
samooh vilamb aur charan vilamb

sanket prasanskaran mein, samooh vilamb aur charan vilamb yeh varnan karane key dou sambandhit tareeke hain kii kaise ack raikhik samay-parivartansheel (ell. tii. aaee.) pranali (jaise microphone, samakshiya cable, pravardhak, loudspeaker, dursanchar pranali, ethernet cable, digital filter, yaa analogue filter) seey gujarane parr ack sanket key aavritti ghatakon mein samay mein deree hoti haye. charan vilamb ack "signsoidal" ghatak (sthir sthiti mein ack saain tarang) key samay parivartan kaa varnan kartaa haye. samooh vilamb ack "tarang paiket" key "lifafe" key samay parivartan kaa varnan kartaa haye, ack "paik" yaa ack saath yatra karane vaali ack aavritti key aspas kendrit dolanon kaa "samooh", udaaharan key liye ack lifafe dwara ack saain tarang koo gunaa karke (ayam modulan) banaaya jaataa haye (jaise kii ack tapering function).
yeye deree aamtaur parr aavritti parr nirbhar hoti hain, jiska arth haye kii vibhinn aavritti ghatakon koo alag-alag deree kaa anubhav hotaa haye. natijatan, sanket key tarang roop mein vikriti kaa anubhav hotaa haye kyonki yeh pranali seey gujarta haye. yeh vikriti analogue video aur analogue audio mein kharaab nishtha, yaa digital bitt stream mein uchch bitt-truti darr jaisi samasyaon kaa kaaran bunn sakati haye. haalaanki, ack baind limitted signal aur sapaat aavritti pratikriya kii poori aavritti seema mein ack nirantar samooh deree key aadarsh mamle key liye, tarang roop mein koee vikriti naheen hogi.
prishthabhoomi.
sanket kii aavritti ghatak.
forier vishleshan seey pataa chalata haye kii samay mein sanketon koo vaikalpik roop seey signsoidal aavritti ghatakon key yog key roop mein vyakt kiya jaa sakata haye, pratyek ack nishchit ayam aur charan key saath trikonamitiya falan sootra _ 1 parr adharit haye aur koee shuruat aur koee anta naheen haye.
raikhik samay-parivartansheel pranaaliyan pratyek signsoidal ghatak koo swatantra roop seey sansaadhit karati hain; raikhikta key guna kaa arth haye kii way superposition siddhant koo santusht karate hain.
parichay.
ack raikhik samay-parivartansheel (ell. tii. aaee.) pranali key samooh vilamb aur charan vilamb guna aavritti key kaary hain, joe usa samay seey dete hain jaba ack samay kii aavritti ghatak bhautik matra mein bhinn hoti haye-udaaharan key liye ack voltage sanket-ell. tii. aaee. pranali input parr dikhaai detaa haye, usa samay taka jaba usee aavritti ghatak kii ack prati-shayed ack alag bhautik ghatana kii-ell. tii. aaee. pranali output parr dikhaai detee haye.
aavritti key ack kaary key roop mein ack alag charan pratikriya, jisase samooh deree aur charan deree kii ganana kii jaa sakati haye, aamtaur parr microphone, emplifier, loudspeaker, chumbakiya recorder, headphone, samakshiya cable aur antialiasing filter jaise upkaranon mein hoti haye. sanket key sabhi aavritti ghatakon mein deree hoti haye jaba aise upkaranon key madhyam seey paarit kiya jaataa haye, yaa jaba antariksh yaa madhyam key madhyam seey prasaar kiya jaataa haye, jaise kii havaa yaa paani. 
jabaki ack charan pratikriya koniya ikaaiyon (jaise degree yaa radian) mein charan parivartan kaa varnan karati haye, charan deree samay kii ikaaiyon mein hoti haye aur pratyek aavritti parr charan parivartan key nakaratmak key barabar hoti haye jise usa aavritti key moolya seey vibhajit kiya jaataa haye. samooh vilamb aavritti key sambandh mein charan parivartan kaa nakaratmak vyutpann haye. 
charan vilamb.
