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Asach i\", Iasi, Facultatea de Electronica si Telecomunicatii" }}{PARA 19 " " 0 "" {TEXT -1 43 "Laboratorul de Semnale, Circuite si Sisteme" }} {PARA 19 "" 0 "" {URLLINK 17 "http://scs4.etc.tuiasi.ro" 4 "http://scs 4.etc.tuiasi.ro/scslabs/Simbolice/simbolice.htm" "" }{TEXT -1 0 "" }} {SECT 0 {PARA 3 "" 0 "" {TEXT -1 11 "Breviar teo" }{TEXT 256 0 "" } {TEXT -1 5 "retic" }}{PARA 0 "" 0 "" {TEXT 260 16 "Scopul lucrarii:" } }{PARA 0 "" 0 "" {TEXT -1 133 "Familiarizarea cu formele de unda ale u nui semnal cu modulatie in am plitudine. Calcularea si reprezentarea s pectrului semnalului MA." }}{PARA 0 "" 0 "" {TEXT 261 17 "Rezumat teor etic:" }}{PARA 0 "" 0 "" {TEXT -1 13 "Modulatia \356n " }{TEXT 257 11 "amplitudine" }{TEXT 258 1 " " }{TEXT -1 232 "a unui purtator armonic \+ este procesul de transferare a caracteristicilor semnalului modulator \+ asupra amplitudinii semnalului purtator. Din punct de vedere matematic , cea mai simpla modulatie \356n amplitudine este modulatia de produs. " }}{PARA 0 "" 0 "" {TEXT -1 39 "Presupunem semnalul modulator de for ma " }{XPPEDIT 18 0 "sm(t);" "6#-%#smG6#%\"tG" }{TEXT -1 28 " avand tr ansformata Fourier " }{XPPEDIT 18 0 "Sm(omega);" "6#-%#SmG6#%&omegaG" }{TEXT -1 23 " iar semnalul purtator " }{XPPEDIT 18 0 "sp(t);" "6#-%#s pG6#%\"tG" }{TEXT -1 16 " avand spectrul " }{XPPEDIT 18 0 "Sp(omega); " "6#-%#SpG6#%&omegaG" }{TEXT -1 38 ". Semnalul MA este definit de rel atia " }{XPPEDIT 18 0 "sMA(t) = sm(t)*sp(t);" "6#/-%$sMAG6#%\"tG*&-%#s mG6#F'\"\"\"-%#spG6#F'F," }{TEXT -1 49 ", adica produsul celor doua se mnale. Vom nota cu " }{XPPEDIT 18 0 "SMA(omega);" "6#-%$SMAG6#%&omegaG " }{TEXT -1 26 ", spectrul semnalului MA. " }}{PARA 0 "" 0 "" {TEXT -1 34 "Principial, realizarea semnalului " }{XPPEDIT 18 0 "sMA(t);" "6 #-%$sMAG6#%\"tG" }{TEXT -1 130 " consta \356n utilizarea unui multipli cator ideal descris de pe intrarile caruia se aplica semnalul modulat or si respectiv purtator:" }}{PARA 0 "" 0 "" {OLE 1 82954 1 "[xm]Br=Wf oRrB:::wk;nyyI;G:;:J;j:J:ZJJ;j:JyyyyyI<:n?vyyyyy=::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::uyyyyyS:wAwyyyqj>J?j?JykLJAjA>:[Z:F=F=N=V=^=nYn=v=>>BGFGNG VG^GfGnGvG>H:;`:Z@[::JjmKN@uqAj`Aj;JZC:j:vCSmlJ::::::::::OJ;@j yyyyyI:;Z:::::::^<>:F@cljNFS=>:::::::::WJ;@:xy;jysy;Z::::::J:F: AlqfG[maNFO=;::::::::_J;vyyuy:>:<::::::=J:NG>:nYN::yA::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::j:b:< Z:::>r=V;>:::::::=Jyyy;d:yayqZCN:>:;H:<:TNFj``pkDqqHqqTPt\\:>Z:vdiKQLnqHptZh>AcYH_WVB::::::yayY:^:F:; jysy?:;:WEA>mFJqAH=j>r:gB:>:EJ:>:E:Qb:B:E:Sb:IY:KvHA:;:::Ja@Na`>;B:::: ::::::::::::::::::::::::::::::::cjAN;=jnv;AJ:>:JVBJ]yy?JV^;GJavG_mpFFS 