{VERSION 4 0 "IBM INTEL NT" "4.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Helvetica" 1 10 255 0 0 1 2 1 2 0 1 2 0 0 0 1 }{CSTYLE "2D Math" -1 2 "Helvetica" 1 10 128 0 0 1 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "Hyperlink" -1 17 "" 0 1 0 128 128 1 2 0 1 0 0 0 0 0 0 1 }{CSTYLE "2D Comment" 2 18 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }{CSTYLE "2D Output" 2 20 "Helvetica" 0 0 128 0 0 1 1 2 2 0 0 0 0 0 0 1 }{CSTYLE "" -1 256 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 262 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 264 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 266 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 267 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 268 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 269 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 270 "" 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 271 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 272 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 273 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 274 "" 0 1 0 0 0 0 1 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 275 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 276 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 277 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 278 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 3 0 3 0 2 2 0 1 }{PSTYLE "Heading 1" -1 3 1 {CSTYLE "" -1 -1 "Helvetica" 1 16 128 0 0 1 2 2 2 2 2 2 1 1 1 1 } 1 1 0 0 8 4 3 0 3 0 2 2 0 1 }{PSTYLE "Heading 2" -1 4 1 {CSTYLE "" -1 -1 "Helvetica" 1 14 128 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 8 2 3 0 3 0 2 2 0 1 }{PSTYLE "Heading 3" -1 5 1 {CSTYLE "" -1 -1 "Helvetica" 1 12 128 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 3 0 3 0 2 2 0 1 } {PSTYLE "Maple Output" -1 11 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 128 0 0 1 1 2 2 2 2 2 1 1 1 1 }3 3 0 0 0 0 3 0 3 0 2 2 0 1 }{PSTYLE "Maple Output" -1 12 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Maple Plot" -1 13 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 128 0 0 1 1 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 3 0 3 0 2 2 0 1 }{PSTYLE "Bullet Item" -1 15 1 {CSTYLE "" -1 -1 "Times" 1 12 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 3 3 1 0 1 0 2 2 15 2 }{PSTYLE "Title" -1 18 1 {CSTYLE "" -1 -1 "Helvetica" 1 16 128 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 12 12 3 0 3 0 2 2 19 1 }{PSTYLE "Auth or" -1 19 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 0 0 0 1 2 1 2 2 2 2 1 1 1 1 }3 1 0 0 8 8 3 0 3 0 2 2 0 1 }{PSTYLE "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "Times" 1 10 0 0 0 1 1 1 2 2 2 2 1 1 1 1 }1 1 0 0 0 0 1 0 1 0 2 2 0 1 }{PSTYLE "Normal" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }3 1 0 0 0 0 3 0 3 0 2 2 0 1 }} {SECT 0 {PARA 18 "" 0 "" {TEXT -1 42 "Semnale cu modulatie de frecvent a sau faza" }}{PARA 19 "" 0 "" {TEXT -1 86 "Universitatea Tehnica \"Gh . Asachi\", Iasi, Facultatea de Electronica si Telecomunicatii" }} {PARA 19 "" 0 "" {TEXT -1 43 "Laboratorul de Semnale, Circuite si Sist eme" }}{PARA 19 "" 0 "" {URLLINK 17 "http://scs4.etc.tuiasi.ro" 4 "htt p://scs4.etc.tuiasi.ro/scslabs/Simbolice/simbolice.htm" "" }{TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 16 "Breviar teoretic" }}{PARA 0 "" 0 "" {TEXT 272 16 "Scopul lucrarii:" }}{PARA 0 "" 0 "" {TEXT -1 129 "Familiarizarea cu formele de unda ale unui semnal cu modulatie in frecventa. Calcularea si reprezentarea spectrului semnalului MF" }} {PARA 0 "" 0 "" {TEXT 273 17 "Rezumat teoretic:" }}{PARA 0 "" 0 "" {TEXT -1 350 "Modulatia in general este un proces de grefare a informa tiei continute de semnalul util (modulator) de frecventa joasa pe un s emnal purtator de frecventa ridicata, semnalul obtinut in urma unui pr oces de modulatie numindu-se semnal modulat. In cazul in care semnalul modulator influenteaza frecventa sau faza semnalului purtator, proces ul corespunde " }{TEXT 271 23 "modulatiei de frecventa" }{TEXT 270 12 ", respectiv " }{TEXT 274 18 "modulatiei de faza" }{TEXT -1 1 "." }} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 27 "Modulatia de frecventa (MF)" }} {PARA 0 "" 0 "" {TEXT -1 105 "Acest proces pesupune in esenta grefarea semnalului modulator pe frecventa instantanee a unei purtatoare." }} {PARA 0 "" 0 "" {TEXT -1 5 "Daca " }{XPPEDIT 18 0 "p(t) = A0*cos(omega [p]*t);" "6#/-%\"pG6#%\"tG*&%#A0G\"\"\"-%$cosG6#*&&%&omegaG6#F%F*F'F*F *" }{TEXT -1 4 " si " }{XPPEDIT 18 0 "m(t);" "6#-%\"mG6#%\"tG" }{TEXT -1 52 " este semnalul modulator, semnalul MF este de forma " } {XPPEDIT 18 0 "s[MF](t) = A0*cos(phi[i](t));" "6#/-&%\"sG6#%#MFG6#%\"t G*&%#A0G\"\"\"-%$cosG6#-&%$phiG6#%\"iG6#F*F-" }{TEXT -1 7 ", unde " } {XPPEDIT 18 0 "phi[i](t) = int(omega[i](t),t);" "6#/-&%$phiG6#%\"iG6#% \"tG-%$intG6$-&%&omegaG6#F(6#F*F*" }{TEXT -1 28 ", iar frecventa insta ntanee " }{XPPEDIT 18 0 "omega[i](t);" "6#-&%&omegaG6#%\"iG6#%\"tG" } {TEXT -1 15 " este de forma:" }}{PARA 0 "" 0 "" {XPPEDIT 18 0 "omega[i ](t) = omega[p]*t+Kf*m(t);" "6#/-&%&omegaG6#%\"iG6#%\"tG,&*&&F&6#%\"pG \"\"\"F*F0F0*&%#KfGF0-%\"mG6#F*F0F0" }{TEXT -1 35 ". Asadar semnalul M F este de forma:" }}{PARA 