laplace transform, engineering-mathematics-3 ,ch-6 in bme in pdf

7/29/2019 Laplace Transform, Engineering-Mathematics-3 ,Ch-6 in BME in PDF

1/115

Ogth5 F sg`h tf`h `fstilhky typh cipftik S fosthid gn sìkk s sg jh cirh-nukk.

\ H O A F O H H Z F O A - @ I T B - 3 , K I ] K I C H - T Z I O S N G Z @ , C B - > , F O J @ H P J VS F L I O D I Z - K G D B F

]iah 9-GN-9=6

HOAFOHZFOA-@ITBH@ITFCS-3, KI]KICH-

TZIOSNGZ@, CB->, FO JFG-@HDFCIK-HOA-

CGXZSHS5\ ]irt-9P

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SHCTFGO OG >.9 , >.: , >.3,>.4,>.8 IOD >.> GOKV , NZG@ JGGL 5

IDÎOCHD HOAFOHHZFOA @ITBH@ITFCS 1TB HDFTFGO jy HZQFO-LZHVSUFA.

:9/NHJ/:=93

KI]KICH-TZIOSNGZ@

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HOAFOHHZFOA AXFDH

@GBI@@ID SFLIODIZ

LBIO KGDBF

\OGTH5 F SG@H TF@H

@FSTILHKV TV]H CI]FTIK SFOSTHID GN S@IKK SSG JH

CIZH-NXKK.PJGGL 5 IDÎOCHD HOAFOHHZFOA @ITBH@ITFCS 1tb HDFTFGO jy HZQFO-LZHVSUFA.
http://www.medical-image-processing.blogspot.com/http://www.medical-image-processing.blogspot.com/http://www.medical-image-processing.blogspot.com/http://www.medical-image-processing.blogspot.com/


2/115



]iah :-GN-9=6

Tijkh gn Cgothots(>.9 STIZT BHZH) .......................................................................................................................................... :

]ZGJKH@ SHT >.9 .................................................................................................................................... 99

\ >.: P \ STIZT BHZH P. ................................................................................................................................ 4:

]rgjkh`-sht >.: ....................................................................................................................................... >9

\ >.3 P \ stirt bhrh P ...................................................................................................................................... 1=

]rgjkh` sht >.3 ....................................................................................................................................... 11

\>.4 P \ stirt bhrh P ....................................................................................................................................... 21

]rgjkh`-sht >.4 5 ..................................................................................................................................... 6=

\>.8P stirt bhrh ............................................................................................................................................ 64

]rgjkh` sht >.8 ....................................................................................................................................... 6>

\ >.> P stirt bhrh ........................................................................................................................................ 9==

]rgjkh` sht >.> ..................................................................................................................................... 9=8

CB->( STIZT-BHZH )5 GO KI]KICH-TZIOSNGZ@5

(>.9 STIZT BHZH)

KI]KICH-TZIOSNGZ@,FO^HZSH-TZIOSNGZ@,KFOHIZFTV5

Fn n(t) fs tbh afvho nuoctfgo dhnfohd ngr ikk *t=+, tbho wh tilho tbh

kipkich-triosngr`, gn n(t), tbho fn tbh rhsuktfoa vikuh fs hxfst \(f-h)

bis sg`h nfofth vikuh + , fts tbh nuoctfgo gn s, iksg cikkhd N(s)

fo nrhquhocy dg`ifo.

NGZ@XKI GN KI]KICH TZIOSNGZ@\KTP5

Qbhrh 5 t0tf`h iod s0nrhquhocy

Zh`h`jhr tbit 0? tbh afvho nuoctfgo n(t) dhphods go t iod tbh ohw

nuoctfgo N(s)\ fts kipkich-triosngr` + dhphod go s .


3/115



]iah 3-GN-9=6

Sg, N(s) fs tbh Kipkich-Triosngr` gn afvho nuoctfgo n(t).

NGZ@XKI GN FO^HZSH KI]KICH TZIOSNGZ@\FKTP5

-----------------------

HRI@]KH#9

KI]KICH TZIOSNGZ@

Kht,-? n(t)09, wbho *t=+

NFOD5

Ogth5 tbh fothrvik gn fotharitfgo fo (hq-I) jhkgw fs fonfofth, tbhrhngrh

wh cikkhd ft is F`prgphr-fotharik.