ack raikhik samay-parivartansheel pranali yaa upkaran mein ack charan pratikriya guna aur ack charan vilamb guna hotaa haye, jahan ack kii ganana dusare seey thheek kii jaa sakati haye. charan vilamb seedhe sthir sthiti mein vyaktigat "signsoidal" aavritti ghatakon key upkaran yaa pranali samay vilamb koo maapata haye. yadi kissy bhee dee gaee aavritti parr charan vilamb kaary-byaaj kii aavritti seema key bheetar-ack chayanit aavritti parr charan aur chayanit aavritti key beach samanupatita kaa sthiraank haye, tou pranali/upkaran mein raikhik charan kaa aadarsh hoga, jisake parinamswarup ack nirantar samooh vilamb hoga. choonki charan vilamb aavritti dene kaa ack kaary haye, isaliye isake kaary graph kii sapaatata seey prasthaan vibhinn sanket aavritti ghatakon key beach samay deree key antar koo prakat curr sakata haye, iss mamle mein way antar sanket viroopan mein yogdan denge, joe output sanket tarang key roop mein prakat hotaa haye.
samooh vilamb.
jabaki charan vilamb sthir avastha signsoidal ghatakon key liye pranali kii pratikriya kaa varnan kartaa haye, samooh vilamb ayam modulated signsoids key liye pratikriya kaa varnan kartaa haye.
samooh vilamb ack modulan pranali mein aavritti key sambandh mein charan kii raikhikta kaa ack suvidhajanak upaay haye. ack modulan sanket (passband sanket) key liye, sanket dwara leey jaaee gaee jaankaari vishesh roop seey tarang lifafe mein leey jaaya jaataa haye. isaliye samooh vilamb kewal lifafe seey praapt aavritti ghatakon key saath sanchaalit hotaa haye.
buniyaadi modulan pranali.
ack upkaran key samooh kii deree kii ganana upkaran kii charan pratikriya seey kii jaa sakati haye, lekin isake vipareet naheen.
samooh vilamb key liye sabse saral upayog kaa mamla chitra 1 mein darshaaya gayaa haye joe ack vaichaarik modulan pranali koo darshaata haye, joe swayam ack baseband output key saath ack ell. tii. aaee. pranali haye joe aadarsh roop seey baseband signal input kii ack sateek prati haye. iss pranali koo yahaan baahari ell. tii. aaee. pranali/upkaran key roop mein sandarbhit kiya gayaa haye, jisamen ack aantarik (laal khand) ell. tii. aaee. pranali/upkaran hotaa haye. jaisa kii aksar ack radio pranali key liye hotaa haye, anjir 1 mein aantarik laal ell. tii. aaee. pranali cascade mein dou ell. tii. aaee. pranaliyon kaa pratinidhitva curr sakati haye, udaaharan key liye ack emplifier bhejane vaale chhor parr ack sanchaarak antina chalaa rhaa haye aur doosara ack antina aur praapt karane vaale chhor parr emplifier.
ayam modulan.
ayam modulan aadhar-patti aavritti ghatakon koo bahut adhik aavritti seema mein sthanantarit karke passband sanket banaata haye.  halanki aavrittiyaan alag-alag hoti hain, passband sanket baseband sanket key samaan jaankaari rakhta haye. demodulator vyutkram kartaa haye, passband aavrittiyon koo mool baseband aavritti seema mein vaapas sthanantarit kartaa haye. aadarsh roop seey, output (baseband) signal input (baseband) signal kaa ack samay vilambit sanskaran haye jahaan output kaa tarang aakar input key samaan hotaa haye.
