sayısal İşaret İşleme - sakarya Üniversitesi - sayısal filtre tasarımı

8/10/2019 Sayısal İşaret İşleme - Sakarya Üniversitesi - Sayısal Filtre Tasarımı

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_cyĳsci Nhitrk Pcscrĳdĳ

• _cyĳsci nhitrk tcscrĳdĳg`c cdcå, vkrhikg lhr nrkmcgs ycgĳtĳgĳ ycmicőĳm aicrcm scđicycg ekråkmikgklhihr lhr trcgsnkr nagmshyaguE ( z ) ki`k ktdkmthr.

•

Åađu uyeuicdc`c scyĳsci nhitrkghg tcscrĳdĳ håhg ekgihm vk/vkycncz ycgĳtĳ lkihrthihr. Lczĳ `urudicr`c, hdpuis vkyc lcscdcm ycgĳtĳ

lkihrthiklhihr.

• Zrcthm åađu uyeuicdc`c, vkrhikg lhr ekgihm ycgĳtĳgĳ ycmicőĳm aicrcm scđicycg ekråkmikgklhihr lhr trcgsnkr nagmshyagu ki`kktdkm hstkghr. Lu gk`kgik, lu `krstk lhz sc`kok ekgihmycmicőĳmiĳđĳgĳ kik cicocđĳz.



Nhitrk Mcrcmtkrhsthmikrhghg Lkihrthidksh

• @þrt tùr h`kci nhitrkyk mcrőĳiĳm ekikg hdpuis ycgĳticrĳgĳg gk`kgskiaidc`ĳmicrĳg`cg vk sagsuz uzugiumiu ai`umicrĳg`cg h`kci nhitrkikrekråkmikgkdkz.

•

Zrcthmtk,scyĳsci lhr nhitrkghg ekgihmycgĳtĳ ekåhrdk vk sþg`ùrdk lcg`ĳg`c mclui k`hiklhihr taikrcgsicric lkihrthihr. Cyrĳoc, ekåhrdk vk sþg`ùrdk lcg`icrĳ crcsĳg`c lhr ekåhő lcg`ĳ vcr`ĳr .

• Þrgkđhg, scyĳsci ciåcm ekåhrkg lhr nhitrkghg ekgihmycgĳtĳ |E (k b )|

cőcđĳ`c eþstkrhidhőthr .




p 2 ekåhrdk lcg`ĳ mkgcr nrkmcgsĳ s 2 sþg`ùrdk lcg`ĳ mkgcr nrkmcgsĳ

p 2 ekåhrdk lcg`ĳg`cmh dcmshdud `ciecicgdc s 2 sþg`ùrdc lcg`ĳg`cmh dhghdud `ciecicgdc




• Mcrcmtkrhsthmikr ekgki`k `L aicrcm

C( ) 4 -<:iae 3: |E (k b )|

hiktcgĳdicgcg mcyĳp nagmshyagu ohgshg`kg vkrhihr.

• Lkgzkr őkmhi`k, `L ohgshg`kg ekåhrdk lcg`ĳ dcmshdud`ciecicgdcsĳ p vk sþg`ùrdk lcg`ĳ dhghdud zcyĳnictdcsĳ s

p 4 -<:iae 3: (3- p) s 4 -<:iae 3: ( s)

aicrcm fkscpicgĳr .




Nhitrk mcrcmtkrhsthmikrh citkrgcthn aicrcmcőcđĳ`cmh eþstkrhi`hđh ehlh lkihrthiklhihr. Citkrgcthn eþstkrhihd`k, ekgihđhg ekåhrdk lcg`ĳg`cmh dcmshdud `kđkrhghg 3 ai`uđu vcrscyĳir .



Nhitrk Pùrùgùg _kåhidksh

• Lkihrthikg nrkmcgs ycgĳtĳ þzkiihmikrhgh scđicycg trcgsnkrnagmshyagu F ( z ) gk`kgski lhr trcgsnkr nagmshyagu aidciĳ`ĳr .

• _agsuz hdpuis ycgĳtiĳ (HH\) nhitrk ùrudug`c trcgsnkr nagmshyagu

őkmihg`k ekråki lhr rcsyagki nagmshyagùr. Lu ùrud`c, F ( z )

mcrcriĳ aidcgĳg ycgĳg`c fkscp yùmùgù kg czc hg`hrdkm håhg mùåùm `krkokyk ( G ) scfhp aidciĳ`ĳr .



Nhitrk Pùrùgùg _kåhidksh

• _agiu hdpuis ycgĳtiĳ (NH\) nhitrk ùrudug`c trcgsnkr nagmshyagu

őkmihg`k ekråki mctscyĳiĳ lhr paihgadùr.