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::::::::Z::xI:B:Zy=:::::::::::J::ya::xI::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::B:>:jysy::::::::::::::::::::>:jy;;:vY:: :::::::::::<:;Zymy;::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::B::Zy=:::::::::::::<:ry::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::Z:J:ryvY:::::::::::::J:B:vYxI:::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::B:Zy=::::::::::::<:ry :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::>:<:yay=::::::::::<:;Zymy;::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::;Z:jy sy::::::::Z:J:ryvY:::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::::::::::::::::::::::::::J:B:vYxI::::::B:>:xIyA:::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: ::::::::::::::::>:<::ryvY:J:B::Zymy;:::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::B:>::jy sy:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::f:;j=F:;B:K B:n^@J=vYxy:^:;jM@jyyy@n\\H:^:f?;j;::::WTJZ::::::::::::::::::::::::::::::::::::::::::: :::::::::::::::::::::::::::::::3:" }{TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT -1 312 "\316n functie de domeniul de valori pentru care sunt con struite, multiplicatoarele fizice sunt \356n patru cadrane (ambele int rari pot avea orice polaritate), \356n doua cadrane (numai una dintre \+ intrari accepta semnale de orice polaritate) si \356ntr-un singur cadr an (ambele intrari trebuie sa aiba o singura polaritate). " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "restart:with(inttrans):assume(wm " 0 "" {MPLTEXT 1 0 42 "addtable(fourier,sm(t ),Sm(omega),t,omega):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "ad dtable(fourier,sp(t),Sp(omega),t,omega):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "sMA:=(t)->k*sm(t)*sp(t):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 38 "SMA:=(omega)->fourier(sMA(t),t,omega):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sMA(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(%\"kG\"\"\"-%#smG6#%\"tGF%-%#spGF(F%" }}}{PARA 0 "" 0 "" {TEXT -1 51 "In acest caz, spectrul semnalului MA este de forma: " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "SMA(omega);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&*&%\"kG\"\"\"-%$intG6$*&-%#SmG6#%$_U1GF'-%# SpG6#,&%&omegaGF'F/!\"\"F'/F/;,$%)infinityGF5F9F'F'%#PiGF5#F'\"\"#" }} }{PARA 0 "" 0 "" {TEXT -1 67 "In ce ce urmeaza, vom considera ca purta toarea este semnal armonic:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "sp:=(t)->Ap*cos(wp*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#spGR6 #%\"tG6\"6$%)operatorG%&arrowGF(*&%#ApG\"\"\"-%$cosG6#*&%#wpGF.9$F.F.F (F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 15 "avand spectrul:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "SMA(omega);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*(%\"kG\"\"\"%#ApGF%,&-%#SmG6#,&%&omegaGF%%$wp|irG!