chitra 1 mein, baahari pranali charan deree saarthak pradarshan metrick haye. "ayam modulan key liye, aantarik laal ell. tii. aaee. upkaran samooh kii deree baahari ell. tii. aaee. upkaran charan kii deree bunn jaati haye. yadi aantarik laal upkaran samooh kii deree ruchi kii aavritti seema mein poori tarah seey sapaat haye, tou baahari upkaran mein ack charan deree kaa aadarsh hoga joe poori tarah seey sapaat bhee haye, jahaan baahari ell. tii. aaee. upkaran kii charan pratikriya key kaaran vikriti kaa yogdan-poori tarah seey aantarik upkaran kii sambhavatah alag charan pratikriya dwara nirdhaarit-samaapt hoe jaataa haye. usa sthiti mein, aantarik laal upkaran kii samooh deree aur baahari upkaran kii charan deree, aadhar-patt input seey aadhar-patt output taka, poore sanket key liye samaan samay deree kaa aankada detee haye. yeh dhyaan rakhna mahatvapurna haye kii aantarik (laal) upkaran key liye bahut hii gair-sapaat charan deree (lekin sapaat samooh deree) honah sambhav haye, jabaki baahari upkaran mein poori tarah seey sapaat charan deree kaa aadarsh haye.  yeh bhagyashali haye kyonki ell. tii. aaee. upkaran key design mein, ack sapaat samooh deree koo ack sapaat charan deree kii tulanaa mein praapt karna aasaan haye.
konn modulan.
ack konn-modulan pranali mein-jaise aavritti modulan (fm) yaa charan modulan (pm) key saath-ack lti pranali input parr lagu (fm yaa pm) passband sanket kaa vishleshan dou alag-alag passband sanketon key roop mein kiya jaa sakata haye, ack inn-phase (i) ayam modulan aim passband sanket aur ack quadrature-phase (kyu) ayam modulan aim passband sanket, jahaan unakaa yog mool konn-modulan (fm yaa pm) passband sanket kaa thheek seey punarnirmaan kartaa haye. jabaki (aff. aim./pee. aim.) passband sanket ayam modulan naheen haye, aur isaliye koee spasht baahari lifafa naheen haye, aaee aur kyu passband sanketon mein vaastav mein ayam modulan lifafe hain. (haalaanki, niyamit ayam modulan key vipareet, i aur q lifafe baseband sanketon key tarang aakar seey milate-julate naheen hain, bhale hii 100 pratishat baseband sanket koo unake lifaafon dwara jatil tareeke seey darshaaya jaataa haye.) tou, pratyek i aur q passband sanketon key liye, ack sapaat samooh deree yeh sunishchit karati haye kii naa tou i paas baind lifafa aur naa hii q passband lifafa mein tarang aakar vikriti hogi, isaliye jaba i passband sanket aur q passband sanket koo ack saath jodaa jaataa haye, tou yog mool fm/PM passband sanket haye, joe bhee aparivartit hoga.
siddhant.
ell. tii. aaee. pranali siddhant (niyantran siddhant aur digital yaa analogue sanket prasanskaran mein upayog kiya jaataa haye) key anusaar, ack ell. tii. aaee. pranali key output sanket sootra _ 2 koo ell. tii. aaee. pranali key samay-domen aaveg pratikriya sootra _ 3 koo input sanket sootra _ 4 key saath jodkar nirdhaarit kiya jaa sakata haye.
jahan sootra _ 6 convolution operation koo darshaata haye, sootra _ 7 aur sootra _ 8 kramshah input sootra _ 4 key lapless parivartan hain aur aaveg pratikriya sootra _ 3, jatil aavritti haye, aur sootra _ 11 vyutkram lapless parivartan haye. sootra _ 8 koo ell. tii. aaee. pranali kaa sthanantaran kaary kahaa jaataa haye aur aaveg pratikriya sootra _ 3 kii tarah, "poori tarah seey" ell. tii. aaee. pranali kii input-output visheshtaon koo paribhaashit kartaa haye. iss convolution kaa mulyankan samay kshetra mein abhinn abhivyakti kaa upayog karke kiya jaa sakata haye, yaa (sabse sahee abhivyakti key anusaar) lapless kshetra mein gunan kaa upayog karke aur phir samay kshetra mein lautane key liye vyutkram parivartan koo lagu karke kiya jaa sakata haye.
lahar paiket key liye ell. tii. aaee. pranali pratikriya.
