane yogya dee. aiss. pee. sanchaalan key madhyam seey lachilaapan, nishtha key nuksan key binaa sanket bhandaran, sanchaar mein encryption kaa avsar, hardware sahishnuta key prati cumm samvedansheelta shamil hain. iss prakaar, digital vidhiyaan ack saath shaktishali aur lachili donon hain. kaee anuprayogon mein, way apane anuroop samkakshon key liye cumm mahange vikalp key roop mein kaary karate hain. kabhi-kabhi, digital hardware kaa upayog karke lagu kiye gaye algorithm itane jatil hotey hain kii unake paas koee analogue samkaksh naheen hotey hain. bahuayami digital sanket prasanskaran prasanskaran sanketon key saath sambandhit haye joe bahuayami saraniyon key roop mein darshaae jaate hain jaise kii 2-dee anukram yaa namuna chhaviyaan. digital domen mein inn sanketon koo sansaadhit karane seey digital hardware kaa upayog karane kii anumati milati haye jahaan sanket prasanskaran sanchaalan mein algorithm dwara nirdisht kiya jaataa haye. choonki vaastavik duniya key sanket nirantar samay sanket hain, isaliye bahuayami namunakaran vaastavik duniya key sanketon koo alag karane mein mahatvapurna bhoomika nibhaata haye. alag samay sanketon koo badale mein sanket seey jaankaari nikaalane key liye digital hardware kaa upayog karke sansaadhit kiya jaataa haye.
praarambhik.
samarthan kaa kshetra.
jiss kshetra key baahar sanket key namoone shoonya maan lete hain, usey samarthan kshetra (aar. oh. aiss.) key roop mein jaanaa jaataa haye. paribhasha seey, yeh spasht haye kii sanket key samarthan kaa kshetra advitiya naheen haye.
forier parivartan.
forier parivartan ack aisaa upkaran haye joe hamein sanket parr kiye gaye ganitiya sanchaalan koo saral banaane kii anumati detaa haye. parivartan mool roop seey signsoids key bhaarit sanyojan key roop mein kissy bhee sanket kaa pratinidhitva kartaa haye. ack aim-ayami sanket key forier aur vyutkram forier parivartan koo nimnanusar paribhaashit kiya jaa sakata haih
topi prateek ingit kartaa haye kii operation vactor parr kiya jaataa haye. namuna sanket kaa fourier parivartan sanket key nirantar samay fourier parivartan kaa ack aavadhik vistaar maanaa jaataa haye. ise ganitiya roop seey iss prakaar darshaaya gayaa haih
iss prakaar sthaanik kshetra mein namoone lene seey forier kshetra mein aavadhikta aatee haye.
aliasing.
ack seemit baind sanket koo samay-samay parr kaee tarikon seey dohraya jaa sakata haye. yadi pratikriti key parinamswarup pratikriti vaale kshetron key beach ack ativyaapi hotaa haye, tou sanket aliasing seey peedit hotaa haye. aisee sthitiyon mein, ack nirantar samay sanket koo isake namoonon seey poori tarah seey punarpraapt naheen kiya jaa sakata haye. iss prakaar nirantar sanket kii sahee vasuli sunishchit karane key liye, parivartit kshetra mein pratikriti vaale kshetron kaa shoonya ativyaapi bahuayami namuna honah chaahiye. 1-ayami sanketon key mamle mein, yadi nirantar samay sanket kaa paryaapt uchch darr parr namuna liya jaataa haye tou upnaam koo rokaa jaa sakata haye.
namuna ghanatva.
yeh prati ikai kshetra mein namoonon kii sankhya kaa ack maap haye. ise iss prakaar paribhaashit kiya gayaa haih
nirantar samay sanket koo poori tarah seey punarpraapt karane key liye aavashyak prati ikai kshetra mein namoonon kii nyuntam sankhya koo ishtatam namuna ghanatva kahaa jaataa haye. una anuprayogon mein jahaan smriti yaa prasanskaran kaa samay seemit haye, sanket koo poori tarah seey pradarshit karane key liye aavashyak namoonon kii sankhya koo cumm karane parr jore diyaa jaanaa chaahiye.
maujooda drishtikon.