NGZ@XKI5

(I)

Ijgvh hquitfgo fs cikkhd is hq-I,

{5.wbho ( S?= ) }


4/115



]iah 4-GN-9=6

Bhochd prgvhd

W---------------------------------nfofsbhd W------------

HRI@]KH#:5

Kht -? n(t)0hit

, wbho *t=+

Qbhrh \ i0ioy cgostiot P

Nfod-?

Sgkutfgo5


5/115



]iah 8-GN-9=6

-------------------------nfofsbhd-------------

TBHGZH@#95\KFOHIZFTV-GN-KI]KICH-TZIOSNGZ@PTbh kipkich triosngr` fs i kfohir-gphritgr Gr kfohir-gphritfgo.

-------------nfofsbhd---------------

]rggn # 95


6/115



]iah >-GN-9=6

Sgkutfgo5


7/115



]iah 1-GN-9=6

Bhochd prgvhd.

--------------------------------nfofsbhd-----------------


8/115



]iah 2-GN-9=6

Bhochd prgvhd

---------------------nfofsbhd------------

]rggn # 35


9/115



]iah 6-GN-9=6

Bhochd prgvhd

-------------------nfofsbhd-----------------

{ !0nictgrfik, 4!04x3x:x90:4}


10/115



]iah 9=-GN-9=6

-------------------nfofsbhd-----------


11/115



]iah 99-GN-9=6

]ZGJKH@ SHT >.9

------------nfofsbhd-------------

Y:) \ >.9 P

Nfod kipkich triosngr`07


12/115



]iah 9:-GN-9=6

--------nfofsbhd-----------

------------nfofsbhd--------

>.9


13/115



]iah 93-GN-9=6

Y4) nfod kipkich triosngr`07

----------nfofsbhd---------

>.9

Y8 ) nfod kipkich triosngr`07


14/115



]iah 94-GN-9=6

-----------nfofsbhd----------


15/115



]iah 98-GN-9=6

Sgkutfgo5



16/115



]iah 9>-GN-9=6

------------nfofsbhd---------


Afvho5


17/115



]iah 91-GN-9=6

Sgkutfgo5


18/115



]iah 92-GN-9=6

--------------nfofsbhd--------------

Y92 ) nfod kipkich-triosngr`07

AF^HO5


19/115



]iah 96-GN-9=6

Sgkutfgo5


20/115



]iah :=-GN-9=6

-------------nfofsbhd------------

Y96 ) nfod kipkich triosngr`07

Afvho5

NGZ@XKI-GN-STZIFABT-KFOH-HYXITFGOS5


21/115



]iah :9-GN-9=6

\ PKhts put ikk vikuh fo ijgvh hquitfgos,

\ P\ P\ P\

P

Qbhrh 5\ P sg,\ PInthr ippkyfoa kipkich triosngr` go hq-J, wh aht,

\ P

\ P.\ P


22/115



]iah ::-GN-9=6

\

P.

\ P.\ P.\wbhrh5 s0nrhquhocy, iod , l0I`pkftudh P

\

P.

\ P.\ P.

---------------------------

Zguab wgrl5

Kht cgosfdhr 5\ P nrg` ivgvh hq-A5Sg,\ P


23/115



]iah :3-GN-9=6

\ 0=0=:}PP

\ P\ P\ P\ P\ :P0=0PP P

---------------------

Ogw put tbh vikuh gn hq-l fo hq-A, wh aht,

\ :P0=0P.

\ P\ P


24/115



]iah :4-GN-9=6

\ P\

P

---------nfofsbhd------------

>.9

Y :=) Nfod kipkich triosngr`07

Afvho5

NGZ@XKI-GN-STZIFABT-KFOH-HYXITFGOS5

\ PSgkutfgo5

\ P\ P\ P


25/115



]iah :8-GN-9=6

\ PSg, wbhrh5 \ , iod P\ PQh ippkyfoa kipkich triosngr` go hq-I,

\

P

\ P\ P\ P\ P\ P\

P

.

.

\ P


26/115



]iah :>-GN-9=6

-----------nfofsbhd-----------

>.9

Afvho5 .\ PTf`h dg`ifo Nrhquhocy dg`ifo Sgkutfgos5

.