0 "" 0 "" {XPPEDIT 18 0 "s[MF](t) = A0*cos(o mega[p]*t+Kf*int(m(t),t));" "6#/-&%\"sG6#%#MFG6#%\"tG*&%#A0G\"\"\"-%$c osG6#,&*&&%&omegaG6#%\"pGF-F*F-F-*&%#KfGF--%$intG6$-%\"mG6#F*F*F-F-F- " }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 169 "Tratarea semnalelor \+ MF | MP, incazul modulatoarelor oarecare este in general dificila. Din acest motiv, in continuare se prezinta in detaliu cazul modulatoarei \+ armonice." }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 24 "Semnal modulator arm onic" }}{PARA 0 "" 0 "" {TEXT -1 24 "Pentru semnal modulator " } {XPPEDIT 18 0 "m(t);" "6#-%\"mG6#%\"tG" }{TEXT -1 15 " este de forma \+ " }{XPPEDIT 18 0 "m(t) = Am*cos(omega[m]*t);" "6#/-%\"mG6#%\"tG*&%#AmG \"\"\"-%$cosG6#*&&%&omegaG6#F%F*F'F*F*" }{TEXT -1 61 ", ceea ce conduc e la urmatoarea expresie pentru semnalul MF: " }{XPPEDIT 18 0 "s[MF](t ) = Ap*cos(omega[p]*t+Kf*Am*int(cos(omega[m]*t),t));" "6#/-&%\"sG6#%#M FG6#%\"tG*&%#ApG\"\"\"-%$cosG6#,&*&&%&omegaG6#%\"pGF-F*F-F-*(%#KfGF-%# AmGF--%$intG6$-F/6#*&&F46#%\"mGF-F*F-F*F-F-F-" }{TEXT -1 8 ", adica " }{XPPEDIT 18 0 "s[MF](t) = Ap*cos(omega[p]*t+Kf*Am*sin(omega[m]*t)/ome ga[m]+phi0);" "6#/-&%\"sG6#%#MFG6#%\"tG*&%#ApG\"\"\"-%$cosG6#,(*&&%&om egaG6#%\"pGF-F*F-F-**%#KfGF-%#AmGF--%$sinG6#*&&F46#%\"mGF-F*F-F-&F46#F @!\"\"F-%%phi0GF-F-" }{TEXT -1 30 ", unde constanta de integrare " } {XPPEDIT 18 0 "phi0;" "6#%%phi0G" }{TEXT -1 49 " are semnificatia faze i initiale a semnalului MF." }}{PARA 0 "" 0 "" {TEXT -1 46 "In expresi a anterioara se introduce notatiile:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{XPPEDIT 18 0 "Delta(omega) = Kf*Am;" "6#/-%&DeltaG6#%&omegaG*&%#KfG \"\"\"%#AmGF*" }{TEXT -1 9 ", pentru " }{TEXT 256 28 "deviatia maxima \+ de frecventa" }{TEXT -1 17 " a semnalului MF." }}{PARA 0 "" 0 "" {XPPEDIT 18 0 "beta = Kf*Am/omega[m];" "6#/%%betaG*(%#KfG\"\"\"%#AmGF' &%&omegaG6#%\"mG!\"\"" }{TEXT -1 9 ", pentru " }{TEXT 257 35 "indicele de modulatie in frecventa." }}{PARA 0 "" 0 "" {TEXT -1 73 "In aceste \+ conditii, expresia semnalului MF cu modulatoare armonica este: " } {XPPEDIT 18 0 "s[MF](t) = A[p]*cos(omega[p]*t+beta*sin(omega[m]*t));" "6#/-&%\"sG6#%#MFG6#%\"tG*&&%\"AG6#%\"pG\"\"\"-%$cosG6#,&*&&%&omegaG6# F/F0F*F0F0*&%%betaGF0-%$sinG6#*&&F76#%\"mGF0F*F0F0F0F0" }{TEXT -1 10 " ( pentru " }{XPPEDIT 18 0 "phi0 = 0;" "6#/%%phi0G\"\"!" }{TEXT -1 2 " )." }}{SECT 0 {PARA 20 "" 0 "" {TEXT -1 53 "Forma de unda a semnalelor MF cu modulatoare armonica" }}{PARA 0 "" 0 "" {TEXT -1 36 "Forma de u nda a unui semnal MF este:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "libname:=\"../ SCSlib\",libname:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "assume (_wm,positive):assume(_wp,positive):assume(_k,integer);" }}}{PARA 0 " " 0 "" {TEXT -1 25 "Fie semnalul MF de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "sMF:=Ap*cos(wp*t+beta*sin(wm*t)):" }}}{PARA 0 " " 0 "" {TEXT -1 82 "Ne propunem sa reprezentam acest semnal in doua ca zuri particulare semnificative: " }{XPPEDIT 18 0 "beta = .1;" "6#/%%be taG$\"\"\"!\"\"" }{TEXT -1 4 " si " }{XPPEDIT 18 0 "beta = 4.0;" "6#/% %betaG$\"#S!\"\"" }{TEXT -1 42 ". Celelalte marimi au urmatoarele valo ri: " }{XPPEDIT 18 0 "Ap = 1;" "6#/%#ApG\"\"\"" }{TEXT -1 2 ", " } {XPPEDIT 18 0 "wp = 1;" "6#/%#wpG\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "wm = .1;" "6#/%#wmG$\"\"\"!\"\"" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 111 "plot(eval(sMF,[Ap=1,wp=1,wm=0.1,beta=0.2 ]),t=-20*Pi..20*Pi,title=\"Forma de unda a unui semnal MF cu beta=0.1 \");" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVE SG6$7_im7$$!3;++i%H&=$G'!#;$\"2y\"**************!#<7$$!3#*e)))\\SY*[iF *$\"3g4CPefM'R*!#=7$$!3o'F*$ \"36w$fX?jZU'F37$$!3YwlsD'o/='F*$\"3Ww+\"=(G(e*\\F37$$!3[05\"4=\\L;'F* $\"3LSY![7?^T$F37$$!3ANa4O(Hi9'F*$\"3$zY\"3WNfI6'F*$!38yz!)\\%\\Ku\"F37$$!3-B([;Sr[4'F* $!3)QPYrSUpU$F37$$!3w_J$o&>vxgF*$!3t')[m<&yj+&F37$$!3]#evLdLkF37$$!3_6??nI^VgF*$!39S%>=-)=lwF37$$!3aSkQAOREgF*$!3m.*=4SXQm)F 37$$!3Gq3dxTF4gF*$!3+!\\eTIk#*R*F37$$!3A;ShX)**)**F37$$!3]N(ySLN?(fF*$!3_\"=.+e_^***F37$$!373 .QlvekfF*$!3MGdQHcxU**F37$$!3u!)=o'zRr&fF*$!36#\\s84jJ$)*F37$$!33aM)z- #p\\fF*$!3IDIluR&pm*F37$$!3'fu*=`4!*>fF*$!3+%*48'=/-Y)F37$$!3'y.'Ry)4, *eF*$!3C0!4f8b0['F37$$!3#Q=**4M9_(eF*$!3K$zmBaI_D&F37$$!3wHBg.)=.'eF*$ !3)**[Pjzj$4RF37$$!3qva?mKUXeF*$!3+Q*)p\"\\-RZ#F37$$!3l@'3)Gx_IeF*$!38 l;^8gL=)*!#>7$$!3fnKc\"eF*$\"3#H<:J@kdK&F\\t7$$!3a8\\,amt+eF*$\"3 7\\R[>,dM?F37$$!3?g!=m6Tey&F*$\"3'o]6e)yp*[$F37$$!3;17Azb%4x&F*$\"3C^ \\1!y3Y'[F37$$!3-?Ga*)R>adF*$\"3e6W'3*G#fF'F37$$!3>LW')*RUut&F*$\"3J6% Q\"eT@0vF37$$!31Zg=53p?dF*$\"3ZR-[!Gsp^)F37$$!3$4m20ARRq&F*$\"3MGdK#>= ?G*F37$$!3#[FH3j(=(o&F*$\"3'ebyb%>My(*F37$$!3q))3:TgVqcF*$\"3=p:nT8t\" ***F37$$!3c-DZ^Wo`cF*$\"32'*3D![th\"**F37$$!3W;TzhG$pj&F*$\"3!e6Re.=Sb *F37$$!3JId6s7=?cF*$\"3)z)p$e-)*e\"*)F37$$!3=WtV#oHMg&F*$\"3#pg[\"))3T ?!)F37$$!3Od*eF4yme&F*$\"3U*pK%Q'pN*oF37$$!3Ar03.l#*pbF*$\"3_Ys=B0/obF 37$$!35&=-M\"\\<`bF*$\"3Ii$3It*=#3%F37$$!3F)zBPKBk`&F*$\"3Ku5@8s'*yCF3 7$$!397a/MbF*$\"3%=#p#z\\-m/)F\\t7$$!3,EqOW,#H]&F*$!3NSRZV\"oW#*)F \\t7$$!3A(RyU^dg[&F*$!3W/mJW\"\\Vd#F37$$!37p(*=%)[>paF*$!3EoR&R*ey!=%F 37$$!3-T65aAL_aF*$!3]?Uc0E)\\m&F37$$!3A7D,C'paV&F*$!3)p]/xI%y$)pF37$$! 