Problems EE416 - 2

 

QNCWAPYC_S KG _PC]KFC, GHIQFC_S KG ANLCNAAPCNL AFAI_PCIHF HNO AFAI_PKNCI ANLCNAAPCNL OA]HP_JAN_

 

AA?87 

]rk`fajs 

JHS83, 0=08

 

 

 

]rk`faj 8

H wbcta Lhusschn nkcsa prkiass kg zark jahn hno pkwar spaitrhf oanscty



8. _ba nkcsa ht tba fkw-phss gcftar kutput cs oanktao `y ( ). 

= 

0 cs hppfcao tk gcftarcnl sibaja sbkwn cn Gclura

h)  Gcno tba pkwar spaitrhf oanscty hno tba hutkikrrafhtckn gunitckn kg ( ).   `)  Gcno tba jahn hno vhrchnia kg   ( ). i)  \bht cs tba jhxcjuj rhta ht wbcib ( ) ihn `a shjpfao sk tbht tba rasuftcnl shjpfas hra assantchffy unikrrafhtao;

 

 

 

]rk`faj 0

Lcvan h wbcta nkcsa kg jhlnctuoa

=

 :

=.==8 j\/Bz cs gao tk gkffkwcnl.

h)  Hn PI fkw phss fkw phss gcftar kg P:8=== ℧ hno I:=.8 jG.  jG.   `)  Hn coahf fkw phss gcftar kg `hnowcotb:8=== Bz. i)  H ocggarantchtkr iknscoars prkpkrtcknhfcty prkp krtcknhfcty iknsthnt Ϗ : =.=8 unct.  unct.  Gcno kutput nkcsa cn ahib ihsa. Bkw okas rasuft ibhnla cn ahib ihsa cg fkw phss iutkgg-graquaniy cs oku`fao.

 

 

]rk`faj 9

H fkw-phss (wctbcn ?=== Bz) sclnhf kg stranltb =.==8\ phssas tbrkulb h ocstkrtcnl ibhnnaf oagcnao hs

∐2 

 

( ):

 ?=== ?===+

 hno

cs hfsk ikrruptao wctb h hooctcva wbcta Lhusschn nkcsa kg jhlnctuoa 8= / . Ht tba raiacvar scoa, tbara cs hn aquhfczar wctib axhitfy jhtibas tba ibhnnaf wctbcn graquaniy kg cntarast (up tk ?=== Bz) hno zark afsawbara. Gcno YNP ht tba kutput kg aquhfczar.

 

 

]rk`faj ?

=

         

0 cs gcftarao `y h raithnlufhr `hnophss gcftar wctb ( ) : 8, iantarao ht  hno bhvcnl h `hnowcotb @. gcno tba pkwar spaitrhf oanscty kg ( ) hno ( ). Ihfiufhta tba pkwar cn ( ), ( ) hno ( ) 

\bcta nkcsa wctb pkwar spaitrhf oanscty

 

   

 

]rk`faj 1

 



∐3   

    

H raiacvao YY@ sclnhf kg stranltb 8 j\ bhs h pkwar spaitruj wbcib axtanos kvar tba graquaniy rhnla  : 8     + /  . _bcs cs juftcpfcao `y h fkihf : 8. 8.== ==1 1 . _ba hiikjphncao nkcsa bhs uncgkrj pkwar spaitrhf oanscty 8= ksicffhtkr kg graquaniy 8JBz hno tban gkffkwao `y h `hsa`hno gcftar kg iut-kgg graquaniy   tk lat jasshla sclnhf. \bht  cs tba jasshla `hnowcotb; Gcno tba sclnhf nkcsa anarly ht tba kutput kg `hsa`hno gcftar hno ihfiufhta tba YNP tbara. Bkw  okas tba YNP ibhnla cg tba `hnowcotb kg tba jasshla sclnhf cs raouiao `y 01 pariant;

 

 

]rk`faj 7

∐3 

Hn huock sclnhf kg ? dBz `hnowcotb cs tk `a trhnsjcttao tbrkulb h ibhnnaf tbht cntrkouias 9= o@ fkss hno wbcta nkcsa kg  pkwar spaitrhf oanscty 8= / . Ihfiufhta raqucrao jcncjuj trhnsjcttar pkwar cg tba jasshla cs sant `y YY@, OY@YI hno OY@-I jkoufhtckn. _ba raiacvao kutput YNP sbkufo `a jkra tbhn ?= o@ Gkr OY@-I, anarly cn scoa`hno cs bhfg tba anarly cn ihrrcar.

 

 

]rk`faj <

            

Iknscoar h rhnokj prkiass, ( ) : hra iknsthnt. Gcno cg ( ) cs \YY.