ack bandlimitted tarang key liye, forier domen mein upnaamon kaa utpaadan kiye binaa sanket kaa namuna lene key kaee tareeke hain. lekin aamtaur parr kewal dou ranneetiyon kaa upayog kiya jaataa haih aaytaakaar namunakaran aur shatkon namunakaran.
aaytaakaar aur shatkon namunakaran.
aaytaakaar namoone mein, udaaharan key liye, ack 2-ayami sanket koo nimnalikhit v matricks key anusaar namuna liya jaataa haih
shatkon namoone mein, "v" matricks nimnalikhit samanya roop dhaaran kartaa haih
donon yojanaon kii dakshata mein antar koo trijya r key samarthan key ack golakar kshetra key saath ack bandlimitted signal kaa upayog karke ujagar kiya jaataa haye. vritt koo 2r lambai key varg mein yaa lambai sootra _ 15 key niyamit shatkon mein utkeern kiya jaa sakata haye. isake parinamswarup, samarthan kaa kshetra abb kramshah ack varg aur ack shatkon mein badal gayaa haye.
yadi inn kshetron koo aavadhikta kshetra mein iss tarah seey dohraya jaataa haye kii kissy bhee dou kshetron key beach shoonya ativyaapi haye, tou samay-samay parr samarthan key varg kshetra koo dohrakar, humm ack aaytaakaar jaali parr nirantar sanket kaa prabhaavi dhang seey namuna lete hain. isi tarah ack shatkon jaali parr nirantar sanket kaa namuna lene key liye samarthan maanchitron key shatkon kshetra kii aavadhik pratikriti.
yuu, aavadhikta matricks seey, humm aaytaakaar aur shatkon donon yojanaon key liye ishtatam namuna ghanatva kii ganana curr sakate hain. yeh paaya gayaa haye kii golakar baind-seemit sanket koo poori tarah seey punarpraapt karane key liye, shatkon namuna yojana key liye aaytaakaar namuna yojana kii tulanaa mein 13.4% cumm namoonon kii aavashyakta hoti haye. 2-ayami sanket key liye kamee kaa bahut cumm mahatva prateet hoe sakata haye. lekin jaise-jaise sanket kii ayamita badhegi, shatkon namuna yojana kii dakshata kaheen adhik spasht hoe jaayegi. udaaharan key liye, 8-ayami sanket key liye praapt kamee 93.8% haye. 
praapt parinam key mahatva koo ujagar karane key liye, ack chhavi koo anant sankhya mein namoonon key sangrah key roop mein dekhane kaa prayaas karein. drishti key liye jimmedaar praathamik ikai, i.ee. sabhi standhaariyon key retina parr photoreceptor (chhad aur shanku) maujood hotey hain. yeye kaksh panktiyon aur stambhon mein vyavasthit naheen hain. shatkon namuna yojana koo anukoolit karke, hamari aankhen chhaviyon koo adhik kushalata seey sansaadhit karane mein saksham hoti hain. shatkon namunakaran kaa mahatva iss tathya mein nihit haye kii maanav drishti pranali key photoreceptor ack shatkon namuna jaali parr sthit hain aur iss prakaar, shatkon namunakaran karate hain. vaastav mein, yeh dikhaaya jaa sakata haye kii shatkon namuna yojana ack golakar baind-seemit sanket key liye ishtatam namuna yojana haye.
anuprayog.
ishtatam namuna grid key upayog seey aliasing prabhaav cumm hoe jaate hain.
see. see. dee. praudyogiki mein haal kii pragati ney vaastavik jeevan anuprayogon key liye shatkon namoone koo sambhav banaa diyaa haye. aitihaasik roop seey, praudyogiki kii baadhaon key kaaran, detector saraniyon koo kewal aaytaakaar aakar detectors key saath 2-ayami aaytaakaar namuna jaali parr lagu kiya gayaa thaa. lekin fuji dwara pesh kiye gaye super [see. see. dee.] detector mein shatkon grid mein ack ashtakoniya aakar kaa pixel hotaa haye. saiddhaantik roop seey, ack ashtakoniya pixel pesh karke detector key pradarshan mein bahut vriddhi hui thee. namoone koo prastut karane key liye aavashyak pixel kii sankhya cumm curr dee gaee thee aur aaytaakaar pixel kii tulanaa mein sanket-seey-shore anupaat (aiss. aine. aar.) mein mahatvapurna sudhaar huaa thaa. lekin shatkon pixel kaa upayog karane kii kamee yeh haye kii sambandhit bharane kaa kaarak 82 pratishat seey cumm hoga. ack vaikalpik vidhi shatkon pixel koo iss tarah seey prakshepit karna hoga kii humm antatah ack aaytaakaar grid key saath samaapt hoe jaaen. spott 5 upgrah mein ack samaan takneek shamil haye jahan dou samaan raikhik see. see. dee. dou ardh-samaan chhaviyon koo prasaarit karate hain jinhen aadhe pixel dwara sthanantarit kiya jaataa haye. dou chhaviyon koo prakshepit karane aur unhein sansaadhit karane parr, shatkon pixel key saath ack detector key kaary kii nakal kii jaati haye.