3ga_$QOW!o`F*$!3p)*)zCJDW$**F37$$!3 \"3u![VQHM`F*$!3U#HU*\\]:W(*F37$$!3>$[.Leo0I&F*$!3Ayi`^/(4V)F37$$!3Sa[ @`fq$G&F*$!3_M`Q73X'R(F37$$!3IEi7BL%oE&F*$!3k4X9Vz(y9'F37$$!3?)fPIp!)* \\_F*$!30CrX2zf@ZF37$$!3Sp*[H1=JB&F*$!3IUVQ@:0fJF37$$!3MTw*zdNj@&F*$!3 #)\\rd?Lc8:F37$$!3G8j/$4`&*>&F*$\"3%)\\UHo`(zu\"F\\t7$$!3A&)\\431x#=&F *$\"3e.B>**Rmd=F37$$!3)ylVJ7))f;&F*$\"3#yP')[5(*o[$F37$$!3aIB>Qc?\\^F* $\"34gPoQH'f,&F37$$!3Z-5C`JUK^F*$\"3qUf2^*f7S'F37$$!3Tu'*Go1k:^F*$\"3Z !e+c\")eLg(F37$$!3OY$QL=e))4&F*$\"3_'pYal>\")e)F37$$!3I=qQ)pv?3&F*$\"3 Xpm&=7bwK*F37$$!3C!pNM@$Hl]F*$\"3^)>&*HM76!)*F37$$!3AE+'4(>!p0&F*$\"3a `G(3`:O$**F37$$!3=iV[G2^[]F*$\"35;'p\"[?D&***F37$$!3:)p3g[>,/&F*$\"3Ot 88udh&)**F37$$!37MI`V#G<.&F*$\"3Ns>2`!4[!**F37$$!3113T*zF37$$!3gAxs.$)fk\\F*$\"35-&pPZu>(oF37$$!3]K-(=zQ!\\\\F*$\"3 g+KCJ:&pl&F37$$!3qTF,!GzM$\\F*$\"3FUTs!4_VI%F37$$!3*3Db\"o(>z\"\\F*$\" 3k&fuv*QEZGF37$$!34gxHc-O-\\F*$\"33QU%)H,F@8F37$$!3Ip-WW2!o)[F*$!3[ag0 BSAkBF\\t7$$!3[yFeK7Cr[F*$!3%[$3\")y@*yy\"F37$$!3o(GD2s\"ob[F*$!3')3aY jnU&H$F37$$!3(ozn)3A7S[F*$!37J$)Q[*QCs%F37$$!321.,(piX#[F*$!3U!zip+`V. 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F+-%'COLOURG6&%$RGBG$\"#5!\"\"$\"\"!FgezFfez-%+AXESLABELSG6$Q\"t6\"Q!6 \"-%&TITLEG6#QKForma~de~unda~a~unui~semnal~MF~cu~beta=4.0F\\fz-%%VIEWG 6$;$!+3`=$G'!\")$\"+3`=$G'Fifz%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT -1 138 "Din graficele anterioare se observa ca variatia frecventei ins tantanee a semnalului MF este cu atat mai mare cu cat indicele de modu latie " }{XPPEDIT 18 0 "beta;" "6#%%betaG" }{TEXT -1 15 " este mai mar e." }}}{SECT 0 {PARA 20 "" 0 "" {TEXT -1 46 "Spectrul semnalelor MF cu modulatoare armonica" }}{PARA 0 "" 0 "" {TEXT -1 139 "Spectrul semnal elor MF se calculeaza folosind descompunerea in serie Fourier complexa a echivalentului de joasa frecventa al semnalului MF." }}{PARA 0 "" 0 "" {TEXT -1 60 "Semnalul analitic corespunzator semnalului MF este d e forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "sa:=Ap*exp(I*wp* t+I*beta*sin(wm*t)):" }}}{PARA 0 "" 0 "" {TEXT -1 73 "Echivalentul de \+ joasa frecventa al semnalului MF se defineste cu relatia:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "sj:=simplify(sa*exp(-I*wp*t));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#sjG*&%#ApG\"\"\"-%$expG6#*(^#F'F'%% betaGF'-%$sinG6#*&%#wmGF'%\"tGF'F'F'" }}}{PARA 0 "" 0 "" {TEXT -1 170 "Dupa cum se poate observa, echivalentul de joasa frecventa este un se mnal periodic deci se poate descompune in serie Fourier complexa. Acea sta descompunere este de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sj:=cs(sj);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#sjG*&%#ApG\" \"\"-%$sumG6$*&-%(BesselJG6$%\"kG%%betaGF'-%$expG6#**^#F'F'F/F'%#wmGF' %\"tGF'F'/F/;,$%)infinityG!\"\"F;F'" }}}{PARA 0 "" 0 "" {TEXT -1 35 "S emnalul analitic rezulta de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "sa:=sj*exp(I*wp*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#>%#saG*(%#ApG\"\"\"-%$sumG6$*&-%(BesselJG6$%\"kG%%betaGF'-%$expG6#** ^#F'F'F/F'%#wmGF'%\"tGF'F'/F/;,$%)infinityG!\"\"F;F'-F26#*(F5F'%#wpGF' F7F'F'" }}}{PARA 0 "" 0 "" {TEXT -1 124 "Semnalul MF reprezinta partea reala a semnalului analitic. Ca urmare, decsompunerea spectrala a sem nalului MF este de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "sMF:=cs(sMF);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$sMFG*&%#ApG\"\"\" -%$sumG6$*&-%(BesselJG6$%\"kG%%betaGF'-%$cosG6#,&*&%#wpGF'%\"tGF'F'*(F /F'%#wmGF'F7F'F'F'/F/;,$%)infinityG!\"\"F=F'" }}}{PARA 0 "" 0 "" {TEXT -1 72 "Din expresia anterioara deducem ca spectrul semnalului MF este de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "SMF:=subs ([_wm=wm,_wp=wp,_k=k],FOURIER(subs([wm=_wm,wp=_wp,k=_k],sMF),t,omega)) ;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$SMFG*&%#ApG\"\"\"-%$sumG6$,&*( -%(BesselJG6$%\"kG%%betaGF'%#PiGF'-%&DiracG6#,(%&omegaGF'%#wpG!\"\"*&% #wmGF'F0F'F9F'F'*(F-F'F2F'-F46#,(F7F'F8F'F:F'F'F'/F0;,$%)infinityGF9FC F'" }}}{PARA 0 "" 0 "" {TEXT -1 94 "Se observa ca spectrul semnalului \+ MF este real. In functie de valoarea indicelui de modulatie " } {XPPEDIT 18 0 "beta;" "6#%%betaG" }{TEXT -1 94 ", banda semnalului MF \+ se modifica, iar semnalele MF se clasifica din acest punct de vedere i n:" }}{PARA 15 "" 0 "" {TEXT -1 14 "semnale MF de " }{TEXT 262 13 "ban da ingusta" }{TEXT -1 36 ": astfel de semnale se obtin pentru " } {XPPEDIT 18 0 "beta < .4;" "6#2%%betaG$\"\"%!\"\"" }{TEXT -1 52 " expr esia benzii in acest caz fiind data de relatia " }{XPPEDIT 18 0 "B = 2 *wm;" "6#/%\"BG*&\"\"#\"\"\"%#wmGF'" }}{PARA 15 "" 0 "" {TEXT -1 14 "s emnale MF de " }{TEXT 263 11 "banda larga" }{TEXT -1 36 ": astfel de s emnale se obtin pentru " }{XPPEDIT 18 0 "1.0 < beta;" "6#2$\"#5!\"\"%% betaG" }{TEXT -1 52 " expresia benzii in acest caz fiind data de relat ia " }{XPPEDIT 18 0 "B = 2*wm*(1+beta+sqrt(beta));" "6#/%\"BG*(\"\"#\" \"\"%#wmGF',(F'F'%%betaGF'-%%sqrtG6#F*F'F'" }}{PARA 0 "" 0 "" {TEXT -1 97 "Reprezentarea grafica a acestuia este data mai jos pentru doua \+ situatii particulare semnicative: " }{XPPEDIT 18 0 "beta = .1;" "6#/%% betaG$\"\"\"!\"\"" }{TEXT -1 33 " (semnal MF de banda ingusta) si " } {XPPEDIT 18 0 "beta = 4.0;" "6#/%%betaG$\"#S!