\yeebtry Lnjfatanjs aj Cnurabr \brabs OIVB \tufy Eitbraik aj TFC Aj tmb prbvanus OIVB stufy eitbraik kbirjt tmb `isals ijf prnpbrtabs nc Cnurabr \brabs. Aj tmbsb
, wb wakk kbirj i`nut tmb
Vmbsb stufy eitbraik lnvbrs bvbrytmajo tmit as jblbssiry cnr
,
is wbkk is ntmbr bxies kahb A\PN, AB\, @IPL, @\JK, FPFN btl. Vmbsb jntbs lij iksn `b
sn tmit ynur bxie prbpiritanj as eifb bisy ijf ynu ilb ynur
bxie. Qnu smnukf prn`i`ky on tmrnuom tmb `isals lnvbrbf aj prbvanus irtalkbs, `bcnrb stirtajo ncc watm tmas enfukb. Pblneebjfbf Pbifajo “ Kipkilb Vrijscnres Kaeats, Lnjtajuaty & Faccbrbjtai`akaty Ebij Sikub Vmbnrbes Faccbrbjtaitanj Tirtaik Faccbrbjtaita F accbrbjtaitanj nj Eixaei ijf Eajaei Ebtmnfs nc Ajtboritanj & \tijfirf Ajtboriks Sbltnr Liklukus Sbltnr Ajtboritanj Vaeb \aojiks & \aojik Vrijscnreitanj \tijfirf Vaeb \aojiks \aojik Lkissacalitanj Vypbs nc Vaeb \ystbes Ajtrnfultanj tn Kajbir Vaeb Ajviraijt \ystbes
9|Tiob
Trnpbrtabs nc KVA \ystbes Ajtrnfultanj tn Cnurabr \brabs Trnpbrtabs nc Cnurabr \brabs
Ippkyajo nc syeebtry lnjfatanjs rbfulbs tmb lnepkbxaty aj cajfajo Cnurabr sbrabs nr Cnurabr sbrabs lnbccalabjts. Ac wb mivb tmb hjnwkbfob i`nut tmb syeebtral lnjfatanj nc tmb oavbj saojik, tmbj wb lij farbltky liklukitb sneb lnbccalabjts. Vypbs nc \yeebtrabs aj Lnjtajunus Vaeb \aojiks7 9. Bvbj \yeebtry 0. Nff \yeebtry <. Mikc wivb syeebtry / Pntitanjik syeebtry _b lij jnw sbb mnw at as ippkali`kb tn Vraonjnebtral ijf Bxpnjbjtaik Cnurabr Cnurabr \brabs.
\yeebtry Lnjfatanjs aj Vraonjnebtral Cnurabr \brabs Bvbj \yeebtry Ac x(t) as ij bvbj pbranfal saojik, tmbj
i V9 xtft V0 xtft ⁆ i V6 xt lnsjρtft ij 0V V xtlnsjρ4tft ⁆ & ` 4 ρ ρ ijf ∨nff saojikft4
Vmas as `bliusb lns(j Bvbj ß Nff 5 Nff
4t)
as ij bvbj saojik wmakb saj(e
4t)
as nff saojik. _b hjnw tmit-
Vmbrbcnrb, Vmbrbcnrb, cnr bvbry bvbj saojik ` j 5 4. Mbjlb, Cnurabr \brabs nc ij bvbj saojik lnjtiajs FL tbre ijf lnsajb tbres njky.
Nff \yeebtry Ac x(t) as ij nff cujltanj tmbj
i V9 xtft V9 nff saojik ft 4
0|Tiob
i V0 xtlns xtlnsjρtft 4 ∲nff4 ` V0 xt.sajjρtft Mbjlb,` V6 xt sajjρtft ⁆ is ∨ bvbj0 ∨⁆ bvbj _b hjnw tmit, nff ß nff 5 bvbj
Vmbrbcnrb, Vmbrbcnrb, cnr bvbry nff saojik i 4 5 4 ijf ij 5 4. Mbjlb, Cnurabr sbrabs lnjtiajs njky sajb tbres.
Mikc-_ivb \yeebtry Jnw, i saojik x(t) as mikc wivb syeebtral ac
xt “ x t ¹ V0
_mbrb V as tmb cujfiebjtik pbranf nc tmb saojik.
Mikc wivb syeebtry as fbcajbf njky cnr pbranfal saojiks. Cnr ajstijlb,
I mikc syeebtral pbranfal saojik wivbcnre
<|Tiob
Trbvanus saojik ictbr mikc nc taeb pbranf
Bxiepkb 97 x(t) 5 I saj( nt). Lmblh tmb syeebtry nc tmas saojik.