buddhiman drishti key liye shatkon sanrachana.
computer graphics key kshetra mein saamane aaney vaali pramukh chunautiyon mein seey ack bhautik screen parr binduon key ack asatat sett key roop mein vaastavik duniya key nirantar sanket kaa pratinidhitva karna haye. yeh lambe samay seey gyaat haye kii aaytaakaar grid kii tulanaa mein shatkon namuna grid key kaee laabh hain. pieterson aur middleton ney tarang sankhya seemit aim ayami karyon key namoone aur punarnirmaan kii jaanch kii aur iss nishkarsh parr pahunche kii ishtatam namuna jaali, samanya roop seey, shatkon naheen haye.
 russell aim. mercero ney shatkon asatat fourier parivartan (dee. aff. tii.) aur shatkon seemit seema aaveg pratikriya filter vikasit kiye. vaha yeh dikhaane mein saksham they kii golakar bandlimit sanketon key liye, shatkon namunakaran aaytaakaar namoone kii tulanaa mein adhik kushal haye. cramblit aur alback ney ishtatam shatkon samay-anukramik namuna pattern koo design karane key liye vidhiyon kaa vikas kiya aur ack aaytaakaar namuna grid key liye design kiye gaye gunon key saapeksh unake gunon parr charcha kii. 
shatkon namuna grid kii anoothi visheshtaon mein seey ack yeh haye kii iska fourier parivartan abhee bhee shatkon haye. kramik panktiyon aur stambhon key beach kii doori key beach ack vyutkram sambandh bhee haye (yeh maanate hue kii namoone shatkon key kendra mein sthit hain). yeh vyutkram sambandh upnaam koo cumm karane aur nyuntam namuna ghanatva koo adhikatam karane mein ack badee bhoomika nibhaata haye. nirantar vaastavik duniya key sanketon koo alag karate samay matratmak truti maujood rahane key liye baadhya haye. yeh nirdhaarit karane key liye prayog kiye gaye hain kii kaun saa detector vinyas cumm seey cumm matratmak truti dega. hexagonal sthaanik namunakaran samvedak key diye gaye resolution key liye cumm seey cumm matratmak truti dene key liye paaya gayaa thaa.
shatkon grid kii susangat samparkah ack shatkon grid mein, humm kewal 6 pados key namoonon kii prishthabhoomi koo paribhaashit curr sakate hain. haalaanki, ack vargakar grid mein, humm 4 yaa 8 pados key namoonon kii prishthabhoomi koo paribhaashit curr sakate hain (yadi vikarn sampark kii anumati haye). shatkon grid mein iss tarah key vikalp kii anupasthiti key kaaran, kushal algorithm taiyar kiye jaa sakate hain. behtar koniya sankalp key liye bhee susangat sampark jimmedaar haye. yahee kaaran haye kii shatkon jaali aaytaakaar jaali kii tulanaa mein ghumaavdaar vastuon kaa pratinidhitva karane mein bahut behtar haye. inn kaee fayadon key bavjood, shatkon adharit chhaviyon koo sansaadhit karane, pakadane aur pradarshit karane key liye hardware kii kamee key kaaran shatkon grid kaa upayog vyaavhaarik roop seey computer drishti mein isaki adhikatam kshamata key liye naheen kiya gayaa haye. jaisa kii pahale spott 5 upgrah key saath ujagar kiya gayaa thaa, iss hardware kathinaaee koo door karane key liye dekhe jaa rahey tarikon mein seey ack varg pixel kaa upayog karke shatkon pixel kii nakal karna haye.