\"\"" }{TEXT -1 59 " (sem nal MF de banda larga). Celelalte marimi au valorile: " }{XPPEDIT 18 0 "Ap = 1;" "6#/%#ApG\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "wp = 1; " "6#/%#wpG\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "wm = .1;" "6#/%#wm G$\"\"\"!\"\"" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 154 "PLOT(rpa(ts(eval(evalf(SMF),[Ap=1,wp=1,wm=0.1,beta=0.1]),k=-10. .10),omega,interval=-2..2,tipgrafic=real),TITLE(\"Spectrul semnalului \+ MF pentru beta=0.1\"));" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6`p-%'CURVESG6&7dw7$$!\"#\"\"!$F*F*7$$!3_(\\**)z&p*y>!#Q7r1'>F/F+7$$!3d/4='f#4S>F/F+7$$!3c>F/F+7$$!3W#\\)pz6 w)*=F/F+7$$!3'zc8F1Z'z=F/F+7$$!3uU&3<]b)f=F/F+7$$!3.D]+TqQR=F/F+7$$!3' Hd9HA%)*==F/F+7$$!3;!)f\"F/F+7$$!3-)f>R-/#y:F/F+7$$!3!=Ryc8Hvb\"F/F+7$$!3pc8 FMJaQ:F/F+7$$!3yqT$o;k!=:F/F+7$$!3azeQJf@\"F/F+7$$!35^-0q8#f>\"F/F+7$$!3Iq S\"GCea<\"F/F+7$$!3)\\,.1ck^:\"F/F+7$$!3nc8Fun^O6F/F+7$$!3;oOt1V9:6F/F +7$$!3kC\\)p^Gg4\"F/F+7$$!3A_/4)4Zc2\"F/F+7$$!3#**)zfz%Rh0\"F/F+7$$!3% 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41" "Curve 42" "Curve 43" "Curve 44" "Curve 45 " "Curve 46" "Curve 47" "Curve 48" "Curve 49" "Curve 50" "Curve 51" "C urve 52" "Curve 53" "Curve 54" "Curve 55" "Curve 56" "Curve 57" "Curve 58" "Curve 59" "Curve 60" "Curve 61" "Curve 62" "Curve 63" "Curve 64 " "Curve 65" "Curve 66" "Curve 67" "Curve 68" "Curve 69" "Curve 70" "C urve 71" "Curve 72" "Curve 73" "Curve 74" "Curve 75" "Curve 76" "Curve 77" "Curve 78" "Curve 79" "Curve 80" "Curve 81" "Curve 82" "Curve 83 " }}}}}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 22 "Modulatia de faza (MP)" }}{PARA 0 "" 0 "" {TEXT -1 100 "Acest proces pesupune in esenta grefar ea semnalului modulator pe faza instantanee a unei purtatoare." }} {PARA 0 "" 0 "" {TEXT -1 5 "Daca " }{XPPEDIT 18 0 "p(t) = Ap*cos(omega [p]*t);" "6#/-%\"pG6#%\"tG*&%#ApG\"\"\"-%$cosG6#*&&%&omegaG6#F%F*F'F*F *" }{TEXT -1 4 " si " }{XPPEDIT 18 0 "m(t);" "6#-%\"mG6#%\"tG" }{TEXT -1 52 " este semnalul modulator, semnalul MP este de forma " } {XPPEDIT 18 0 "s[MP](t) = A0*cos(phi[i](t));" "6#/-&%\"sG6#%#MPG6#%\"t G*&%#A0G\"\"\"-%$cosG6#-&%$phiG6#%\"iG6#F*F-" }{TEXT -1 7 ", unde " } {XPPEDIT 18 0 "phi[i](t) = omega[p]*t+Kp*m(t);" "6#/-&%$phiG6#%\"iG6#% \"tG,&*&&%&omegaG6#%\"pG\"\"\"F*F1F1*&%#KpGF1-%\"mG6#F*F1F1" }{TEXT -1 7 ", unde " }{XPPEDIT 18 0 "Kp;" "6#%#KpG" }{TEXT -1 53 " este o co nstanta. Asadar semnalul MF este de forma: " }{XPPEDIT 18 0 "s[MP](t) \+ = Ap*cos(omega[p]*t+Kp*m(t));" "6#/-&%\"sG6#%#MPG6#%\"tG*&%#ApG\"\"\"- %$cosG6#,&*&&%&omegaG6#%\"pGF-F*F-F-*&%#KpGF--%\"mG6#F*F-F-F-" }{TEXT -1 1 "." }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 24 "Semnal modulator armon ic" }}{PARA 0 "" 0 "" {TEXT -1 24 "Pentru semnal modulator " } {XPPEDIT 18 0 "m(t);" "6#-%\"mG6#%\"tG" }{TEXT -1 15 " este de forma \+ " }{XPPEDIT 18 0 "m(t) = Am*sin(omega[m]*t);" "6#/-%\"mG6#%\"tG*&%#AmG \"\"\"-%$sinG6#*&&%&omegaG6#F%F*F'F*F*" }{TEXT -1 61 ", ceea ce conduc e la urmatoarea expresie pentru semnalul MF: " }{XPPEDIT 18 0 "s[MP](t ) = Ap*cos(omega[p]*t+Kp*Am*sin(omega[m]*t));" "6#/-&%\"sG6#%#MPG6#%\" tG*&%#ApG\"\"\"-%$cosG6#,&*&&%&omegaG6#%\"pGF-F*F-F-*(%#KpGF-%#AmGF--% $sinG6#*&&F46#%\"mGF-F*F-F-F-F-" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 46 "In expresia anterioara se introduce notatiile:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{XPPEDIT 18 0 "Delta(omega) = Kp*Am*omega[m]; " "6#/-%&DeltaG6#%&omegaG*(%#KpG\"\"\"%#AmGF*&F'6#%\"mGF*" }{TEXT -1 9 ", pentru " }{TEXT 258 28 "deviatia maxima de frecventa" }{TEXT -1 17 " a semnalului MP." }}{PARA 0 "" 0 "" {XPPEDIT 18 0 "alpha = Kp;" " 6#/%&alphaG%#KpG" }{TEXT -1 9 ", pentru " }{TEXT 259 30 "indicele de m odulatie in faza." }}{PARA 0 "" 0 "" {TEXT -1 72 "In aceste conditii, \+ expresia semnalului MP cu modulatoare armonica este:" }{XPPEDIT 18 0 " s[MP](t) = A[p]*cos(omega[p]*t+alpha*sin(omega[m]*t));" "6#/-&%\"sG6#% #MPG6#%\"tG*&&%\"AG6#%\"pG\"\"\"-%$cosG6#,&*&&%&omegaG6#F/F0F*F0F0*&%& alphaGF0-%$sinG6#*&&F76#%\"mGF0F*F0F0F0F0" }{TEXT -1 10 " ( pentru " } {XPPEDIT 18 0 "phi0 = 0;" "6#/%%phi0G\"\"!" }{TEXT -1 2 ")." }}{SECT 0 {PARA 20 "" 0 "" {TEXT -1 53 "Forma de unda a semnalelor MP cu modul atoare armonica" }}{PARA 0 "" 0 "" {TEXT -1 36 "Forma de unda a unui s emnal MF este:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" } }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "libname:=\"../SCSlib\",lib name:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "assume(_wm,positiv e):assume(_wp,positive):assume(_k,integer);" }}}{PARA 0 "" 0 "" {TEXT -1 25 "Fie semnalul MP de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 34 "sMP:=Ap*cos(wp*t+alpha*sin(wm*t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$sMPG*&%#ApG\"\"\"-%$cosG6#,&*&%#wpGF'%\"tGF'F'*&%&al phaGF'-%$sinG6#*&%#wmGF'F.F'F'F'F'" }}}{PARA 0 "" 0 "" {TEXT -1 82 "Ne propunem sa reprezentam acest semnal in doua cazuri particulare semni ficative: " }{XPPEDIT 18 0 "alpha = .1;" "6#/%&alphaG$\"\"\"!\"\"" } {TEXT -1 4 " si " }{XPPEDIT 18 0 "alpha = 4.0;" "6#/%&alphaG$\"#S!\"\" " }{TEXT -1 42 ". Celelalte marimi au urmatoarele valori: " }{XPPEDIT 18 0 "Ap = 1;" "6#/%#ApG\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "wp = \+ 1;" "6#/%#wpG\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "wm = .1;" "6#/%# wmG$\"\"\"!