maan leejiye kii aisee pranali ack tarang paiket dwara sanchaalit haye joe ack sinusoid dwara ack ayam lifafa sootra _ 14 dwara gunaa kiya jaataa haye, isaliye input sootra _ 4 koo nimnalikhit roop mein vyakt kiya jaa sakata haih
yeh bhee maan leejiye kii lifafa sootra _ 17 dheere-dheere signsoid key aavritti sootra _ 18 key saapeksh badal rhaa haye. iss sthiti koo ganitiya roop seey iss prakaar vyakt kiya jaa sakata haih
pahale key convolution sameekaran koo lagu karane seey pataa chalega kii iss tarah kii ell. tii. aaee. pranali kaa utpaadan bahut achchi tarah seey anumaanit haih
yahaan sootra _ 21 samooh vilamb haye aur sootra _ 22 charan vilamb haye, aur way neeche diye gaye abhivyaktiyon dwara diye gaye hain (aur sambhaavit roop seey koniya aavritti sootra _ 18 key kaary hain). signsoid kaa charan, jaisa kii shoonya crossing kii sthiti seey sanket milata haye, samay mein charan deree key barabar raashi seey vilambit hotaa haye, sootra _ 22. signsoid kaa lifafa samooh deree, sootra _ 21 dwara samay mein vilambit hotaa haye.
samooh vilamb aur charan vilamb kii ganitiya paribhasha.
samooh vilamb, sootra _ 21, aur charan vilamb, sootra _ 22, (sambhaavit roop seey) aavritti-nirbhar hain aur unrapped charan shift sootra _ 28 seey ganana kii jaa sakati haye. pratyek aavritti parr charan vilamb usa aavritti key moolya seey vibhajit usa aavritti parr charan shift key nakaratmak key barabar haih
pratyek aavritti parr samooh kii deree "dhalaan" (i.) key nakaratmak key barabar hoti haye.ee. usa aavritti parr charan kaa aavritti key sambandh mein vyutpann):
ack raikhik charan pranali mein (gair-vyutkram laabh key saath), sootra _ 21 aur sootra _ 22 donon sthir hain (i.ee.sootra _ 18 seey swatantra aur samaan, aur unakaa samanya moolya pranali kii samagr deree key barabar haye; aur pranali kaa unrapped charan shift (arthaat sootra _ 34) nakaratmak haye, jisamen aavritti sootra _ 18 key saath raikhik roop seey parimaan badh rhaa haye.
jatil signsoid key liye ell. tii. aaee. pranali pratikriya.
adhik aam taur parr, yeh dikhaaya jaa sakata haye kii ikai ayam key ack jatil signsoid dwara sanchaalit sthanantaran falan sootra _ 8 key saath ack ell. tii. aaee. pranali key liye,
utpaadan haye
jahan charan parivartan sootra _ 39 haye
nakaratmak samooh deree.
filters mein aavritti shreniyon parr "nakaratmak" samooh deree hogi jahaan isaki charan pratikriya sakaratmak-dhalaan vaali haye. yadi koee sanket kuchh adhikatam aavritti bee key bheetar baind-seemit haye, tou yeh ack chhoti degree (samay avadhi seey chhoti avadhi key bheetar) key liye anumaanit haye. ack filter jiska samooh vilamb usa sanket kii poori aavritti seema parr nakaratmak haye, ack gair-kaaran samay agrim kaa bhram pradaan karane key liye sanket kii bhavishyavani kaa upayog karane mein saksham haye. haalaanki, yadi sanket mein ack apratyaashit ghatana hoti haye (jaise kii ack achaanak parivartan joe sanket key spectrum koo apani baind-seema seey adhik banaata haye), tou bhram toot jaataa haye. nakaratmak samooh vilamb key saath paripath (ee.jee., chitra 2) sambhav haye, halanki karyakaran kaa ullanghan naheen kiya gayaa haye.
nakaratmak samooh vilamb filter digital aur analogue donon domen mein banaae jaa sakate hain. anuprayogon mein nimn-paas filters kii antarnihit deree kii bharpai karna, "shoonya charan" filter banaana shamil haye, jiska upayog samvedak detta yaa stock kimaton key rujhaanon mein parivartanon kaa jaldi seey pataa lagaane key liye kiya jaa sakata haye.
audio mein samooh deree.