\"\" #F%\"\"#*&F/F%-F)6#,&F,F%F-F%F%F%F%" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 12 "Mod de lucru" }}{PARA 0 "" 0 "" {TEXT -1 133 "In afara de functiile incluse in libraria standard Maple, in aceasta lucrare vor \+ fi utilizate cateva functii din libraria aditionala " }{TEXT 262 7 "SC Slib." }}{PARA 0 "" 0 "" {TEXT -1 55 "Pentru calcularea transformatei \+ Fourier a unor semnale:" }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " } {TEXT 263 7 "FOURIER" }{TEXT -1 65 " \+ " }{HYPERLNK 17 "help" 1 "..\\Help\\Hel pfile.mws" "Functia FOURIER" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 30 "Pentru trunchierea unor serii:" }}{PARA 15 "" 0 "" {TEXT -1 8 " functia " }{TEXT 264 2 "ts" }{TEXT -1 77 " \+ " }{HYPERLNK 17 "help " 1 "..\\Help\\Helpfile.mws" "Functia ts" }{TEXT -1 1 " " }}{PARA 0 " " 0 "" {TEXT -1 45 "Pentru reprezentarea spectrelor unor semnale:" }} {PARA 15 "" 0 "" {TEXT -1 8 "functia " }{TEXT 265 3 "rpa" }{TEXT -1 74 " \+ " }{HYPERLNK 17 "help" 1 "..\\Help\\Helpfile.mws" "Functia rpa " }{TEXT -1 1 " " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart: " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "libname:=\"c:/Maple/SCS lib\",libname:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "F:=FOURIE R:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "assume(wm " 0 "" {MPLTEXT 1 0 41 "Sm:=(omega)->collect(F(sm(t) ,t,omega),m):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "Sp:=(omega )->F(sp(t),t,omega):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "sMA :=(t)->k*sm(t)*sp(t):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "SM A:=(omega)->collect(F(sMA(t),t,omega),m):" }}}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 7 "Exemple" }}{PARA 0 "" 0 "" {TEXT -1 77 "Peste tot in cel e ce urmeaza vom considera ca semnalul purtator este armonic:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "sp:=(t)->Ap*cos(wp*t);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#spGR6#%\"tG6\"6$%)operatorG%&arrowG F(*&%#ApG\"\"\"-%$cosG6#*&%#wpGF.9$F.F.F(F(F(" }}}{SECT 0 {PARA 257 " " 0 "" {TEXT -1 24 "Semnal modulator armonic" }}{PARA 0 "" 0 "" {TEXT -1 90 "Vom presupune in considratiile ce urmeaza ca semnalul modulator este armonic pe frecventa " }{XPPEDIT 18 0 "wm;" "6#%#wmG" }{TEXT -1 33 ", avand si o componenta continua " }{XPPEDIT 18 0 "A0;" "6#%#A0G" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "sm:=(t)->A 0+Am*cos(wm*t+phi);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#smGR6#%\"tG6 \"6$%)operatorG%&arrowGF(,&%#A0G\"\"\"*&%#AmGF.-%$cosG6#,&*&%#wmGF.9$F .F.%$phiGF.F.F.F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 166 "Raportul dintr e amplitudinea componentei altenative si componenta continua ale semna lului modulator poarta numele de indice de modulatie in amplitudine si noteaza cu " }{XPPEDIT 18 0 "m;" "6#%\"mG" }{TEXT -1 24 ". Putem scri e asadar ca:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "A0:=Am/m;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#A0G*&%#AmG\"\"\"%\"mG!