\"\"" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 113 "plot(eval(sMP,[Ap=1,wp=1,wm=0.1,alpha=0.1]),t=-20*Pi..20*Pi,t itle=\"Forma de unda a unui semnal MP cu alpha=0.1\");" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7]im7$$!3;++i%H& =$G'!#;$\"2+#**************!#<7$$!3#*e)))\\SY*[iF*$\"3![BcDW/!3%*!#=7$ $!3of8-xF37$$!3UZ@aq!)e(>'F*$\"3cwa#4=T+\\'F37$$!3 YwlsD'o/='F*$\"3QGMME?V%3&F37$$!3[05\"4=\\L;'F*$\"3\\Ig]*GNs_$F37$$!3A Na4O(Hi9'F*$\"3%R)oN&*e*['=F37$$!3'\\')z7H5\"HhF*$\"3unz*)eC!*p9!#>7$$ !3)RHkk%3*>6'F*$!3yz<1ZODv:F37$$!3-B([;Sr[4'F*$!3YW/>L][]KF37$$!3w_J$o &>vxgF*$!3h/<5)fi(G[F37$$!3]#efF*$!3\\EN!eYwUk)F37$$!3'y.'Ry)4,*eF*$!3#)4R$fLWuw'F37 $$!3#Q=**4M9_(eF*$!3)eufe9^&)e&F37$$!3wHBg.)=.'eF*$!3=7APnQo$G%F37$$!3 qva?mKUXeF*$!3C.4SAOH#)GF37$$!3l@'3)Gx_IeF*$!34\"yH2#)**fT\"F37$$!3fn< T\">Kc\"eF*$\"36\"y=yr@C@)!#?7$$!3a8\\,amt+eF*$\"3%RYX;0)Hy:F37$$!3?g! 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}{TEXT -1 15 " este mai mare." }}}{SECT 0 {PARA 20 "" 0 "" {TEXT -1 46 "Spectrul semnalelor MP cu modulatoare armonica" }}{PARA 0 "" 0 "" {TEXT -1 139 "Spectrul semnalelor MP se calculeaza folosind \+ descompunerea in serie Fourier complexa a echivalentului de joasa frec venta al semnalului MP." }}{PARA 0 "" 0 "" {TEXT -1 60 "Semnalul anali tic corespunzator semnalului MP este de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 37 "sa:=Ap*exp(I*wp*t+I*alpha*sin(wm*t)):" }}}{PARA 0 "" 0 "" {TEXT -1 73 "Echivalentul de joasa frecventa al semnalului M P se defineste cu relatia:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 30 "sj:=simplify(sa*exp(-I*wp*t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6# >%#sjG*&%#ApG\"\"\"-%$expG6#*(^#F'F'%&alphaGF'-%$sinG6#*&%#wmGF'%\"tGF 'F'F'" }}}{PARA 0 "" 0 "" {TEXT -1 170 "Dupa cum se poate observa, ech ivalentul de joasa frecventa este un semnal periodic deci se poate des compune in serie Fourier complexa. Aceasta descompunere este de forma: " }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 11 "sj:=cs(sj);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#sjG*&%#ApG\"\"\"-%$sumG6$*&-%(BesselJG6$%\"k G%&alphaGF'-%$expG6#**^#F'F'F/F'%#wmGF'%\"tGF'F'/F/;,$%)infinityG!\"\" F;F'" }}}{PARA 0 "" 0 "" {TEXT -1 35 "Semnalul analitic rezulta de for ma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 19 "sa:=sj*exp(I*wp*t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#saG*(%#ApG\"\"\"-%$sumG6$*&-%(Bes selJG6$%\"kG%&alphaGF'-%$expG6#**^#F'F'F/F'%#wmGF'%\"tGF'F'/F/;,$%)inf inityG!\"\"F;F'-F26#*(F5F'%#wpGF'F7F'F'" }}}{PARA 0 "" 0 "" {TEXT -1 124 "Semnalul MP reprezinta partea reala a semnalului analitic. Ca urm are, decsompunerea spectrala a semnalului MP este de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "sMP:=cs(sMP);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$sMPG*&%#ApG\"\"\"-%$sumG6$*&-%(BesselJG6$%\"kG%&alph aGF'-%$cosG6#,&*&%#wpGF'%\"tGF'F'*(F/F'%#wmGF'F7F'F'F'/F/;,$%)infinity G!\"\"F=F'" }}}{PARA 0 "" 0 "" {TEXT -1 72 "Din expresia anterioara de ducem ca spectrul semnalului MP este de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 80 "SMP:=subs([_wm=wm,_wp=wp,_k=k],FOURIER(subs([wm= _wm,wp=_wp,k=_k],sMP),t,omega));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>% $SMPG*&%#ApG\"\"\"-%$sumG6$,&*(-%(BesselJG6$%\"kG%&alphaGF'%#PiGF'-%&D iracG6#,(%&omegaGF'%#wpG!\"\"*&%#wmGF'F0F'F9F'F'*(F-F'F2F'-F46#,(F7F'F 8F'F:F'F'F'/F0;,$%)infinityGF9FCF'" }}}{PARA 0 "" 0 "" {TEXT -1 94 "Se observa ca spectrul semnalului MP este real. In functie de valoarea i ndicelui de modulatie " }{XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 94 ", banda semnalului MP se modifica, iar semnalele MP se clasific a din acest punct de vedere in:" }}{PARA 15 "" 0 "" {TEXT -1 14 "semna le MP de " }{TEXT 264 13 "banda ingusta" }{TEXT -1 36 ": astfel de sem nale se obtin pentru " }{XPPEDIT 18 0 "alpha < .4;" "6#2%&alphaG$\"\"% !\"\"" }{TEXT -1 52 " expresia benzii in acest caz fiind data de relat ia " }{XPPEDIT 18 0 "B = 2*wm;" "6#/%\"BG*&\"\"#\"\"\"%#wmGF'" }} {PARA 15 "" 0 "" {TEXT -1 14 "semnale MP de " }{TEXT 265 11 "banda lar ga" }{TEXT -1 36 ": astfel de semnale se obtin pentru " }{XPPEDIT 18 0 "1.0 < alpha;" "6#2$\"#5!\"\"%&alphaG" }{TEXT -1 52 " expresia benzi i in acest caz fiind data de relatia " }{XPPEDIT 18 0 "B = 2*wm*(1+alp ha+sqrt(alpha));" "6#/%\"BG*(\"\"#\"\"\"%#wmGF',(F'F'%&alphaGF'-%%sqrt G6#F*F'F'" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 97 "Reprezentarea grafica a acestuia este data mai jos pentru doua situatii particulare semnicative: " }{XPPEDIT 18 0 "alpha = .1;" "6#/%&alphaG$\"\"\"!\"\" " }{TEXT -1 33 " (semnal MP de banda ingusta) si " }{XPPEDIT 18 0 "alp ha = 4.0;" "6#/%&alphaG$\"#S!\"\"" }{TEXT -1 59 " (semnal MP de banda \+ larga). Celelalte marimi au valorile: " }{XPPEDIT 18 0 "Ap = 1;" "6#/% #ApG\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "wp = 1;" "6#/%#wpG\"\"\" " }{TEXT -1 2 ", " }{XPPEDIT 18 0 "wm = .1;" "6#/%#wmG$\"\"\"!