• Fkscp mcrdcőĳmiĳđĳgĳg cz aidcsĳ håhg trcgsnkr nagmshyagugug`krkoksh ( G ) dùdmùg aiùđu mc`cr mùåùm aidciĳ`ĳr . F ( z ) mutuphåkrdk`hđhg`kg NH\ nhitrkikrhgmcrcriĳiĳm pralikdh yamtur.

• @ađrusci ncz hstkghyarsc, nhitrk mctscyĳicrĳgĳg f ]gT 4 ∟ f ]G -g Thihőmhshgh scđicdcsĳ ekrkmih`hr.



_cyĳsci Nhitrk Pcscrĳdĳ2 Pkdki Xcmicőĳdicr

• Kg sĳm muiicgĳicg HH\ nhitrktcscrĳd yþgtkdh cőcđĳ`cmh c`ĳdicr`cg aiuőur 2

3. _cyĳsci nhitrk mcrcmtkrhsthmikrh pratathp lhr cgciae ciåcm ekåhrkg nhitrk mcrcmtkrhsthmikrhgk`þgùőtùrùiùr .

<.Cgciae ciåcm ekåhrkg nhitrk tcrcgsnkr nagmshyagu F c( s) lkihrikghr.

?.F c( s), ekrkmihscyĳsci trcgsnkr nagmshyagu E(z)‘yk `þgùőtùrùiùr .

• Lu ycmicőĳdĳg muiicgĳidcsĳgĳg gk`kgikrh őþyik sĳrcicgclhihr 2cgciae nhitrk tcscrĳd yþgtkdikrh ai`umåc ekihődhő aiup ekgki`kcgcihthmåþzùdik saguåicgĳricr . Lu gk`kgik, cgciae nhitrk tcscrĳdĳ håhg tcliaicr dkvouttur. ĺicvk aicrcm, åađu uyeuicdc cgciaeshstkdikrhg scyĳsci shdùicsyagugu ekrkmthrdkmtk`hr.




• ’c— cgciae uzcyĳ lkihrtdkm ùzkrk, cgciae trcgsnkr nagmshyagu

aicrcm lkihrthikokmthr.• F c( s)‘`kg tùrkthikg scyĳsci trcgsnkr nagmshyagu `c cőcđĳ`cmh ehlh

tkdshi k`hikokmthr2

• F c( s), E ( z )‘yk `þgùőtùrdkm, cgciae nrkmcgs ycgĳtĳgĳg tkdkimcrcmtkrhsthmikrh marugcocmőkmhi`k s-uzcyĳg`cg z -uzcyĳgc lhr`þgùőùd uyeuicdcmtĳr . A fci`k, `þgùőùd mcrcriĳ lhr cgciaetrcgsnkr nagmshyagugu mcrcriĳ lhr scyĳsci trcgsnkr nagmshyagugc`þgùőtùrdkih`hr .




• NH\ nhitrk tcscrĳdĳ, lkihrthikg ekgihm ycgĳtĳgĳg `ađru`cg ycmicőĳmiĳđĳgc `cyciĳ`ĳr . Cyrĳoc, ekgki`k nhitrkghg `ađrusci nczcscfhp aidcsĳ hstkghr.

• G . `krkok`kg lhr NH\ nhitrkghg tcscrĳdĳ, yc ( G +3)-uzugiumiuhdpuis ycgĳtĳ mctscyĳicrĳ {f ]gT}, yc `c nrkmcgs ycgĳtĳ |E (k b )|‘gĳg ( G +3) þrgkđh luiugcrcm ycpĳiclhihr . Kg sĳm muiicgĳicg NH\ nhitrktcscrĳd yþgtkdikrh őþyik`hr 2

3. Zkgokrkikgdhő Naurhkr skrhshycmicőĳdĳ <. Nrkmcgsþrgkmikdk ycmicőĳdĳ ?. Lhiehscycr tclcgiĳ apthdhzcsyag yþgtkdikrh



HH\ _cyĳsci Nhitrk Pcscrĳdĳ2 Åhnt @ađrusci @þgù

•

Åhnt `ađrusci `þgùőùd (Å@@) s-uzcyĳg`cmh lhr gamtcyĳ z -uzcyĳg`cmh lhr gamtcyc `þgùőtùrùr vk cőcđĳ`cmh kőhtihmik vkrhihr2

• A fci`k, E ( z ) hik F c( s) crcsĳg`cmh hihőmh őþyik aiur2

• _cyĳsci nhitrk tcscrĳdĳ ùå c`ĳd`cg aiuőur 2 (h) E ( z )‘ghg mcrcmtkrhsthmikrhgk tkrsÅ@@ uyeuicgĳp F c( s)‘ghg mcrcmtkrhsthmikrhki`k k`hihr, (hh) F c( s) lkihrikghr, (hhh) F c( s)‘yk Å@@ uyeuicgĳp E ( z )

lkihrikghr. @þgùőùd nardùiùg`kmh P pcrcdktrkshghg ktmhshaidc`ĳđĳg`cg, ekgki`k P 4 < skåhihr .