\"\"" }}} {PARA 0 "" 0 "" {TEXT -1 43 "Cu aceste notatii, semnalul modulator est e:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 6 "sm(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%#AmG\"\"\"%\"mG!\"\"F&*&F%F&-%$cosG6#,&*&%$wm |irGF&%\"tGF&F&%$phiGF&F&F&" }}}{PARA 0 "" 0 "" {TEXT -1 33 ", iar spe ctrul sau este de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 " Sm(omega);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(%#AmG\"\"\"%#PiGF&,* *&-%$cosG6#%$phiGF&-%&DiracG6#,&%&omegaGF&%$wm|irG!\"\"F&F&*&F*F&-F/6# ,&F2F&F3F&F&F&*(^#F&F&-%$sinGF,F&F.F&F&*(^#F4F&F;F&F6F&F&F&F&*&**\"\"# F&F%F&F'F&-F/6#F2F&F&%\"mGF4F&" }}}{PARA 0 "" 0 "" {TEXT -1 26 "Semnal ul MA este de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sMA(t );" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**%\"kG\"\"\",&*&%#AmGF%%\"mG!\" \"F%*&F(F%-%$cosG6#,&*&%$wm|irGF%%\"tGF%F%%$phiGF%F%F%F%%#ApGF%-F-6#*& %$wp|irGF%F2F%F%" }}}{PARA 0 "" 0 "" {TEXT -1 33 ", iar spectrul sau e ste de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "SMA(omega); " }}{PARA 12 "" 1 "" {XPPMATH 20 "6#,&*,%\"kG\"\"\"%#ApGF&%#AmGF&%#PiG F&,2*&-%$cosG6#%$phiGF&-%&DiracG6#,(%&omegaGF&%$wp|irG!\"\"%$wm|irGF6F &F&*&F,F&-F16#,(F4F&F5F6F7F&F&F&*&F,F&-F16#,(F4F&F5F&F7F6F&F&*&F,F&-F1 6#,(F4F&F5F&F7F&F&F&*(^#F&F&-%$sinGF.F&F0F&F&*(^#F6F&FFF&F9F&F&*(FEF&F FF&F=F&F&*(FIF&FFF&FAF&F&F&#F&\"\"#*&*.FLF&F%F&F'F&F(F&F)F&,&-F16#,&F4 F&F5F6FM*&FMF&-F16#,&F4F&F5F&F&F&F&F&%\"mGF6F&" }}}{PARA 0 "" 0 "" {TEXT -1 209 "Figura Lissajoux care se obtine pe ecranul osciloscopulu i aplicand pe xOsc (CHANNEL1) semnalul modulator si yOsc (CHANNEL2) se mnalul MA este de forma unei armonici incadrate de un trapez cu marime a bazei mici " }{XPPEDIT 18 0 "b;" "6#%\"bG" }{TEXT -1 29 " si marimea bazei bazei mari " }{XPPEDIT 18 0 "B;" "6#%\"BG" }{TEXT -1 20 ", date de relatiile:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "b:=2*Amin; B:=2*Amax;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"bG,$%%AminG\"\"#" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"BG,$%%AmaxG\"\"#" }}}{PARA 0 "" 0 "" {TEXT -1 5 "unde " }{XPPEDIT 18 0 "Amin;" "6#%%AminG" }{TEXT -1 4 " si " }{XPPEDIT 18 0 "Amax;" "6#%%AmaxG" }{TEXT -1 75 " sunt valorile \+ minima si maxima ale semnalului modulator date de relatiile:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 24 "Amin:=A0-Am;Amax:=A0+Am;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%%AminG,&*&%#AmG\"\"\"%\"mG!\"\"F(F'F *" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%AmaxG,&*&%#AmG\"\"\"%\"mG!\"\" F(F'F(" }}}{PARA 0 "" 0 "" {TEXT -1 28 "Inlocuind in expresiile lui " }{XPPEDIT 18 0 "b;" "6#%\"bG" }{TEXT -1 4 " si " }{XPPEDIT 18 0 "B;" " 6#%\"BG" }{TEXT -1 48 ", se obtine urmatoarea expresie pentru raportul " }{XPPEDIT 18 0 "b/B;" "6#*&%\"bG\"\"\"%\"BG!\"\"" }{TEXT -1 1 ":" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "simplify(b/B);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,&!