
sthanantaran kaary

engineering mein, ack pranali, upa-pranali yaa ghatak kaa ack sthanantaran kaary (jise pranali kaary yaa network kaary key roop mein bhee jaanaa jaataa haye) ack ganitiya kaary haye joe pratyek sambhaavit input key liye pranali key output kaa model banaata haye. inca vyaapak roop seey electronic engineering upkaranon jaise circuit simulator aur niyantran pranaliyon mein upayog kiya jaataa haye. kuchh saral mamalon mein, iss kaary koo ack swatantra scalar input banaam aashrit scalar output key dou-ayami graph key roop mein darshaaya jaa sakata haye, jise sthanantaran vakr yaa visheshta vakr kahaa jaataa haye. ghatakon key liye sthanantaran karyon kaa upayog ghatakon seey ikattha kiye gaye pranaliyon koo design aur vishleshan karane key liye kiya jaataa haye, vishesh roop seey electronics aur niyantran siddhant mein block aarekh takneek kaa upayog karate hue.
sthanantaran kaary model key ayam aur ikaaiyaan sambhaavit input kii ack shrinkhala key liye upkaran kii output pratikriya. udaaharan key liye, ack emplifier kii tarah dou-port electronic circuit kaa sthanantaran kaary input parr lagu scalar voltage key kaary key roop mein output parr scalar voltage kaa dou-ayami graph hoe sakata haye; ack electromechanical actuator kaa sthanantaran kaary upkaran parr lagu vidyut dhaara key kaary key roop mein chala bhuja kaa yaantrik visthaapan hoe sakata haye; ack photodetector kaa hastaantaran kaary diye gaye tarang dairdhya key aapatit prakaash kii chamakdaar teevrata key kaary key roop mein output voltage hoe sakata haye.
sthanantaran falan" shabd kaa upayog lapless parivartan jaise parivartan vidhiyon kaa upayog karke pranaliyon key aavritti kshetra vishleshan mein bhee kiya jaataa haye; yahaan iska arth haye input sanket kii aavritti key kaary key roop mein utpaadan kaa ayam. udaaharan key liye, ack electronic filter kaa sthanantaran kaary output parr voltage ayam haye joe input parr lagu sthir ayam saain tarang kii aavritti key kaary key roop mein hotaa haye. optical imaging upkaranon key liye, optical transfer function bindu prasaar function kaa fourier parivartan haye (isaliye sthaanik aavritti kaa ack kaary).
raikhik samay-parivartansheel pranaaliyan.
hastaantaran karyon kaa upayog aamtaur parr sanket prasanskaran, sanchaar siddhant aur niyantran siddhant key kshetron mein ekal-input ekal-output filter jaise pranaliyon key vishleshan mein kiya jaataa haye. iss shabd kaa upayog aksar vishesh roop seey raikhik samay-parivartansheel (ell. tii. aaee.) pranaliyon koo sandarbhit karane key liye kiya jaataa haye. adhikansh vaastavik pranaliyon mein gair-raikhik input/output visheshataaen hoti hain, lekin kaee pranaliyon mein, jaba nammatra key maapdandon key bheetar sanchaalit kiya jaataa haye ("adhik-sanchaalit" naheen) tou vyavhaar raikhik key kaafee karib hotaa haye kii ell. tii. aaee. pranali siddhant input/output vyavhaar kaa ack sweekarya pratinidhitva haye.
neeche diye gaye vivaran ack jatil charr, sootra _ 1 key sandarbh mein diye gaye hain, joe ack sankshipt spashteekaran detaa haye. kaee anuprayogon mein, sootra _ 2 (iss prakaar sootra _ 3) koo paribhaashit karna paryaapt haye, joe vaastavik tark ω key saath jatil tarkon key saath lapless parivartan koo forier parivartan mein cumm curr detaa haye. anuprayog jahan yeh aam haye way hain jahan kewal ack ell. tii. aaee. pranali kii sthir-sthiti pratikriya mein ruchi haye, naa kii kshanik modd-onn aur modd-off vyavhaar yaa sthirata key muddon mein. yeh aamtaur parr sanket prasanskaran aur sanchaar siddhant key liye mamla haye.
iss prakaar, nirantar-samay input sanket sootra _ 4 aur output sootra _ 5 key liye, sthanantaran falan sootra _ 6 input key lapless parivartan kaa raikhik maanchitran haye, sootra _ 7, output sootra _ 8 key lapless parivartan key liyeh
yaa
asatat-samay pranaliyon mein, ack input sanket sootra _ 4 aur output sootra _ 5 key beach key sambandh koo z-parivartan kaa upayog karke nipata jaataa haye, aur phir sthanantaran kaary koo isi tarah sootra _ 13 key roop mein likhaa jaataa haye aur ise aksar puls-hastaantaran kaary key roop mein sandarbhit kiya jaataa haye.