•

P 4 < håhg tkrs Å@@ nardùiù maicyiĳmic ki`k k`hiklhihr2

• s 4 : + b : yczĳp, s hik z crcsĳg`c yumcrĳ`c vkrhikg kőhtihmtkg

ki`k k`hihr. : ‘ĳg ncrmiĳ `kđkrikrh håhg z ‘ghg ekgihmikrh cőcđĳ`c vkrhidhőthr .



HH\ _cyĳsci Nhitrk Pcscrĳdĳ2 Åhnt @ađrusci @þgù • Cőcđĳ`c eþstkrhi`hđh ehlh, sai ycrĳ s-`ùzikdh, mcrdcőĳm z -

`ùzikdhg`k lhrhd åkdlkrhg håhgk, scđ ycrĳ s-`ùzikdh lhrhdåkdlkrhg `ĳőĳgc, b -kmskgh `k lhrhd åkdlkrk `þgùődùőtùr .

• s-`ùzikdhg`k mcrcriĳiĳm maőuiu, mutupicrĳg sai ycrĳ s-`ùzikdhg`k, z -`ùzikdhg`k mcrcriĳiĳm maőuiu hskmutupicrĳg lhrhd åkdlkr håhg`k aidcsĳ`ĳr . A fci`k, Å@@ mcrcriĳ lhr cgciae trcgsnkr nagmshyagugumcrcriĳ lhr scyĳsci trcgsnkr nagmshyagugc `þgùőtùrdkmtk`hr .




ŗhd`h `k cgciae nrkmcgs hik scyĳsci nrkmcgs crcsĳg`cmh hihőmhyh

lkihrikykihd. Å@@ hihőmhshg`k (P 4< håhg) s4 b , z 4k b yczĳiĳrsc

luiugur. Lu hnc`k `ùzkgikghrsk, 4 tcg ( /<) ki`k k`hihr vk cőcđĳ`c eþstkrhi`hđh ehlh crcicrĳg`c `ađrusci aidcycg lhr hihőmh vcr`ĳr




Cgciae nrkmcgs hik scyĳsci nrkmcgs crcsĳg`cmh `ađrusci aidcycg hihőmh nrkmcgs kmskghg`k N\KMCG_ LÙMDK_ĺ `kgkg lhr

lazugud aiuőturur . Nrkmcgs lùmdkshghg ktmhsh cőcđĳ`c eþstkrhidhőthr 2




• Þrgkm 2 Cőcđĳ`c vkrhikg ciåcm ekåhrkg Luttkrwartf cgciaetrcgsnkr nagmshyagugu kik ciciĳd2

• F c( s)‘yk Å@@ uyeuicgĳrsc ciåcm ekåhrkg Luttkrwartf scyĳsci

trcgsnkr nagmshyagu ki`k k`hihr2

• ĺnc`k ykgh`kg `ùzkgikghrsk cőcđĳ`cmh hnc`k ki`k k`hihr2



HH\ _cyĳsci Nhitrk Pcscrĳdĳ2 Åhnt @ađrusci @þgù • Þrgkm 2 Åkgthm nrkmcgsĳ >: Fz, ?-`L åkgthm lcg`ekghőihđh Fz

aicg vk 0:: Fz þrgkmikdk nrkmcgsĳg`c åciĳőcg <. `krkok scyĳsci åkgthm nhitrktcscricyciĳd.•

: 4< ϊ (>:/0::)4:.? ϊ , L w4< ϊ (>/0::)4:.:? ϊ ki`k k`hihr. vk μ fkscpicgĳrsc 4:.8:88?, μ4:.;6556; luiugur. Mcrőĳiĳm ekikgtrcgsnkr nagmshyagu hik ekgihm vk nczycgĳticrĳ cőcđĳ`c vkrhidhőthr .



HH\ _cyĳsci Nhitrk Pcscrĳdĳ2 Åhnt @ađrusci @þgù • Þrgkm 2 Cőcđĳ`c vkrhikg mcrcmtkrhsthmikrk scfhpciåcm ekåhrkg

Luttkrwartf scyĳsci nhitrk tcscricyciĳd2 p4:.<; ϊ , s4:.;; ϊ , p4:.; `L, s43; `L.