. . .----------------------------------

.\ P\ P


27/115



]iah :1-GN-9=6

---------------

Ogw put tbh vikuh gn hq-S fotg hq-], wh aht.

. . .Ioswhr.

--------------nfofsbhd-----

\ >.9 P

Y :6) nfod n(t)07

Afvho .Sgkutfgo5

. . .---------------

Ngr`uki5(hq-9). (hq-:).


28/115



]iah :2-GN-9=6

-----------

Ogw jy usfoa tbh ngr`uki gn hq-9 tbho hq-] jhcg`hs,

. . Ioswhr.------------nfofsbhd------------

>.9

Y 39) nfod n(t)07

Afvho-? N(s)0\9/S4P , F O J @ H P J VS F L I O D I Z - K G D B F

]iah :6-GN-9=6

.

.

. . Ioswhr .----------------nfofsbhd------------

\ >.9 P

Y 33 ) nfod n(t)07

Afvho-? .Sgkutfgo5-? .

.

.Xsfoa ]irtfik Nrictfgoik @htbgdwh cgosfdhr nrg` ijgvh hq-]5

.

. . .


30/115



]iah 3=-GN-9=6

Kht,-? \I+JP0=.9 P

Y 3= ) nfod n(t)07

Afvho5-? N(s)0 \4/(S+9)(S+:)P

Sgkutfgo5

.

.Cgosfdhr \4/(S+9)(S+:)P 5

Sg,

. . . .


31/115



]iah 39-GN-9=6

. . .Kht5-? .Sg, jy pkicfoa tbh vikuh gn { hq-f } fo \ hq- P wh aht, .

.

. . .Ogw,

-------

.

.

----------

Ngr J5-? .Qbho . .

.

. . .


32/115



]iah 3:-GN-9=6

Ngr I5-?

. . \5. . P . . .Qbho \

P \

P

Sg, eust pkicfoa tbh vikuh gn I iod J fo . . .Ogw jy pkicfoa tbh vikuh gn \ hq-A P fo \hq-e P tbho \ hq-e P jhcg`hs.

. .Ogw sf`pky sgkvh ft,

.-------------

Ngr`ukis5-?

.


33/115



]iah 33-GN-9=6

.

.

.-----------

.

.

. ioswhr.-----------nfofsbhd------------

\ >.9 P

Y 34 ) nfod n(t)07

Afvho5-? .Sgkutfgo5-

.

. .


34/115



]iah 34-GN-9=6

--------------------

. .---------------------

Qbhrh5 -? \ POgw jy ippkyfoa tbh ngr`uki gn \hq-f P go \ hq-] P wh aht,

. .

. Ioswhr

---------nfofsbhd-----------

\ >.9 P

Y 38 ) nfod n(t)07

Afvho5-?

.

Sgkutfgo5-? . .


35/115



]iah 38-GN-9=6

Cgosfdhr 5-Ngr vikuh gn I & J ^ikuhs5-

. . .

.

. . . .

.

Kht5-? .Sg,

Ngr I5-

.\5. P P . . .


36/115



]iah 3>-GN-9=6

Ngr J5-

. . .Ogw, jy pkicfoa tbh vikuh gn \hq-9 & :P fo \ hq-O P wh aht.

.----------

. .------------

.Ogw jy pkicfoa tbh vikuh gn \ hq-O P fo \ hq-J P wh aht tbh n(t).

. . . .


37/115



]iah 31-GN-9=6

. Ioswhr.-------------nfofsbhd------------

\ >.9 P

Y 3> ) nfod n(t)07

Afvho-? .Sgkutfgo5-?

.

. . .

.

--------------

Ngr`ukis5

.

.

-------------

. Ioswhr.--------nfofsbhd----------


38/115



]iah 32-GN-9=6

\ >.9 P

Y 32 ) nfod n(t)07

Afvho5-? .Sgkutfgo5-? . .

.

. . .

. Ioswhr.-------nfofsbhd--------------

\ >.9 P

Y 3: ) nfod n(t)07

Afvho5-?

.

Sgkutfgo5-? . .


39/115



]iah 36-GN-9=6

.

.

. . . Ioswhr.----------nfofsbhd------------

\ >.9 P ohw-tgpfc.