\"\"\"\"\"%\"mGF'F',&F'F'F(F'F&F&" }}} {PARA 0 "" 0 "" {TEXT -1 164 "Vom particulariza in cele ce urmeaza amp litudinea si pulsatia semnalelor modulator si purtator si vom discuta \+ influenta indicelui de modulatie asupra semnalului MA:" }}{PARA 0 "" 0 "" {TEXT -1 72 "In functie de valoarea indicelui de modulatie exista mai multe situatii:" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 24 "Cazul m<1 (submodulatie)" }}{PARA 0 "" 0 "" {TEXT -1 113 "In acest caz componen ta continua a semnalului modulator este mai mare decat componenta alte rnativa a semnalului (" }{XPPEDIT 18 0 "Am < A0;" "6#2%#AmG%#A0G" } {TEXT -1 105 "). Reprezentarile grafice s-au obtinut pentru m = 0.5 da r concluziile sunt valabile pentru orice valoare " }{XPPEDIT 18 0 "m < 1;" "6#2%\"mG\"\"\"" }{TEXT -1 2 " :" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 53 "numvalues:=\{k=1,Ap=1,wp=10,Am=1,wm=1,phi=Pi/4,m=0.5 \}:" }}}{PARA 0 "" 0 "" {TEXT -1 80 "Forma de unda a semnalului MA est e cuprinsa intre o anvelopa superioara data de " }{XPPEDIT 18 0 "sm(t) ;" "6#-%#smG6#%\"tG" }{TEXT -1 34 " si o anvelopa inferioara data de \+ " }{XPPEDIT 18 0 "-sm(t);" "6#,$-%#smG6#%\"tG!\"\"" }{TEXT -1 1 "." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 205 "plot(eval([sm(t),-sm(t),sMA (t)],numvalues),t=-2*Pi..2*Pi,numpoints=400,color=[red,gray,black],lin estyle=[1,1,1],labels=[\"t\",\"\"],title=\"Forme de unda pentru m<1: s m(t) (rosu),-sm(t) (gri), sMA(t) (negru)\");" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6%7\\dl7$$!3)****>YH&=$ G'!#<$\"3hybIsn52FF*7$$!3W\"y!H\"eL-D'F*$\"3]3!4&\\nU$o#F*7$$!3'=)[rrC 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~(negru)Fa]bl-%%VIEWG6$;$!+3`=$G'!\"*$\"+3`=$G'F^^bl%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" }}}}{PARA 0 "" 0 "" {TEXT -1 82 "Spectrele semnalului modula tor si al semnalului MA sunt date in figura de mai jos:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 296 "PLOT3D(rpa(eval(SMA(omega),numvalu es),omega,tipgrafic=D3,interval=-12..12,culoare=[0,0,0]),rpa(eval(Sm(o mega),numvalues),omega,tipgrafic=D3,interval=-12..12,culoare=[1,0,0]), AXESSTYLE(NORMAL),AXESLABELS(\"omega\",\"Re\",\"Im\"),TITLE(\"Spectre \+ pentru m=infinity: Sm(omega) (rosu), SMA(omega) (negru)\"));" }}{PARA 13 "" 1 "" {GLPLOT3D 400 300 300 {PLOTDATA 3 "63-%'CURVESG6&7dw7%$!#7 \"\"!$F*F*F+7%$!+)pRz=\"!\")F+F+7%$!+'Rze<\"F/F+F+7%$!+%4>Q;\"F/F+F+7% $!+#ze<:\"F/F+F+7%$!+!\\)pR6F/F+F+7%$!+)=Qw7\"F/F+F+7%$!+')yd:6F/F+F+7 %$!+%e5F/F+F+7%$!+o^. 25F/F+F+7%$!+l'[(\\**!\"*F+F+7%$!+]c9H)*FjnF+F+7%$!+NEa3(*FjnF+F+7%$!+ 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,&F3F.%$tauG!\"\"F8F.F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 35 "Spectrul \+ semnalului modulator este:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "Sm(omega):simplify(%);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&*(^#! \"\"\"\"\"%#AmGF',(F'F'-%$cosG6#*&%$tauGF'%&omegaGF'F&*&^#F'F'-%$sinGF ,F'F'F'F'F/F&" }}}{PARA 0 "" 0 "" {TEXT -1 26 "Semnalul MA este de for ma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 7 "sMA(t);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#*,%\"kG\"\"\"%#AmGF%,&-%*HeavisideG6#%\"tGF%-F)6 #,&F+F%%$tauG!