\"\"" } {TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 145 "PLOT(rpa(t s(eval(SMP,[Ap=1,wp=1,wm=0.1,alpha=0.1]),k=-10..10),omega,interval=-2. .2,tipgrafic=real),TITLE(\"Spectrul semnalului MP cu alpha=0.1\"));" } }{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6`p-%'CURVESG6&7d w7$$!\"#\"\"!$F*F*7$$!3_(\\**)z&p*y>!#Q7r1'>F/F+7$$!3d/4=' f#4S>F/F+7$$!3c>F/F+7$$!3W#\\)pz6w)*=F/F+7$$!3'zc8F1Z'z=F/F+7$$ !3uU&3<]b)f=F/F+7$$!3.D]+TqQR=F/F+7$$!3'Hd9HA%)*==F/F+7$$!3;!)f\"F/F+7$$!3-) f>R-/#y:F/F+7$$!3!=Ryc8Hvb\"F/F+7$$!3pc8FMJaQ:F/F+7$$!3yqT$o;k!=:F/F+7 $$!3azeQJf@\"F/F+7$$!35^-0q8#f>\"F/F+7$$!3IqS\"GCea<\"F/F+7$$!3)\\,.1ck^: \"F/F+7$$!3nc8Fun^O6F/F+7$$!3;oOt1V9:6F/F+7$$!3kC\\)p^Gg4\"F/F+7$$!3A_ /4)4Zc2\"F/F+7$$!3#**)zfz%Rh0\"F/F+7$$!3%pS\"Gw(yW.\"F/F+7$$!3(*pRz)>A 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fdn7$$!+LE%3.%F_bmFe\\o7$$!+nt:pRF_bmFe\\oF_amFhfn-F]fn6%7%F]en7$$!+#H :(HnF_bmFggo7$$!+3ZGqsF_bmFggoF_amFhfn-F]fn6%7%Fden7$$!+TN&4q\"F[fmF_[ o7$$!+fk/*p\"F[fmF_[oF_amFhfn-F]fn6%7%F[fn7$$\"+nt:pRF_bmFe\\o7$$\"+LE %3.%F_bmFe\\oF_amFhfn-%&TITLEG6#QDSpectrul~semnalului~MP~cu~alpha=4.06 \"" 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" "Curve 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" "Curve 9" "Curve 10" "Curve 11" "Curve 12" "Curve 13" "Curve 14" "Curv e 15" "Curve 16" "Curve 17" "Curve 18" "Curve 19" "Curve 20" "Curve 21 " "Curve 22" "Curve 23" "Curve 24" "Curve 25" "Curve 26" "Curve 27" "C urve 28" "Curve 29" "Curve 30" "Curve 31" "Curve 32" "Curve 33" "Curve 34" "Curve 35" "Curve 36" "Curve 37" "Curve 38" "Curve 39" "Curve 40 " "Curve 41" "Curve 42" "Curve 43" "Curve 44" "Curve 45" "Curve 46" "C urve 47" "Curve 48" "Curve 49" "Curve 50" "Curve 51" "Curve 52" "Curve 53" "Curve 54" "Curve 55" "Curve 56" "Curve 57" "Curve 58" "Curve 59 " "Curve 60" "Curve 61" "Curve 62" "Curve 63" "Curve 64" "Curve 65" "C urve 66" "Curve 67" "Curve 68" "Curve 69" "Curve 70" "Curve 71" "Curve 72" "Curve 73" "Curve 74" "Curve 75" "Curve 76" "Curve 77" "Curve 78 " "Curve 79" "Curve 80" "Curve 81" "Curve 82" "Curve 83" }}}}}}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}}{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 275 7 "SCSlib." }}{PARA 0 " " 0 "" {TEXT -1 55 "Pentru calcularea transformatei Fourier a unor sem nale:" }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " }{TEXT 276 7 "FOURIER " }{TEXT -1 65 " \+ " }{HYPERLNK 17 "help" 1 "..\\Help\\Helpfile.mws" "Functia \+ FOURIER" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 30 "Pentru trunchi erea unor serii:" }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " }{TEXT 277 2 "ts" }{TEXT -1 77 " \+ " }{HYPERLNK 17 "help" 1 "..\\Help\\Helpfi le.mws" "Functia ts" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 45 "Pe ntru reprezentarea spectrelor unor semnale:" }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " }{TEXT 278 3 "rpa" }{TEXT -1 74 " \+ " }{HYPERLNK 17 " help" 1 "..\\Help\\Helpfile.mws" "Functia rpa" }{TEXT -1 1 " " }} {PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "libname:=\". ./SCSlib\",libname:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 61 "assu me(_wm,positive):assume(_wp,positive):assume(_k,integer);" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 7 "Exemple" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 10 "Exemplul I" }}{PARA 0 "" 0 "" {TEXT -1 77 "Ne prounem sa \+ analizam forma de unda si spectrul semnalului MF | MP de forma:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "s:=Ap*cos(wp*t+im*sin(wm*t+p hi));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG*&%#ApG\"\"\"-%$cosG6#, &*&%#wpGF'%\"tGF'F'*&%#imGF'-%$sinG6#,&*&%#wmGF'F.F'F'%$phiGF'F'F'F'" }}}{PARA 0 "" 0 "" {TEXT -1 5 "unde " }{XPPEDIT 18 0 "im;" "6#%#imG" } {TEXT -1 29 " este indicele de modulatie (" }{XPPEDIT 18 0 "beta;" "6# %%betaG" }{TEXT -1 15 " pentru MF sau " }{XPPEDIT 18 0 "alpha;" "6#%&a lphaG" }{TEXT -1 12 " pentru MP)." }}{PARA 0 "" 0 "" {TEXT -1 93 "Form a de unda a semnalului MF | MP anterior este data mai jos pentru o val oare a defazajului " }{XPPEDIT 18 0 "phi = Pi/4;" "6#/%$phiG*&%#PiG\" \"\"\"\"%!\"\"" }{TEXT -1 44 " in doua situatii particulare semnificat ive " }{XPPEDIT 18 0 "im = .1;" "6#/%#imG$\"\"\"!\"\"" }{TEXT -1 30 " \+ (semnal de banda ingusta) si " }{XPPEDIT 18 0 "im = 4.0;" "6#/%#imG$\" #S!\"\"" }{TEXT -1 65 " (semnal de banda larga). Celelalte marimi au u rmatoarele valori " }{XPPEDIT 18 0 "Ap = 1;" "6#/%#ApG\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "wp = 1;" "6#/%#wpG\"\"\"" }{TEXT -1 2 ", " } {XPPEDIT 18 0 "wm = .1;" "6#/%#wmG$\"\"\"!\"\"" }{TEXT -1 1 "." }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "plot(eval(s,[Ap=1,wp=1,wm=0 .1,im=0.1,phi=Pi/4]),t=-20*Pi..20*Pi,title=\"Forma de unda a semnalulu i MF|MP cu indice de modulatie 0.1\");" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVESG6$7aim7$$!3;++i%H&=$G'!#;$\"3Cyuc D.,v**!#=7$$!3#*e)))\\SY*[iF*$\"3[hkf@:B\\\"*F-7$$!3o'F*$\"3S3\"eiME&efF-7$$!3YwlsD'o/='F*$\"3?We +A9`$\\%F-7$$!3[05\"4=\\L;'F*$\"3/cZpn\\q&*GF-7$$!3ANa4O(Hi9'F*$\"3YeF vY3R77F-7$$!3'\\')z7H5\"HhF*$!3#z;%HZpol]!#>7$$!3)RHkk%3*>6'F*$!3A'*=0 -0J5AF-7$$!3-B([;Sr[4'F*$!3;OXp#Qc%[QF-7$$!3w_J$o&>vxgF*$!3_7W\\XFgs`F -7$$!3]#e7&[()e$))F-7$$!3Gq3dxTF4gF*$!3`*fQ0=(42&*F-7$$!3A;S fF *$!3i#4^G>Y5N)F-7$$!3'y.'Ry)4,*eF*$!33p*Q$G%\\%fjF-7$$!3#Q=**4M9_(eF*$ !3@qGGu'Q*Q^F-7$$!3wHBg.)