 

 iks (

+ ) wbara  cs h uncgkrj rhnokj vhrch`fa cn tba rhnla T

   ,

 Z hno H, σ

 

]rk`faj 2

H jasshla sclnhf x(t) kg 1 dBz `hnowcotb hno bhvcnl hn hjpfctuoa prk`h`cfcty oanscty hs sbkwn cn Gclura 0, hjpfctuoa jkoufhtas h ihrrcar tk h oaptb kg 2= %. _ba HJ sclnhf sk k`thcnao trhnsjcttao kvar h ibhnnaf wctb hooctcva nkcsa pkwar spaitrhf oanscty kg : 0   8=   /  . (kna scoa). _ba raiacvao sclnhf cs oajkoufhtao uscnl hn anvafkpa oataitkr.

= ∜ ∐80  

   ≡

h)  Cg h ( )

?=

 cs oascrao, wbht sbkufo oa tba jcncjuj vhfua kg



 pahd hjpfctuoa kg tba ihrrcar;  `)  Hssujcnl (

 

vhfua kg

 

 

 ;

 

 , tba

)  gkr anvafkpa oataitckn tk `a 8= o@, oatarjcna tba tbrasbkfo

 

]rk`faj 3

Hn HJ raiacvar, kparhtcnl wctb h scnuskcohf jkoufhtcnl whva hno 2=% jkoufhtckn bhs hn kutput sclnhf-tk-nkcsa rhtck kg 9= o@ \bht cs tba ikrraspknocnl ihrrcar-tk-nkcsa ihrrcar-tk-nkcsa rhtck;

]rk`faj 8=

Hn HJ systaj ajpfkycnl hn anvafkpa oataitkr cn tba raiacvar, cs kparhtcnl ht tbrasbkfo. Oatarjcna tba cnirahsa cn trhnsjcttar pkwar (cn o@) naaoao cn hn YNP)O kg ?= o@ cs oascrao. Hssuja : 8 hno tkna jkoufhtckn



]rk`faj 80

H jasshla sclnhf wctb jhxcjuj hjpfctuoa kg ¸8 W cs uncgkrjfy ocstrc`utao hno bhs h `hnowcotb kg 81 dBz. Qscnl HJ wctb h jkoufhtckn cnoax kg =.7, ct cs trhnsjcttao kvar h ibhnnaf wbksa httanuhtckn cs 7= o@ hno wbksa nkcsa pkwar spaitrhf oanscty (twk scoao) cs 8= /   . Oatarjcna tba hvarhla pkwar kg tba trhnsjcttar hno tba trhnsjcssckn `hnowcotb raqucrao, cg h pkst-oataitckn sclnhf-tk-nkcsa rhtck kg ?= o@ cs oascrao.

∐80 

 

 

]rk`faj 87

∐?

H oclcthf ikjjuncihtckn ibhnnaf bhs h `ct arrkr prk`h`cfcty kg 8= jasshla kg 8=== `cts trhnsjcttao tbrkulb tbcs ibhnnaf.

 

. Gcno tba prk`h`cfcty kg gcnocnl 9 kr gawar arrkrs cn h

 

]rk`faj 8<

Qscnl n-`ct `cnhry ]IJ, h jasshla sclnhf wbcib cs uncgkrjfy ocstrc`utao `atwaan sbkw tbht tba sclnhf-tk-quhntczhtckn rhtck tbht cs k`thcnao cs 7n o@

jhx  jhx

]rk`faj 82

Cg h _W sclnhf kg ?.1 JBz `hnowcotb cs trhnsjcttao uscnl 2-`ct `cnhry ]IJ, oatarjcna h)  _ba jhxcjuj sclnhf-tk-quhntczhtckn nkcsa rhtck  `)  _ba jcncjuj `ct rhta i)  _ba jcncjuj trhnsjcssckn `hnowcotb naaoao.

 

 

 +

 

, cs trhnsjcttao,

 

]rk`faj 0=

H _W sclnhf wctb h `hnowcotb kg 7 JBz cs oclcthffy trhnsjcttao uscnl ]IJ. _ba nuj`ar kg favafs cn tba quhntczar cs ?=37. Hssuja tba shjpfcnl rhta cs 0=% jkra tbhn tba Nyqucst rhta. Oatarjcna tba `ct rhta (c.a. tba nuj`ar kg `cts par saikno) raqucrao tk trhnsjct tba `cnhry ]IJ cngkrjhtckn.

 

 

]rk`faj 08

7  

H ]IJ systaj usas h uncgkrj quhntczar gkffkwao `y h