vibhedak samikaranon seey pratyaksh vyutpatti.
sthir gunank key saath ack raikhik vibhedak sameekaran parr vichaar karein
jahan "u" aur "r" "t" key upayukt roop seey chikane kaary hain, aur "l" praasangik kaary sthaan parr paribhaashit prachaalak haye, joe "u" koo "r" mein badal detaa haye. usa tarah key sameekaran kaa upayog "forcing" function "r" key sandarbh mein output function "u" koo baadhit karane key liye kiya jaa sakata haye. sthanantaran falan kaa upayog ack prachaalak sootra _ 15 koo paribhaashit karane key liye kiya jaa sakata haye joe "l" key sahee vyutkram key roop mein kaary kartaa haye, jiska arth haye kii sootra _ 16.
sajaatiya", sthir-gunank avkal sameekaran sootra _ 17 key samadhan sootra _ 18 kaa prayaas karke paae jaa sakate hain. kii pratisthaapan seey visheshta bahupad praapt hotaa haye.
inhomogenous cases koo aasaani seey hull kiya jaa sakata haye yadi input function "r" bhee formula _ 20 kaa haye. usa mamle mein, formula _ 21 koo pratisthaapit karke, aggar humm usa formule _ 22 koo paribhaashit karate hain tou vaha sootra mill jaataa haye.
ise sthanantaran kaary kii paribhasha key roop mein lene key liye jatil banaam jatil key beach saavdhaanipoorvak aspashtata kii aavashyakta hoti haye. vaastavik moolya, joe paaramparik roop seey laabh key roop mein abbs ("aich" ("aiss")) aur charan antaral key roop mein-atton ("aich" ("aiss")) kii vyakhya seey prabhaavit hotey hain. sthanantaran falan kii anya paribhashaon kaa upayog kiya jaataa haih udaaharan key liye sootra _ 24
laabh, kshanik vyavhaar aur sthirata.
aavritti sootra _ 25 kii pranali key liye ack samanya signsoidal input sootra _ 26 likhaa jaa sakata haye. samay sootra _ 27 seey shuru honey vaale signsoidal input key liye ack pranali kii pratikriya mein sthir-sthiti pratikriya aur ack kshanik pratikriya kaa yog hoga. sthir-avastha pratikriya anant samay kii seema mein pranali kaa utpaadan haye, aur kshanik pratikriya pratikriya aur sthir avastha pratikriya key beach kaa antar haye (yeh uparokt vibhedak sameekaran key sajaatiya samadhan seey mell khaati haye). ack ell. tii. aaee. pranali key liye sthanantaran kaary koo utpaad key roop mein likhaa jaa sakata haih
jahan "spi" visheshta bahupad key "n" mool hain aur isaliye sthanantaran falan key dhruv honge. ekal dhruv sootra _ 29 key saath ack sthanantaran falan key mamle parr vichaar karein jahaan sootra _ 30. ikai ayam key samanya signsoid kaa lapless parivartan sootra _ 31 hoga. output kaa lapless parivartan sootra _ 32 hoga aur laukik output usa falan kaa vyutkram lapless parivartan hogaah
ansh mein doosara pada kshanik pratikriya haye, aur anant samay kii seema mein yeh anant mein badal jaayega yadi "σp" sakaratmak haye. ack pranali key sthir honey key liye, isake sthanantaran kaary mein koee dhruv naheen honah chaahiye jisake vaastavik bhaag sakaratmak houn. yadi sthanantaran kaary sakhti seey sthir haye, tou sabhi dhruvon key vaastavik bhaag nakaratmak honge, aur kshanik vyavhaar anant samay kii seema mein shoonya hoe jaayega. sthir-avastha utpaadan hogaah
pranali kii aavritti pratikriya (yaa "laabh") "g" koo sthir-avastha input ayam key liye utpaadan ayam key anupaat key nirpeksh moolya key roop mein paribhaashit kiya gayaa haih
joe kii sootra 37 parr mulyankan kiye gaye sthanantaran falan sootra _ 36 kaa kewal poorna moolya haye. iss parinam koo kissy bhee sankhya mein sthanantaran falan dhruvon key liye maanya dikhaaya jaa sakata haye.
sanket prasanskaran.
maan leejiye kii sootra _ 38 ack samanya raikhik samay-parivartansheel pranali key liye input haye, aur sootra _ 39 output haye, aur sootra _ 38 aur sootra _ 39 kaa dwaipaakshik laplas parivartan hoga.