samooh vilamb kaa audio kshetra mein aur vishesh roop seey dhwani prajanan kshetra mein kuchh mahatva haye. audio prajanan shrinkhala key kaee ghatak, vishesh roop seey loudspeaker aur multiway loudspeaker crossover network, audio signal mein samooh deree kaa parichay dete hain. isaliye aavritti key sambandh mein samooh deree kii shravan kshamata kii seema koo jaanana mahatvapurna haye, vishesh roop seey yadi audio shrinkhala uchch nishtha prajanan pradaan karati haye. shravyata talika kii sabse achchi seemaaen bloart aur kaanoonon dwara pradaan kii gaee hain.
flangun, moor aur stone kaa nishkarsh haye kii 1,2 aur 4 kilohertz parr, lagbhag 1.6 ms kii ack samooh deree ack gair-reverberent sthiti mein headphone key saath sunai detee haye. anya prayogaatmak parinam bataate hain kii jaba samooh kii aavritti seema 300 heartz seey 1 heartz taka 1 ms seey cumm hoti haye, tou yeh ansuna hotaa haye.
kissy bhee sanket key tarang roop koo thheek ack pranali dwara punah prastut kiya jaa sakata haye jisamen ack sapaat aavritti pratikriya hoti haye aur sanket kii bandwidth parr samooh deree hoti haye. leach ney vibhedak samay-vilamb viroopan kii avadharana kii shuruat kii, jise charan vilamb aur samooh vilamb key beach key antar key roop mein paribhaashit kiya gayaa haih
ack aadarsh pranali koo shoonya yaa nagany antar samay-vilamb vikriti pradarshit karni chaahiye.
multy-way loudspeaker system mein crossover network key upayog key kaaran utpann honey vaale samooh deree vikriti koo thheek karane key liye digital signal processing takneekon kaa upayog karna sambhav haye. isamen park-mcclellan phir equirple filter design algorithm kaa upayog karke deree barabari koo safaltapurvak lagu karane key liye loudspeaker pranaliyon kaa kaafee computational modeling shamil haye.
prakashiki mein samooh vilamb.
samooh vilamb bhautiki mein mahatvapurna haye, aur vishesh roop seey prakashiki mein.
ack optical fiber mein, samooh deree optical shakti key liye aavashyak pargaman samay haye, joe ack diye gaye mode key samooh wegg parr yatra karate hue, ack dee gaee doori kii yatra karane key liye aavashyak haye. optical fiber failaav maap uddeshyon key liye, byaaj kii matra prati ikai lambai mein samooh deree haye, joe ack vishesh mode key samooh wegg kaa parasparik haye. ack optical fiber key madhyam seey ack sanket kii maapi gaee samooh deree fiber mein maujood vibhinn failaav tantra key kaaran ack tarang dairdhya nirbharta pradarshit karati haye.
samooh key liye sabhi aavrittiyon mein nirantar deree karna aksar vaanchhaniya hotaa haye; anyatha sanket kaa asthaayi smearing hotaa haye. kyonki samooh vilamb sootra _ 42 haye, isaliye yeh iss prakaar haye kii ack sthir samooh vilamb praapt kiya jaa sakata haye yadi upkaran yaa madhyam key sthanantaran kaary mein ack raikhik charan pratikriya (i.ee.sootra _ 43 jahan samooh vilamb sootra _ 44 ack sthiraank haye). charan kii araikhikta kii degree samooh key vilamb key ack sthir moolya seey vichalan koo ingit karati haye.
sahee samay mein deree.
ack sanchaaran upkaran koo "sahee samay deree" (tii. tii. dee.) kahaa jaataa haye yadi samay deree vidyut sanket kii aavritti seey swatantra haye. tii. tii. dee. ack vyaapak twarit sanket bandwidth key liye anumati detaa haye jisamen lagbhag koee sanket vikriti naheen hoti haye jaise kii spandit sanchaalan key dauran puls kaa vistaar.
tii. tii. dee. haani rahit aur cumm haani, failaav mukt, sancharan lines kii ack mahatvapurna visheshta haye. yeh pataa chalata haye kii ack vitarit preran aur dhaarita key liye sanket sootra _ 45 kii gati seey unake madhyam seey prasaarit hotey hain. isaliye, rekha key madhyam seey kissy bhee sanket key prasaar mein deree iss gati seey vibhajit rekha kii lambai key barabar hoti haye.