=.'eF*$!3Dd]O-N&R!QF-7$$!3qva?mKUXeF*$!3?qZnM bJ%Q#F-7$$!3l@'3)Gx_IeF*$!3'zi>'[V8<\"*FQ7$$!3fnKc\"eF*$\"3&3oh.% [05eFQ7$$!3a8\\,amt+eF*$\"3!)\\#f_eo01#F-7$$!3?g!=m6Tey&F*$\"3I,MOx(>S \\$F-7$$!3;17Azb%4x&F*$\"3y'*f-xLX\\[F-7$$!3-?Ga*)R>adF*$\"3CrIv>Z:ViF -7$$!3>LW')*RUut&F*$\"3+qaAF!y4Y(F-7$$!31Zg=53p?dF*$\"3'*o,`7Vvo%)F-7$ $!3$4m20ARRq&F*$\"3=Wg/W)[#Q#*F-7$$!3#[FH3j(=(o&F*$\"31jC^v\"[zu*F-7$$ !3q))3:TgVqcF*$\"39%REU2dO)**F-7$$!3G&p6jCg?m&F*$\"3#)oZ2u1V'***F-7$$! 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[QyfF*$\"3QMRR;g0NOF-7$$\"3Y^WzRYE%*fF*$\"3?`J`pu%z`&F-7$$\"3t(*fluW95 gF*$\"3#yl?#oxv#=(F-7$$\"3zZP!f_4s-'F*$\"3Ygm^n([!z&)F-7$$\"3&y\\^rduU /'F*$\"3rU^(e2pA_*F-7$$\"3as`x-r!G0'F*$\"3LJ&em-\\'3)*F-7$$\"3#zC*RG'R 81'F*$\"3EN$[gabm'**F-7$$\"3IBJ-a@()pgF*$\"3;p(o&*HZZ***F-7$$\"3)z*pkz YSygF*$\"3ibSDe<4$*)*F-7$$\"3/[Z*3tpa4'F*$\"3)y&Q/u*>'4$*F-7$$\"35)\\U @yMD6'F*$\"3Q5`_Ux]]#)F-7$$\"3))[-RL)*fHhF*$\"3;zpL\"*4'Rx'F-7$$\"3%*) *zj%)[mYhF*$\"35&f6KQX'e\\F-7$$\"3Mu=E5u>bhF*$\"3'z(oG'F*$!3W6Y%z%)zW_\"F-7$$\"3AD^+kDR1iF*$!3+2$GyA$48EF-7$$\"3!**** G'*3D\\@'F*$!3I(3m6D(enOF-7$$\"3'*\\n(39!*>B'F*$!3C\">vv7\"eBcF-7$$\"3 /+X7#>b!\\iF*$!3uS]4E%Q*)H(F-7$$\"35]APV-7miF*$!3SL%f_BTah)F-7$$\"3;++ i%H&=$G'F*$!3TpR*[yIO^*F--%'COLOURG6&%$RGBG$\"#5!\"\"$\"\"!F_`zF^`z-%& TITLEG6#QfnForma~de~unda~a~semnalului~MF|grMP~cu~indice~de~modulatie~4 .06\"-%+AXESLABELSG6$Q\"tFd`zQ!6\"-%%VIEWG6$;$!+3`=$G'!\")$\"+3`=$G'Fa az%(DEFAULTG" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" }}}}{PARA 0 "" 0 "" {TEXT -1 100 "Spectrul semnalului MF | M P anterior se obtine utilizand descompunerea in serie armonica a acest uia:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 9 "s:=cs(s);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"sG*&%#ApG\"\"\"-%$sumG6$*&-%(BesselJG6$% \"kG%#imGF'-%$cosG6#,&*&%#wpGF'%\"tGF'F'*&F/F',&*&%#wmGF'F7F'F'%$phiGF 'F'F'F'/F/;,$%)infinityG!\"\"F@F'" }}}{PARA 0 "" 0 "" {TEXT -1 41 "Spe ctrul acestui semnal rezulta de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 76 "S:=subs([_wm=wm,_wp=wp,_k=k],FOURIER(subs([wm=_wm,wp= _wp,k=_k],s),t,omega));" }}{PARA 12 "" 1 "" {XPPMATH 20 "6#>%\"SG*&%#A pG\"\"\"-%$sumG6$,***-%(BesselJG6$%\"kG%#imGF'-%$cosG6#*&F0F'%$phiGF'F '%#PiGF'-%&DiracG6#,(%&omegaGF'%#wpG!\"\"*&F0F'%#wmGF'F>F'F'**F-F'F2F' F7F'-F96#,(FF'F- F'FGF'F7F'FBF'F'/F0;,$%)infinityGF>FNF'" }}}{PARA 0 "" 0 "" {TEXT -1 202 "Se observa ca in general spectrul acestui semnalul MF | MP este c omplex (are atat parte reala nenula cat si parte imaginara nenula). Ma i jos s-a reprezentat acest spectru pentru o valoare a defazajului " } {XPPEDIT 18 0 "phi = Pi/4;" "6#/%$phiG*&%#PiG\"\"\"\"\"%!\"\"" }{TEXT -1 33 " in doua situatii semnificative: " }{XPPEDIT 18 0 "im = .1;" "6 #/%#imG$\"\"\"!\"\"" }{TEXT -1 30 " (semnal de banda ingusta) si " } {XPPEDIT 18 0 "im = 4.0;" "6#/%#imG$\"#S!\"\"" }{TEXT -1 55 " (semnal \+ de banda larga). 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"Curve 76" "Curve 77" "Curve 78" "Curve 79" "Curve 80" "C urve 81" "Curve 82" "Curve 83" }}}}{PARA 0 "" 0 "" {TEXT 266 10 "Obser vatie" }{TEXT 267 0 "" }{TEXT -1 62 ". Spre deosebire de situatia clas ica cand defazajul este nul (" }{XPPEDIT 18 0 "phi = 0;" "6#/%$phiG\" \"!" }{TEXT -1 84 "), componentele spectrale sunt acum defazate suplim entar cu multipli intregi ai lui " }{XPPEDIT 18 0 "phi;" "6#%$phiG" } {TEXT -1 45 ". Altfel spus, componenta spectrala de ordin " }{XPPEDIT 18 0 "k;" "6#%\"kG" }{TEXT -1 30 " este defazata suplimentar cu " } {XPPEDIT 18 0 "k*phi;" "6#*&%\"kG\"\"\"%$phiGF%" }{TEXT -1 1 "." }}} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 11 "Exemplul II" }}{PARA 0 "" 0 "" {TEXT -1 77 "Ne prounem sa analizam forma de unda si spectrul semnalul ui MF | MP de forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 33 "s:=A p*cos(wp*t+phi+im*sin(wm*t));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"s G*&%#ApG\"\"\"-%$cosG6#,(*&%#wpGF'%\"tGF'F'%$phiGF'*&%#imGF'-%$sinG6#* &%#wmGF'F.F'F'F'F'" }}}{PARA 0 "" 0 "" {TEXT -1 5 "unde " }{XPPEDIT 18 0 "im;" "6#%#imG" }{TEXT -1 29 " este indicele de modulatie (" } {XPPEDIT 18 0 "beta;" "6#%%betaG" }{TEXT -1 15 " pentru MF sau " } {XPPEDIT 18 0 "alpha;" "6#%&alphaG" }{TEXT -1 12 " pentru MP)." }} {PARA 0 "" 0 "" {TEXT -1 93 "Forma de unda a semnalului MF | MP anteri or este data mai jos pentru o valoare a defazajului " }{XPPEDIT 18 0 " phi = Pi/4;" "6#/%$phiG*&%#PiG\"\"\"\"\"%!\"\"" }{TEXT -1 44 " in doua situatii particulare semnificative " }{XPPEDIT 18 0 "im = .1;" "6#/%# imG$\"\"\"!\"\"" }{TEXT -1 30 " (semnal de banda ingusta) si " } {XPPEDIT 18 0 "im = 4.0;" "6#/%#imG$\"#S!\"\"" }{TEXT -1 65 " (semnal \+ de banda larga). Celelalte marimi au urmatoarele valori " }{XPPEDIT 18 0 "Ap = 1;" "6#/%#ApG\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "wp = \+ 1;" "6#/%#wpG\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "wm = .1;" "6#/%# wmG$\"\"\"!\"\"" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 133 "plot(eval(s,[Ap=1,wp=1,wm=0.1,im=0.1,phi=Pi/4]),t=-20*Pi..20* Pi,title=\"Forma de unda a semnalului MF|MP cu indice de modulatie 0.1 \");" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6&-%'CURVE SG6$7ahm7$$!3;++i%H&=$G'!#;$\"3'fi()[\"p1rq!