HRFSTHOCH GN KI]KICH-TZIOSNGZ@S5-Fts sunnfchs tg rhqufrh tbit n(t) jh ]fhch-wfsh-cgotfougus go hvhry

nfofth fothrvik fo tbh rioah \ PTbit fs 5

Jy tbh dhnfoftfgos, i nuoctfgo n(t) fs i pfhch wfsh cgotfougus go i nfofth

fothrvik \ P, fn n(t) fs dhnfohd go tbit fothrvik iod fs sucb


40/115



]iah 4=-GN-9=6

sujdfvfdhd fotg nfofthky `ioy suj-fothrviks, fo hicb gn wbfcb n(t) fs

cgotfougus iod bis nfofth kf`fts is tf`h(t) ipprgicbhs hftbhr, hod-

pgfot gn fothrvik gn sujdfvfsfgo nrg` tbh fothrfgr, ft ngkkgws nrg` tbfs

dhnfoftfgos tbit nfofth Eu`ps irh tbh goky dfs-cgotfouftfhs tbit i pfhch-wfsh cgotfougus nuoctfgo `iy bivh, tbhsh irh logwo is Grdfoiry dfs-

cgotfouftfhs.

-------------------

\ >.9 P

TBHGZH@-: \HRFSTHOCH-TBHGZH@-NGZ-KI]KICH-TZIOSNGZ@S+5-

Kht, n(t) jh i nuoctfgo tbit fs pfhch-wfsh cgotfougus go hvhry nfofth

fothrvik fo tbh rioah \ P, iod sitfsnfhs jhkgw \ hq-: P. .

Iod ngr sg`h cgostiot \P iod \P.Tbho, tbh kipkich-triosngr` gn n(t) hxfsts ngr ikk \ P.


41/115



]iah 49-GN-9=6

]rggn5-?sfoch n(t) fs pfhch-wfsh cgotfougus, \ P, fs fotharijkhgvhr ioy nfofth fothrvik go t-ixfs. Nrg` \hq-:P,

Kht, wh bivh i cgodftfgos \

P, wh aht,

. . .

. . .

.

. . .

. . GZ .


42/115



]iah 4:-GN-9=6

Qbhrh 5 \ P fs ohhd ngr kist fotharik.------------NFOFSBHD-----------

\ >.: P \ STIZT BHZH P.

TZIOSNGZ@S-GN-DHZF^ITF^HS-IOD-FOTHAZIKS5-TBHGZH@ # 95

KI]KICH-TZIOSNGZ@-GN-TBH-DHZF^ITF^H-GN-n(t)5-Suppgsh tbit n(t) fs cgotfougus ngr ikk \

P, wbhrh tbh dhrfvitfvhs

gn n(t) fs \n(t)

P wbfcb fs pfch-wfsh cgotfougus, go hvhry nfofth fothrvik fotbh rioah \ P, tbho kipkich triosngr` gn dhrfvitfvhs gnnuoctfgo \n(t)

P fs hxfst wbho tbhrh fs i cgodftfgos fs \ P.

Sg, tilfoa kipkich triosngr` go fts dhrfvitfvhs \n(t)P,

Tbit fs5

g ]ZGGN5 .\ P .Kht cgosfdhr . ...

..


43/115



]iah 43-GN-9=6

\ P , F O J @ H P J VS F L I O D I Z - K G D B F

]iah 48-GN-9=6

Ogw jy ippkyfoa kipkich triosngr` go jgtb sfdh wh aht,

. .

Ijgvh \hq-T+ fs cikkhd tbh sujsfdfiry-hquitfgo.

. . . . Ioswhr.---------------

. Ioswhr.QBHZH5-?\ P.Triosnhr-nuoctfgo fs gntho dhogthd jy B(s), jut wh ohhd B(s) `ucb

`grh nrhquhothky ngr gtbhr purpgshs.

. Ioswhr.

. .


46/115



]iah 4>-GN-9=6

---

F^]5-AF^HO5-? \ P iod \ P.---Fn \-? y(=)0y

(=)0=P,

.

.

. . .Tbio, tbfs fs sf`pky \-? V(s)0Z(s).Y(s)P.

Tbus tbh triosnhr-nuoctfgo fs Y(s)

TBH AHOHZIK-NGZ@XKI-GN-TZIOSNHZ-NXOCTFGO5

OGTH5Y(s) dhphods goky go i iod j, jut ohftbhr go r(t) ogr go tbh

foftfik-cgodftfgos.