• ^krhikgikr`kg <4:.3<<:36;, C<4?3.><<555 luiugur. Pkrs Å@@ muiicgĳicrcm mcrőĳiĳm ekikg cgciae nrkmcgsicr

aicrcm ki`k k`hihr. 3/ m vk 3/ m 3

őkmihg`k ki`k k`hihr. @krkok fkscpicgĳrsc luiugur. G 4? skåhihr .




o‘yh fkscpicdcm håhg

kőhtihđh muiicgĳiĳrsc o43.03883;( p)4:.;66306 luiugur. o 4 3 håhg ?. `krkok ciåcm ekåhrkg Luttkrwartf trcgsnkr nagmshyagu

őkmihg`k tcliaicr`c dkvouttur. o4 :.;66306 aicocm őkmhi`k gardciikőthrdk ycpĳiĳrsc ekrkmih cgciae trcgsnkr nagmshyagu

aicrcm luiugur.




F c( s)‘yk Å@@ uyeuicgĳrsc ekrkmihscyĳsci trcgsnkr nagmshyagu ki`k

k`hihr.

E ( z )‘ghg ekgihm vkmczcgå ycgĳticrĳ cőcđĳ`c åhzhidhőhthr .



XE, LE vk L_ HH\ _cyĳsci Nhitrk Pcscrĳdĳ

Lu cdcåic hmhycmicőĳd dkvouttur. ĺmh ycmicőĳdĳg `c `ktcyicrĳ

cőcđĳ`c vkrhidhőthr 2• Lhrhgoh ycmicőĳd

3. Ekrkmih scyĳsci nhitrkE @( z )‘ghg nrkmcgs mcrcmtkrhsthmikrhgkþg

lùmdk uyeuicgcrcm cygĳ tùr cgciae nhitrk F @( s)‘ghg nrkmcgsmcrcmtkrhsthmikrh lkihrikghr.<. F @( s)‘ghg mcrcmtkrhsthmikrh uyeug lhr nrkmcgs̀þgùőùdùyik

pratathp ciåcm ekåhrkg nhitrk F IZ ( s)‘yk `þgùőtùrùiùr .?. Cgciae ciåcm ekåhrkg nhitrk F IZ ( s) tcscricgĳr .

0. ĺmhgoh c`ĳd`c muiicgĳicg nrkmcgs `þgùőùdùgùg tkrshmuiicgĳicrcm F IZ ( s), F @( s)‘yk `þgùőtùrùiùr .

;. F @( s)‘yk Å@@ uyeuicgcrcm ekrkmih scyĳsci nhitrk E @( z ) ki`kk`hihr.

(PK\_ Å@@)




•

ĺmhgoh ycmicőĳd 3. Ekrkmih scyĳsci nhitrkE @( z )‘ghg nrkmcgs mcrcmtkrhsthmikrhgkþg

lùmdk uyeuicgcrcm cygĳ tùr cgciae nhitrk F @( s)‘ghg nrkmcgsmcrcmtkrhsthmikrh lkihrikghr.

<. F @( s)‘ghg mcrcmtkrhsthmikrh uyeug lhr nrkmcgs̀þgùőùdùyik pratathp ciåcm ekåhrkg nhitrk F IZ ( s)‘yk `þgùőtùrùiùr .

?. Cgciae ciåcm ekåhrkg nhitrk F IZ ( s) tcscricgĳr .0. F IZ ( s)‘yk Å@@ `þgùőùd uyeuicgcrcm scyĳsci ciåcm ekåhrkg

trcgsnkr nagmshyagu E IZ ( z ) ki`k k`hihr.

;. _cyĳsci uzcy`c uyeug lhr nrkmcgs `þgùőùdù muiicgĳicrcm E IZ ( z ), ekrkmihscyĳsci nhitrkE @( z )‘yk `þgùőtùrùiùr .

(PK\_ Å@@)



XE, LE vk L_ HH\ _cyĳsci Nhitrk Pcscrĳdĳ • Þrgkm 2 3. ycmicőĳdĳ muiicgcrcm cőcđĳ`cmh mcrcmtkrhsthmikrk scfhp

3. tùr Ofklysfkv HH\ scyĳsci yùmskm ekåhrkg nhitrk tcscricyciĳd2 N p45:: Fz, N s4;:: Fz, p43`L, s4?< `L, N P 4< mFz.

• ĺim þgok, rc`ycg ohgshg`kg lcg` mkgcr nrkmcgsicrĳ fkscpicgĳr 2

• _agrc, þg lùmdkyik mcrőĳiĳm ekikg cgciae nrkmcgsicr luiugur2

• Zratathp ciåcm ekåhrkg cgciae nhitrk håhg Ψ p 4 3 skåhihp hihőmhshg`kg Ψ s 4 3.8><3:; luiugur.

• A fci`k, cgciae ciåcm ekåhrkg nhitrk mcrcmtkrhsthmikrhőþyik ki`kk`hidhő ai`u2 Ψ p 4 3, Ψ s 4 3.8><3:;, p43`L, s4?< `L.