taba output sthanantaran falan sootra _ 36 dwara input seey sambandhit haye
aur isaliye sthanantaran kaary swayam haye
vishesh roop seey, yadi ayam sootra _ 46 key saath ack signsoidal ghatak key saath ack jatil harmonic sanket, koniya aavritti sootra _ 47 aur charan sootra _ 48, jahaan aarg tark haye.
ack raikhik samay-parivartansheel pranali mein input haye, phir output mein sambandhit ghatak haih
dhyaan dein kii, ack raikhik samay-parivartansheel pranali mein, input aavritti sootra _ 52 naheen badala haye, kewal system dwara signsoid kaa ayam aur charan konn badal diyaa gayaa haye. aavritti pratikriya sootra _ 53 pratyek aavritti sootra _ 52 key liye "laabh" key sandarbh mein iss parivartan kaa varnan kartaa haih
aur "charan parivartan":
charan vilamb (i.ee.sthanantaran falan dwara signsoid mein shuru kii gaee deree kii aavritti-nirbhar raashi) haih
samooh vilamb (i.ee., sthanantaran falan dwara signsoid key lifafe mein shuru kii gaee deree kii aavritti-nirbhar raashi) koniya aavritti sootra _ 52 key sambandh mein charan parivartan key vyutpann kii ganana karke paaee jaati haye,
sthanantaran kaary koo forier parivartan kaa upayog karke bhee dikhaaya jaa sakata haye joe usa mamle key liye kewal ack vishesh mamla haye jahaan sootra _ 60 haye.
samanya sthanantaran kaary parivaar.
jabaki kissy bhee ell. tii. aaee. pranali koo kissy sthanantaran kaary yaa kissy anya dwara varnit kiya jaa sakata haye, vishesh hastaantaran karyon key kuchh "parivaar" hain joe aamtaur parr upayog kiye jaate hain.
kuchh samanya sthanantaran kaary parivaar aur unaki vishesh visheshtaen hainh
engineering koo niyantrit karein.
niyantran engineering aur niyantran siddhant mein sthanantaran kaary koo lapless parivartan kaa upayog karke praapt kiya jaataa haye.
sthanantaran kaary shaastriya niyantran engineering mein upayog kiya jaane vaalaa praathamik upkaran thaa. haalaanki, yeh bahu-input bahu-output (mimo) pranaliyon key vishleshan key liye bhaari saabit huaa haye, aur iss tarah kii pranaliyon key liye raajya sthaan pratinidhitva dwara kaafee hudd taka pratisthaapit kiya gayaa haye. isake bavjood, kissy bhee raikhik pranali key liye ack sthanantaran matricks hamesha praapt kiya jaa sakata haye, taaki isaki gatishilata aur anya gunon kaa vishleshan kiya jaa sakeh ack sthanantaran matricks kaa pratyek tatva ack vishesh input charr seey sambandhit ack sthanantaran kaary haye.
haward aich dwara ack upayogi pratinidhitva bridging state space aur transfer function vidhiyon kaa prastaav kiya gayaa thaa. rosenbrock aur ise rosenbrock system matricks key roop mein sandarbhit kiya jaataa haye.
prakashiki.
prakashiki mein, modulan sthanantaran kaary prakaashik vipareet sancharan kii kshamata koo ingit kartaa haye.
udaaharan key liye, jaba ack vishisht sthaanik aavritti key saath kheenche gaye kaale-safed-prakaash kinaaron kii ack shrinkhala kaa avalokan kiya jaataa haye, tou chhavi kii gunavatta kshay hoe sakati haye. safed kinare feeke parh jaate hain jabaki kaale kinare adhik chamkile hoe jaate hain.
ack vishisht sthaanik aavritti mein modulan hastaantaran kaary dwara paribhaashit kiya jaataa haye
jahan modulan (aim) kii ganana nimnalikhit chhavi yaa prakaash chamak seey kii jaati haih
imaging.
imaging mein, sthanantaran karyon kaa upayog drishya prakaash, chhavi sanket aur pradarshit prakaash key beach sambandh kaa varnan karane key liye kiya jaataa haye.
gair-raikhik pranaaliyan.
kaee gair-raikhik pranaliyon key liye sthanantaran kaary thheek seey maujood naheen hain. udaaharan key liye, way vishram ausilator key liye maujood naheen hain; haalaanki, karyon kaa varnan karane key liye kabhi-kabhi aisee gair-raikhik samay-parivartansheel pranaliyon kaa anuman lagaane key liye upayog kiya jaa sakata haye.