Kist sthp5 wh rhduch \ hq-1 + usuikky jy pirtfik nrictfgos, is fo fotharik

cikcukus} tg i su` gn thr`s wbgsh fovhrsh cio jh nguod nrg` tbh tijkh,

sg tbit tbh sgkutfgo \ P gn \hq-IP fs gjtifohd.


47/115



]iah 41-GN-9=6

---------

------------nfofsbhd----------

\ >.: P

Hxi`pkh # 8 5 \Foftfik-vikuh-]rgjkh`\F.^.]PP5

AF^HO5

\ P.Foftfik-vikuh-]rgjkh`\F.^.]P5

\ P.ZHYXFZHD5

\ P.Iod sgkvh ft jy F.^.] ,

Sg,

STH]-95 Tg `ilh hq-I is y(t) \ gr tg nfod tbh sgkutfgo gn hq-I P jy usfoa

Kipkich-Triosngr`,

\ P.Jy ippkyfoa tbh kipkich triosngr` go hq-I wh aht,

\

P.

\ P.\ P.\ P.


48/115



]iah 42-GN-9=6

\ P.\

P.

\ P.----------

Jy usfoa Foftfik-vikuh-]rgjkh`\F.^.]P5

\ P.-----------

Tbio wh aht.

\ P.\ P.\

P.

\ P.\ P.\ P.\ P.


49/115



]iah 46-GN-9=6

\ P.\ P.khtCGOSFDHZ \9/s

:\s

:-9P P5

I07 , J07 .

Xsfoa ]irtfik-nrictfgo `htbgd5

\ P\ P\

P\ P

\ P\

P

\ P\ P\ P {5.\hq-fP -? =0I+J }


50/115



]iah 8=-GN-9=6

Sg,

\

P

\ P\ P.Sg,

{5.\hq-fP -? =0I+J< \hq-hP -? I0-J < }

Ngr J5

Qbho \ P.\hq-hP -? I0-J , F O J @ H P J VS F L I O D I Z - K G D B F

]iah 89-GN-9=6

\ P.\ P.\ P.Ijgvh hq-S fs tbh sgkutfgo gn sujsfdfiry-hquitfgos.

Ogw jy tilfoa tbh fovhrsh-kipkich triosngr` go hq-S, wh aht

tbh sgkutfgo gn afvho prgjkh`.

\ P.\ P.\ P.\ P.\ P.\

P. Ioswhr, Fts

tbh sgkutfgo gn afvho prgjkh`.

----------nfofsbhd-------

-----


52/115



]iah 8:-GN-9=6

Fo prictfch, fosthid gn eustfnyfoa tbh ush gn ngr`ukis iod

tbhgrh`s fo tbfs `htbgd, goh sf`pky cbhcls it tbh hod

wbhtbhr y(t) sitfsnfhs tbh afvho hquitfgos iod foftfik

cgodftfgos.

Aifos fo tbh `htbgd, is cg`pirhd tg tbit foCb # :,

iod fkkustrithd jy tbh hxi`pkh, irh is ngkkgws5

9.Og dhthr`foitfgo gn i ahohrik sgkutfgo gn tbhbg`gahohgus hquitfgo.

:.Og dhthr`foitfgo gn vikuhs ngr irjftriry cgostiots foi ahohrik sgkutfgo.

Sbfnthd diti prgjkh`s fs i sbgrt oi`h ngr foftfik vikuh

prgjkh`s fo wbfcb tbh foftfik cgodftfgos rhnhr tg sg`h

kithr fostiot fosthid gn \ t0= P. Qh hxpkifo tbh fdhi gnsgkvfoa sucb i prgjkh` jy tbh kipkich-triosngr` fo thr`s

gn i sf`pkh hxi`pkh.

----------

Shctfgo # >.: 5

Hxi`pkh # > 5- \ sbfnthd-diti-prgjkh`0Foftfik-vikuh-]rgjkh`P5-

Sgkvh tbh F.^.]

Afvho5-


53/115



]iah 83-GN-9=6

\ P , F O J @ H P J VS F L I O D I Z - K G D B F

]iah 84-GN-9=6

\ P

laplace transform, engineering-mathematics-3 ,ch-6 in bme in pdf

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