•

Nhitrk tcscrĳdĳg`c muiicgĳicg DCPICL maduticrĳ vk maduticråciĳőtĳrĳicrcm ki`k k`hikg mczcgå ercnhđh cőcđĳ`c vkrhidhőthr .



XE, LE vk L_ HH\ _cyĳsci Nhitrk Pcscrĳdĳ • Þrgkm 2 Cőcđĳ`cmh mcrcmtkrhsthmikrk scfhp Luttkrwartf HH\scyĳsci

lcg` ekåhrkg nhitrk tcscricyciĳd2 ψ p34:.0; ϊ , ψ p<4:.>; ϊ , ψ s34:.? ϊ ψ s<4:.5; ϊ , p43`L, s40: `L.

• Þg lùmdkyik mcrőĳiĳm ekikg cgciae nrkmcgsicr fkscpicgĳr 2

• Lcg`ekghőihđh ai`uđug`cg

aiup åcrpĳdicr kőht aicocm őkmhi`k lcg` mkgcricrĳgĳg `kđhőthrhidksh ekrkmih`hr. _kåhihrsk åcrpĳdicr kőht aiur.



XE, LE vk L_ HH\ _cyĳsci Nhitrk Pcscrĳdĳ • Zratathp ciåcm ekåhrkg cgciae nhitrk håhg Ψ p 4 3 skåhihp

hihőmhshg`kg

• A fci`k, cgciae ciåcm ekåhrkg nhitrk mcrcmtkrhsthmikrhőþyik ki`kk`hidhő ai`u2 Ψ p 4 3, Ψ s 4 <.?>35><5, p43`L, s40: `L.

• Nhitrk tcscrĳdĳg`c muiicgĳicg DCPICL maduticrĳ vk maduticråciĳőtĳrĳicrcm ki`k k`hikg mczcgå ercnhđh cőcđĳ`c vkrhidhőthr .



XE, LE vk L_ HH\ _cyĳsci Nhitrk Pcscrĳdĳ • Þrgkm 2 Cőcđĳ`cmh mcrcmtkrhsthmikrk scfhp kiihpthm HH\scyĳsci lcg`

sþg`ùrkg nhitrk tcscricyciĳd2 ψ p34:.? ϊ , ψ p<4:.5; ϊ , ψ s34:.0; ϊ ψ s<4:.>; ϊ , p43`L, s40: `L.

• Þg lùmdkyik mcrőĳiĳm ekikg cgciae nrkmcgsicr fkscpicgĳr 2

• Lcg`ekghőihđh ai`uđug`cg

aiup åcrpĳdicr kőht aicocm őkmhi`k lcg` mkgcricrĳgĳg `kđhőthrhidksh ekrkmih`hr. _kåhihrsk åcrpĳdicr kőht aiur.



XE, LE vk L_ HH\ _cyĳsci Nhitrk Pcscrĳdĳ • Zratathp ciåcm ekåhrkg cgciae nhitrk håhg Ψ s 4 3 skåhihp

hihőmhshg`kg

• A fci`k, cgciae ciåcm ekåhrkg nhitrk mcrcmtkrhsthmikrhőþyik ki`kk`hidhő ai`u2 Ψ s 4 3, Ψ p 4 :.0<?03<>, p43`L, s40: `L.

• Nhitrk tcscrĳdĳg`c muiicgĳicg DCPICL maduticrĳ vk maduticråciĳőtĳrĳicrcm ki`k k`hikg mczcgå ercnhđh cőcđĳ`c vkrhidhőthr .

:.;55?:? aicocm



HH\ _cyĳsci Nhitrkikrhg _pkmtrci @þgùőùdikrh • Cdcå 2 ^krhikg lhr ciåcm ekåhrkg scyĳsci trcgsnkr nagmshyagu

E I ( z )‘yh ciåcm, yùmskm, lcg`ekåhrkg vkyc lcg`sþg`ùrkg lhrnhitrkyk mcrőĳiĳm ekikg `hđkr lhr trcgsnkr nagmshyagu yk`þgùőtùrdkm .

• Mcrĳőĳmiĳđĳ þgikdkm håhg pratathp ciåcm ekåhrkg nhitrkghg trcgsnkrnagmshyagug`c lcđĳdsĳz `kđhőmkg håhg z , ekrkmih nhitrkghgmhhåhg hsk muiicgĳidĳőtĳr .

• ĺmh uzcy`cmh lhrhd åkdlkrikr vk uzcyicr crcsĳg`cmh `þgùőùd cőcđĳ`c eþstkrhi`hđh őkmhi`k aiur2



HH\ _cyĳsci Nhitrkikrhg _pkmtrci @þgùőùdikrh • hihőmhshg`kg, ki`k k`hihr. A fci`k,

• Mcrcriĳ lhr tùd ekåhrkg trcgsnkr nagmshyagu C( z ) őu maőuiu scđicr 2

• A fci`k, ekgki őkmih cőcđĳ`c vkrhikg mcrcriĳ lhr tùd ekåhrkg trcgsnkr nagmshyagu aidciĳ`ĳr .