\"\"F0F%%#ApGF%-%$cosG6#*&%$wp|irGF%F+F%F%" }}}{PARA 0 " " 0 "" {TEXT -1 37 "Spectrul semnalului MA este de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "SMA(omega);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&**%\"kG\"\"\"%#AmGF&%#ApGF&,,**^#F&F&-%$sinG6#*&%$tau GF&%&omegaGF&F&-F-6#*&%$wp|irGF&F0F&F&F5F&F&**F+F&-%$cosGF.F&-F8F3F&F1 F&F&*(F7F&F2F&F5F&!\"\"*(F,F&F9F&F1F&F&*&^#F;F&F1F&F&F&F&*&,&F1F&F5F;F &,&F1F&F5F&F&F;" }}}{PARA 0 "" 0 "" {TEXT -1 114 "Pentru obtinerea rep rezentarilor 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"6#>%#smGR6#%\"tG6\"6$%)operatorG%&arrowGF(-%$sumG6$- %$smgG6#,&9$\"\"\"*&*(\"\"#F4%\"nGF4%#PiGF4F4%#wmG!\"\"F;/F8;,$%)infin ityGF;F?F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 35 "Spectrul semnalului mo dulator este:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Sm(omega); " }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&%#AmG\"\"\"-%$sumG6$,(*&*&^#F& F&-%&DiracG6#,&%&omegaGF&*&%\"nGF&%$wm|irGF&!\"\"F&F&F4F6F&*&*(^#F6F&- %$cosG6#*(%$tauGF&F4F&F5F&F&F.F&F&F4F6F&*&*&-%$sinGF " 0 "" {MPLTEXT 1 0 7 " sMA(t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#**%\"kG\"\"\"-%$sumG6$*&%#A mGF%,&-%*HeavisideG6#,&%\"tGF%*&*(\"\"#F%%\"nGF%%#PiGF%F%%$wm|irG!\"\" F7F%-F-6#,(F0F%*&*(F3F%F4F%F5F%F%F6F7F7%$tauGF7F7F%/F4;,$%)infinityGF7 FAF%%#ApGF%-%$cosG6#*&%$wp|irGF%F0F%F%" }}}{PARA 0 "" 0 "" {TEXT -1 44 "Spectrul semnalului modulator este de forma:" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 11 "SMA(omega);" }}{PARA 12 "" 1 "" {XPPMATH 20 "6 #,$**%\"kG\"\"\"%#ApGF&%#AmGF&,&-%$sumG6$,(*&*&^#F&F&-%&DiracG6#,(%&om egaGF&%$wp|irG!\"\"*&%\"nGF&%$wm|irGF&F7F&F&F9F7F&*&*(^#F7F&-%$cosG6#* (%$tauGF&F9F&F:F&F&F1F&F&F9F7F&*&*&-%$sinGF@F&F1F&F&F9F7F7/F9;,$%)infi nityGF7FJ#F&\"\"#*&FKF&-F+6$,(*&*&F0F&-F26#,(F5F&F6F&F8F7F&F&F9F7F&*&* (F=F&F>F&FSF&F&F9F7F&*&*&FEF&FSF&F&F9F7F7FGF&F&F&F7" }}}{PARA 0 "" 0 " " {TEXT -1 104 "Pentru obtinerea reprezentarilor grafice dam valori co nstantelor care intervin in expresiile semanlelor:" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 45 "numvalues:=\{k=1,Ap=1,wp=10,Am=1,tau=Pi,wm=1 \}:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 253 "plot(eval([eval(ts( sm(t),n=-5..5),numvalues),ts(-sm(t),n=-5..5),ts(sMA(t),n=-5..5)],numva lues), t=-5*Pi..5*Pi, numpoints=200, color=[red,red,black], linestyle= [1,2,1], labels=[\"t\",\"sMA(t)\"], title=\"Forme de unda: modulatoare (rosu) si semnal MA(negru)\");" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6(-%'CURVESG6%7g]l7$$!3'****\\OK'zq:!#;$\"\"!F,7$$!3w d1Oq!zUb\"F*F+7$$!3cu3f'\\2*R:F*F+7$$!3Ru2\")e^uB:F*F+7$$!3>6Xc'ovu]\" 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