ρ
_ivbcnre watm mikc wivb syeebtry
\nkutanj7
Mikc syeebtral wivbcnre ictbr mikc taeb pbranf
6|Tiob
V x(t ¹ V⁆0) I saj saj ρ t¹ t ¹ IIsajρ saj sajρtt¹ τ
\n tmas saojik as mikc wivb syeebtral. Ac x(t) as mikc wivb syeebtral tmbj ats Cnurabr sbrabs lnjtiajs nff mirenjals njky. Nff mirenjals irb 4 4 4
“ ρ , <ρ , 2ρ , ……
Bxiepkb 07 Cajf VC\ cnr tmb cnkknwajo saojik
\nkutanj7
V V I 8 ⁆ ; t ; 6 xt I 8 V⁆0 ;t;⁆6V⁆6 ijf V⁆6; t ; V⁆0 xt i + ∙5√ i lns lnsjρt + ` sajjρt
\ajlb, x(t) as bvbj syeebtral. Vmbrbcnrb, `j 5 4 \ajlb, x(t) as syeebtral i`nut mnraznjtik mnraznjtik ixas. Vmbrbcnrb, ivbriob nc x(t) as zbrn. Mbjlb, FL tbre i 4 5 4 Vmbrbcnrb,
xt ∙5√ i lnsjρt i ∨ xtlnsjρ lnsjρtft ∨⁆ xtlnsjρ lnsjρtft ⁆ ⁆ ⁆ {∨ I lnsjρtft+ ∨⁆ I lnsjρt ft} + + ⁆ ⁆ 2|Tiob
i sajjρt|⁆ saj sajjρt|⁆⁆ sajsaj(jρ V⁆0) + saj(jρ V⁆6) \ajlb,V ⇐ ρV0τ i saj saj +saj i X0saj sajτjU sajτj τj 4 i .0saj i saj xt ∙5√ √i lns lnsjρt ⇐ xt ∙5 saj lnsjρt xt sajlns lnsρt + sajτ lns lns0ρt + saj lns lns<ρt xt lnsρt lns<ρt + lns2ρt ………
Maffbj \yeebtry Vmbrb as iksn i pmbjnebjnj likkbf maffbj syeebtry. Vmb syeebtry wmalm as maffbj `y tmb FL lnepnjbjt as hjnwj is maffbj syeebtry. Vmas syeebtry lij `b n`tiajbf `y rbenvajo tmb nccsbt (iffajo nr su`triltajo tmb FL). Ac x(t) mis sneb maffbj syeebtry, tmbj ats Cnurabr sbrabs lnjtiajs FL ijf sajb nr FL ijf lnsajb tbres fbpbjfajo upnj tmb syeebtry. a.b. cnr maffbj nff syeebtry tmb Cnurabr \brabs wakk lnjtiaj FL ijf sajb tbres. Cnr maffbj bvbj syeebtry tmb sbrabs wakk `b mivajo FL ijf lnsajb tbres. Cnr ajstijlb,
3|Tiob
Maffbj FL saojik aj i pbranfal squirb puksb
Nraoajik pbranfal squirb puksb
\yeebtry Lnjfatanjs aj Bxpnjbjtaik Cnurabr \brabs Bvbj \yeebtry
l i, l i0 ijf l∐ i0
Ac x(t) as ij bvbj cujltanj, tmbj `j 5 4 tmbj
a.b. lj 5 l-j
⇐
lj irb rbik Ac x(t) as bvbj saojik, sa ojik, tmbj BC\ lnbccalabjts irb rbik ijf bvbj. Ij bvbj pbranfal saojik lnjtiajs njky FL (ln 4) ijf lnsajb tbres, sn pmisb ijokb wakk `b batmbr zbrn fborbbs nr ¹9=4
∝
≤
Nff \yeebtry Ac x(t) as ij nff saojik, tmbj i4 5 4 ijf ij 5 4 l4 5 4
?|Tiob
l g0` , l∐ g`0 a.b. lj 5 -l-j
⇐ as ikwiys zbrn ijf pmisb ijokb as njky ¹τ lj irb aeioajiry
Ac x(t) as nff, tmbj ats BC\ lnbccalabjts irb aeioajiry ijf nff. Aj tbres nc crbqubjly nc crbqubjly spbltrue ln
Mikc-_ivb \yeebtry
/0.
4∄
Aj tbres nc Cnurabr spbltrue, cnr mikc wivb syeebtral saojik, l j 5 j bvbj. Aj ntmbr wnrf, tmb spbltrue nc i mikc wivb syeebtral saojik lnjtiajs njky nff mirenjals. Mikc wivb syeebtry as fbcajbf njky cnr pbranfal saojiks. Cnr bvbj ijf mikc wivb syeebtral saojiks,
xt xt¹ V0.
Cnr ij bvbj ijf mikc wivb syeebtral saojik, tmb spbltrue sitascabs tmb cnkknwajo lnjfatanjs7 lj 5 4
ijf ∤l
∄ j bvbj
j 5
∝
∝
4 nr 9=4
Cnr nff ijf mikc wivb syeebtral s yeebtral saojiks,
xt xxtt ¹ V0.
Cnr ij nff ijf mikc wivb syeebtral saojik, tmb spbltrue sitascabs tmb cnkknwajo lnjfatanjs7
l 4 ∄ j bvbbvbj,j, ijf ∤ ¹ ∝. lj
=|Tiob
14
_b wakk lnjtajub watm tmb Cnurabr Vrijscnres aj tmb jbxt irtalkb. Faf ynu kahb tmas irtalkb nj \yeebtry Lnjfatanjs aj Cnurabr \brabs> Kbt us hjnw aj tmb lneebjts. Qnu eiy iksn bjgny “
Cnurabr Vrijscnre Trnpbrtabs nc Cnurabr Vrijscnre
1|Tiob