CE- CE _pkmtrci @þgùőùdù • Þrgkm 2 Mkshd nrkmcgsĳ :.<; ϊ aicg cőcđĳ`c vkrhikg scyĳsci ciåcm

ekåhrkg nhitrkghg trcgsnkr nagmshyagug`cg ycrcricgcrcm mkshdnrkmcgsĳ :.?; ϊ aicg ciåcm ekåhrkg nhitrkghg trcgsnkr nagmshyaguguki`k k`hghz.

• @þgùőùd håhg ekrkmih pcrcdktrksh fkscpicgĳr 2

• A fci`k,



CE- XE _pkmtrci @þgùőùdù •

o mkshd nrkmcgsiĳ ciåcm ekåhrkg lhr nhitrk E I ( z )‘yh, mkshd

nrkmcgsiĳ lhr yùmskm ekåhrkg nhitrkyk `þgùőtùrdkm håhg ekrkmih`þgùőùd cőcđĳ`c vkrhidhőthr 2

• CE-XE spkmtrci `þgùőùdù, o mkshd nrkmcgsiĳ yùmskm ekåhrkg lhr nhitrkyh mkshd nrkmcgsiĳ lhr ciåcm ekåhrkg nhitrkyk`þgùőtùrdkm vk : dkrmkz nrkmcgsiĳ lcg`ekåhrkg lhr nhitrkyhdkrmkz nrkmcgsiĳ lcg`sþg`ùrkg lhr nhitrkyk `þgùőtùrdkm cdcoĳyic `c muiicgĳiclhihr .



CE- XE _pkmtrci @þgùőùdù • Þrgkm 2 Mkshd nrkmcgsĳ :.<; ϊ aicg cőcđĳ`c vkrhikg scyĳsci ciåcm

ekåhrkg nhitrkghg trcgsnkr nagmshyagug`cg ycrcricgcrcm mkshdnrkmcgsĳ :.;; ϊ aicg yùmskm ekåhrkg nhitrkghg trcgsnkrnagmshyagugu ki`k k`hghz.

• @þgùőùd håhg ekrkmih pcrcdktrksh fkscpicgĳr 2

• A fci`k,



CE- LE _pkmtrci @þgùőùdù •

o mkshd nrkmcgsiĳ ciåcm ekåhrkg lhr nhitrkyh cit vk ùst

mkshd nrkmcgsiĳ lcg`ekåhrkg nhitrkyk `þgùőtùrdkm håhg ekrkmih`þgùőùd cőcđĳ`c vkrhidhőthr 2

• Gat2 o 4 - `urudug`c `þgùőùd lcshtikőhr 2



CE- L_ _pkmtrci @þgùőùdù •

o mkshd nrkmcgsiĳ ciåcm ekåhrkg lhr nhitrkyh cit vk ùst

mkshd nrkmcgsiĳ lhr lcg`sþg`ùrkg nhitrkyk `þgùőtùrdkm håhg ekrkmih`þgùőùd cőcđĳ`c vkrhidhőthr 2



DCPICL hik Pùd Ekåhrkg Nagmshyagug Ùrkthidksh

]tudekopcy,tudekopcy`cT 4 ciipcssip<fp(wce,wye) % CE-XE

]tudekopcy,tudekopcy`cT 4 ciipcssip<lp(wce,wle) % CE-LE]tudekopcy,tudekopcy`cT 4 ciipcssip<ls(wce,wls) % CE-L_

Þrgkm 2 CE-XE `þgùőùdùg`k wce4 :.<; ϊ vk wye 4 :.;; ϊ håhg

]tudekopcy,tudekopcy`cT 4 ciipcssip<fp(:.<;, :.;;)

madutugug åciĳőtĳrĳidcsĳ saguoug`c cőcđĳ`cmh `þgùőùdù ki`k k`hihr2



DCPICL hik _pkmtrci @þgùőùd

]pcy,pcy`cT 4 hhrip<fp(pcyce, pcy`cce, wce,wye) % CE-XE

]pcy,pcy`cT 4 hhrip<lp(pcyce, pcy`cce, wce,wle) % CE-LE]pcy,pcy`cT 4 hhrip<ls(pcyce, pcy`cce, wce,wls) % CE-L_

Þrgkm 2 Mkshd nrkmcgsĳ :.<; ϊ aicg cőcđĳ`c vkrhikg scyĳsci ciåcm ekåhrkg nhitrkghg trcgsnkr nagmshyagug`cg ycrcricgcrcm mkshd

nrkmcgsĳ :.;; ϊ aicg yùmskm ekåhrkg nhitrkghg trcgsnkr nagmshyaguguki`k k`kihd

Ekrkmih DCPICL sctĳricrĳ őþyik`hr 2 pcyce4:.:>><*]3 ? ? 3T= pcy`cce4]3 -:.8?;? -:.;>>8 -:.3:3; T=]pcy,pcy`cT 4 hhrip<fp(pcyce, pcy`cce, :.<;,:.;;)=



DCPICL hik _cyĳsci HH\ Nhitrk Pcscrĳdĳ

@krkok mksthrhd maduticrĳ2

Þrgkm 2 Cőcđĳ`cmh mcrcmtkrhsthmikrk scfhp <.tùr Ofklysfkv scyĳsci yùmskm ekåhrkg nhitrkghg `krokskgh lkihrikykihd2 N p43 mFz, N s4:.>mFz, p43`L, s40: `L, N P 40 mFz.

ĺim þgok, vkrhikg nrkmcgsicr ]:,3T crciĳđĳgc gardcihzk k`hidkih`hr.^krhikg `kđkrikr`kg ψ p4<x3/04:.;, ψ s4<x:.>/04:.? luiugur.@cfc sagrc, ]G,UgT4ofkl<ar`(:.;, :.?, 3, 0:) madutugugåciĳőtĳrĳidcsĳ saguoug`c G4;, Ug4:.?<<0 ki`k k`hihr.



DCPICL hik _cyĳsci HH\ Nhitrk Pcscrĳdĳ

Þrgkm 2 Cőcđĳ`cmh mcrcmtkrhsthmikrk scfhp kiihpthm HH\scyĳsci ciåcm

ekåhrkg nhitrktcscricyciĳd2 N p4:.6 mFz, N s43 mFz, p4:.; `L, s40:`L, N P 40 mFz.^krhikg `kđkrikr`kg ψ p4<x:.6/04:.0, ψ s4<x3/04:.; luiugur.DCPICL maduticrĳ vk maduticrĳg åciĳőtĳrĳidcsĳ saguoug`c ki`kk`hikg mczcgå ycgĳtĳ cőcđĳ`c vkrhidhőthr .



Lhehscycr @kstkmih _cyĳsci HH\ Nhitrk Pcscrĳd

•

ŗhd`hyk mc`cr tcrtĳőĳicg HH\ nhitrktcscrĳd ciearhtdcicrĳ CE, XE,LE vkyc L_ ekgihm ycgĳtĳgc scfhp nhtrk ekrkmthrkg uyeuicdcicr`cmuiicgĳidcmtc`ĳr .

• @hđkr tùr HH\ nhitrkikrhgtcscrĳdĳ, lhehscycric ùrkthikg nhitrk hik

ekrkmih nhitrk crcsĳg`cmh fctcyĳ dhghdud ycpcg yhgkikdkihapthdhzcsyag yþgtkdikrh håkrdkmtk`hr .

• F (k b ) lhiehscycric ùrkthikg trcgsnkr nagmshyagu F ( z )‘ghg nrkmcgsycgĳtĳgĳ, @(k b ) ekrkmih nrkmcgsycgĳtĳgĳ lkihrtshg. Cdcå, F (k b ) hik

@(k b ) crcsĳg`cmh fctc dhghdud aicocm őkmhi`k F ( z )‘yh tcscricdcmtĳr .




• F (k b ) hik @(k b ) crcsĳg`cmh fctc cőcđĳ`c eþstkrhi`hđh ehlh ekgki`kcđcĳriĳmicg`ĳrĳidĳő lhr fctc nagmshyagu aicrcm lkihrthihr2

• U (k b ) þgok`kg lkihrthidhő pazhthn lhr cđĳriĳmicg`ĳrdc nagmshyaguaidcm ùzkrk, K ( ), : ≠ ≠ ϊ crciĳđĳg`c fkr `kđkrh håhg dhghdud ycpĳiĳr .

• Ofklysfkv vkyc dhghdcms þiåùtù `kgkg sĳmiĳmic muiicgĳicg lhrycmicőĳmiĳm þiåùtù cőcđĳ`c eþstkrhi`hđh ehlh K ( )‘gĳg duticm tkpk

`kđkrhgh dhghdud ycpdcmtĳr 2

• Kőhtihmtkmh \ , ekrkmih nrkmcgsycgĳtĳgĳg tcgĳdicg`ĳđĳ : ≠ ≠ ϊ crciĳđĳg`c mkshődkykg nrkmcgs lcg`icrĳ mùdksh`hr .




• Nhitrkikdk uyeuicdcicrĳg`c, \ tcscricgcocm nhitrkghg ekrkmihekåhrdk vk sþg`ùrdk lcg`icrĳg`cg aiuőur . Þrgkđhg, ciåcm ekåhrkg nhitrktcscrĳdĳg`c p vk s tcscricgcocm nhitrkghg ekåhrdk vk sþg`ùrdk lcg`ĳ mkgcr nrkmcgsicrĳ aidcm ùzkrk, \ ]:, pT hik]:, sT nrkmcgscrciĳmicrĳgĳg lhrikőhdh`hr .

• Kg mùåùm - p þiåùtù `kgkg `hđkr lhr ycmicőĳmiĳm þiåùtù, K ( )‘gĳg p.muvvkthghg hgtkercihgh lkihrthikg nrkmcgscrciĳđĳ \ ùzkrhg`k dhghdud ycpdcmtĳr 2



_cyĳsci HH\ Nhitrkikrhg Erup Ekohmdk @kgmikőthr • Lhr hőcrkthg, vkrhikg nrkmcgs crciĳđĳg`c scyĳsci lhr nhitrk`kg

lazugudsuz hikthdh håhg nhitrkghg trcgsnkr nagmshyagu lhrhdekgihm ycgĳtĳgc vk `ađrusci ncz ycgĳtĳgc, ycgh hiehih nrkmcgscrciĳđĳg`c sclht erup ekohmdkshgk scfhp aidciĳ`ĳr .

• ŗhd`hyk mc`cr tcrtĳőĳicg scyĳsci HH\ nhitrk tcscrĳd yþgtkdikrh `ađrusci aidcycg ncz ycgĳtiĳ trcgsnkr nagmshyagicrĳyic saguåicgĳr .

• A fci`k, sclht erup ekohmdkih scyĳsci HH\ nhitrk ktdkmhåhg prcthm lhr ycmicőĳd lkihrthihkg ekgihmycgĳtĳgĳ scđicycg scyĳsci HH\ nhitrkhik tùd ekåhrkg lhr nhitrkyh tapicd erup ekohmdksh sclht aicocmőkmhi`k skrh lcđicdcmtĳr .

• Pùd ekåhrkg ekohmdk `kgmikőthrhohsh apthdhzcsyag yþgtkdikrh muiicgĳicrcm tcscricgĳr . Cőcđĳ`c lhr yþgtkd vkrhidhőthr .



_cyĳsci HH\ Nhitrkikrhg Erup Ekohmdk @kgmikőthr • F ( z ), erup ekohmdksh π F (ψ) aicg scyĳsci HH\ nhitrkghg trcgsnkr

nagmshyagu aisug. Cdcoĳdĳz, erup ekohmdksh π C(ψ) vk trcgsnkrnagmshyagu

aicg tùd ekåhrkg lhr nhitrkyh, tùd ekåhrkg nhitrk hik F ( z ) cőcđĳ`c eþstkrhi`hđh ehlh skrh lcđicg`ĳđĳg`c tapicd erup ekohmdksh π(ψ) 4π F (ψ) + π C(ψ) sclht aicocm őkmhi`k tcscricdcmtĳr .

• Mcrcriĳiĳđĳ ecrcgthikdkm håhg cőcđĳ`cmh maőui `c scđicgdciĳ`ĳr 2



_cyĳsci HH\ Nhitrkikrhg Erup Ekohmdk @kgmikőthr

•

Pùd ekåhrkg ekohmdk `kgmikőthrhohsh tcscrĳd pralikdh

őkmihg`k vkrhikg fctcgĳg dcmshdud duticm `kđkrhghg dhghdudycpĳi`ĳđĳ lhr apthdhzcsyag pralikdh aicrcm hnc`k k`hiklhihr.

• Fkscpicgcocm pcrcdktrkikr, ekrkmih ekohmdk π: vk tùd ekåhrkg nhitrkghgmctscyĳicrĳ ` 3,i, ` <,i‘`hr .

• DCPICL‘`k, lu apthdhzcsyag pralikdh hhrerp`kicy D- `asycsĳ muiicgĳicrcm åþzùiklhihr .



_cyĳsci HH\ Nhitrkikrhg Erup Ekohmdk @kgmikőthr

•

Þrgkm 2 Ekåhrdk lcg`ĳ mkgcr nrkmcgsĳ :.? ϊ , ekåhrdk lcg`ĳ `ciecicgdcsĳ 3 `L vk sþg`ùrdk lcg`ĳ `ciecicgdcsĳ ?: `L aicg0. `krkok kiihpthm ciåcm ekåhrkg nhitrkghg erup ekohmdkshgh 6.`krkok tùd ekåhrkg `kgmikőthrhoh tcscricycrcm `kgmikőthrkihd.

•

Ciåcm ekåhrkg nhitrkghg vk tapicd shstkdhg erup ekohmdkikrhcőcđĳ`c eþstkrhidhőthr 2

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