#=7$$!3!*HW!)\\e1miF*$\"3[ w;N\">!3\\dF-7$$!3#*e)))\\SY*[iF*$\"31Mmw\"*ykbUF-7$$!3&zGt,'p#=B'F*$ \"3vStX)H8`j#F-7$$!3o7$$!3UZ@aq!)e(>'F*$!38 on!RX%4/zFB7$$!3YwlsD'o/='F*$!39v\"HA^GO\\#F-7$$!3[05\"4=\\L;'F*$!3?/Q O57YATF-7$$!3ANa4O(Hi9'F*$!3W*H=(*3R$GcF-7$$!3'\\')z7H5\"HhF*$!37ke#)y gOmpF-7$$!3)RHkk%3*>6'F*$!3MKcu^wl'4)F-7$$!3-B([;Sr[4'F*$!3%yM[J2Ib)*) F-7$$!3w_J$o&>vxgF*$!3g$fgWA/lg*F-7$$!3in`UMA>pgF*$!3Xkn-!fB/\")*F-7$$ !3]#epoKv1Z)F-7$$!3=irx-J[zfF* $!3I(y^WTQ)yvF-7$$!373.QlvekfF*$!3:.c`tb)f^'F-7$$!33aM)z-#p\\fF*$!3X7> 1)eGhI&F-7$$!3-+me!\\'zMfF*$!3/>EZ,AfwRF-7$$!3'fu*=`4!*>fF*$!3mD*Gz:a+0fF*$!3;fuATad!3\"F-7$$!3'y.'Ry)4,*eF*$\"3-OZ0fvT0UFB 7$$!3#Q=**4M9_(eF*$\"3$\\%*Rm&))37>F-7$$!3wHBg.)=.'eF*$\"3o\"zPVcC/O$F -7$$!3qva?mKUXeF*$\"3\"Gk`vA#*Gt%F-7$$!3l@'3)Gx_IeF*$\"3y[x(*ojb)*fF-7 $$!3fnKc\"eF*$\"3Oc.i[***)GrF-7$$!3a8\\,amt+eF*$\"3i^kSNmY)4)F-7$ $!3?g!=m6Tey&F*$\"3G!z[!=OV&)))F-7$$!3;17Azb%4x&F*$\"3On/,p?5s%*F-7$$! 3-?Ga*)R>adF*$\"3yJjg\"opj()*F-7$$!3>LW')*RUut&F*$\"33#4[AJL$****F-7$$ !31Zg=53p?dF*$\"3^SE!*fFcP)*F-7$$!3$4m20ARRq&F*$\"3GL?`'=QdR*F-7$$!3#[ FH3j(=(o&F*$\"3MM(Gb#=^'o)F-7$$!3q))3:TgVqcF*$\"3KzoqBE9IxF-7$$!3c-DZ^ Wo`cF*$\"3=#QzHY9Rb'F-7$$!3W;TzhG$pj&F*$\"3UG6\"*pZN\">&F-7$$!3JId6s7= ?cF*$\"3]&[\\W*fF\"o$F-7$$!3=WtV#oHMg&F*$\"3_.(R>Ynm1#F-7$$!3Od*eF4yme &F*$\"3_Bh9ELpMRFB7$$!3Ar03.l#*pbF*$!3CT[Mzit!H\"F-7$$!35&=-M\"\\<`bF* $!3`<$oCmz!QHF-7$$!3F)zBPKBk`&F*$!3yo1]KZw,XF-7$$!397a/MbF*$!36qljw $)RPfF-7$$!3,EqOW,#H]&F*$!3Tj#)*Q8]U?(F-7$$!37p(*=%)[>paF*$!3f@a:7b1. \"*F-7$$!3A7D,C'paV&F*$!3s$4pe\"\\'>'**F-7$$!3ga_$QOW!o`F*$!3gwFja3y+$)F-7$$!3ip$pNZc6N&F*$!3))fr4t`9SsF-7 $$!3\"3u![VQHM`F*$!3i\\5$[.Leo0I&F*$!3m0q!eUuH'HF-7$$!3Sa[@`fq$G&F*$!3jS/HU+()38F-7$$!3IEi7BL %oE&F*$\"3F'>p&HlJDQFB7$$!3?)fPIp!)*\\_F*$\"3Y)>e*)[HF1#F-7$$!3Sp*[H1= JB&F*$\"3IpO>Azd$o$F-7$$!3MTw*zdNj@&F*$\"3wormuay\">&F-7$$!3G8j/$4`&*> &F*$\"3'3MQck\"\\_lF-7$$!3A&)\\431x#=&F*$\"3n%Rk*e%prs(F-7$$!3)ylVJ7)) f;&F*$\"3m/=tUbf#o)F-7$$!3aIB>Qc?\\^F*$\"3'H`)*)omy\"R*F-7$$!3Z-5C`JUK ^F*$\"3V#)G/!3eZ$)*F-7$$!3WQ`w5>.C^F*$\"3cF)z;q@A&**F-7$$!3Tu'*Go1k:^F *$\"3/JKo(R#3****F-7$$!3Q5S\"eU\\s5&F*$\"3//!)fTS-v**F-7$$!3OY$QL=e))4 &F*$\"3!\\7RdgL-))*F-7$$!3I=qQ)pv?3&F*$\"3aMC;Gnq\"[*F-7$$!3C!pNM@$Hl] F*$\"3[]vb'>5\\\"))F-7$$!3=iV[G2^[]F*$\"3Qg.8]V$))*yF-7$$!37MI`V#G<.&F *$\"3'y;eN%e]fnF-7$$!311z\"\\F*$!3Q_Lh>5'H)QF-7$$!34gxHc-O-\\ F*$!39.mKxftm_F-7$$!3Ip-WW2!o)[F*$!3hra&QX\"eAlF-7$$!3[yFeK7Cr[F*$!3Y& 4HUy4,i(F-7$$!3o(GD2s\"ob[F*$!3-c!G0r$zK&)F-7$$!3(ozn)3A7S[F*$!3namNV] gQ#*F-7$$!321.,(piX#[F*$!3[:+UHMa?(*F-7$$!3E:G:&=.!4[F*$!3?b\"ekgUq'** F-7$$!3')pSAHMA,[F*$!3%RZb0?W*****F-7$$!3YC`HtOW$z%F*$!3)**yJ-_WA(**F- 7$$!3yzlO1RbQF-7$$!3%p()[T>8tm%F*$! 3vPu`w%>fK#F-7$$!3IXD'3A-7l%F*$!3!*G1gb^4ltFB7$$!3l8idZ74NYF*$\"3RAVB! 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Mai jos s-a reprezentat acest spectru pentru o \+ valoare a defazajului " }{XPPEDIT 18 0 "phi = Pi/4;" "6#/%$phiG*&%#PiG \"\"\"\"\"%!\"\"" }{TEXT -1 33 " in doua situatii semnificative: " } {XPPEDIT 18 0 "im = .1;" "6#/%#imG$\"\"\"!\"\"" }{TEXT -1 30 " (semnal de banda ingusta) si " }{XPPEDIT 18 0 "im = 4.0;" "6#/%#imG$\"#S!\"\" " }{TEXT -1 55 " (semnal de banda larga). Celelate marimi au valorile: " }{XPPEDIT 18 0 "Ap = 1;" "6#/%#ApG\"\"\"" }{TEXT -1 2 ", " } {XPPEDIT 18 0 "wp = 1;" "6#/%#wpG\"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "wm = .1;" "6#/%#wmG$\"\"\"!\"\"" }{TEXT -1 1 "." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 235 "PLOT3D(rpa(ts(eval(S,[Ap=1,wp=1,wm=0.1,i m=0.1,phi=Pi/4]),k=-10..10),omega,interval=-2..2,tipgrafic=D3),TITLE( \"Spectrul semnalului MF|MP cu indice de modulatie 0.1\"),AXESLABELS( \"omega\",\"Re\",\"Im\"),AXESSTYLE(NORMAL),SCALING(CONSTRAINED));" }} {PARA 13 "" 1 "" {GLPLOT3D 603 585 585 {PLOTDATA 3 "6cp-%'CURVESG6&7dw 7%$!\"#\"\"!$F*F*F+7%$!+(\\**)z>!\"*F+F+7%$!+%**)zf>F/F+F+7%$!+\"\\)pR >F/F+F+7%$!+))zf>>F/F+F+7%$!+&[(\\**=F/F+F+7%$!+#)pRz=F/F+F+7%$!+zkHf= F/F+F+7%$!+wf>R=F/F+F+7%$!+ta4>=F/F+F+7%$!+q\\**)z\"F/F+F+7%$!+nW*)yRy;F/F+F+7%$!+\\9He;F/F+F+7%$!+Y4>Q;F/F+F+7%$!+V/4=;F/F+F+7%$ !+S**)zf\"F/F+F+7%$!+P%*)yd\"F/F+F+7%$!+M*)yd:F/F+F+7%$!+J%)oP:F/F+F+7 %$!+Gze<:F/F+F+7%$!+Du[(\\\"F/F+F+7%$!+ApQx9F/F+F+7%$!+>kGd9F/F+F+7%$! +;f=P9F/F+F+7%$!+8a3<9F/F+F+7%$!+5\\)pR\"F/F+F+7%$!+2W)oP\"F/F+F+7%$!+ /Ryc8F/F+F+7%$!+,MoO8F/F+F+7%$!+)*Ge;8F/F+F+7%$!+&R#['H\"F/F+F+7%$!+#* =Qw7F/F+F+7%$!+*Q\"Gc7F/F+F+7%$!+')3=O7F/F+F+7%$!+$Q!3;7F/F+F+7%$!+!)) zf>\"F/F+F+7%$!+x$ze<\"F/F+F+7%$!+u)yd:\"F/F+F+7%$!+r$yc8\"F/F+F+7%$!+ oyd:6F/F+F+7%$!+ltZ&4\"F/F+F+7%$!+ioPv5F/F+F+7%$!+fjFb5F/F+F+7%$!+ceRF]uF+F+7%$!+IFf=PF]uF+F+7%$!+0xeF]uF+F+7%$!+![U&3F]uF+F+7%$\"+'*Hb5@F]uF+F+ 7%$\"+@!e:J#F]uF+F+7%$\"+YIc7DF]uF+F+7%$\"+r!oNr#F]uF+F+7%$\"+'4tX\"HF ]uF+F+7%$\"+@\"yb6$F]uF+F+7%$\"+YJe;LF]uF+F+7%$\"+r\")e$f=PF]uF+F+7%$\"+@#)f>RF]uF+F+7%$\"+YKg?TF]uF+F+7%$\"+r#3;K%F]uF+F+7 %$\"+'H8E_%F]uF+F+7%$\"+@$=Os%F]uF+F+7%$\"+YLiC\\F]uF+F+7%$\"+r$Gc7&F] uF+F+7%$\"+'RLmK&F]uF+F+7%$\"+@%Qw_&F]uF+F+7%$\"+YMkGdF]uF+F+7%$\"+r%[ 'HfF]uF+F+7%$\"+'\\`18'F]uF+F+7%$\"+@&e;L'F]uF+F+7%$\"+YNmKlF]uF+F+7%$ \"+r&oOt'F]uF+F+7%$\"+'ftY$pF]uF+F+7%$\"+@'yc8(F]uF+F+7%$\"+YOoOtF]uF+ F+7%$\"+r')oPvF]uF+F+7%$\"+'p$pQxF]uF+F+7%$\"+@()pRzF]uF+F+7%$\"+YPqS \")F]uF+F+7%$\"+r(3\"F/F+F+7%$\"+I/3;7F/F+F+7%$\"+L4=O7F/F+F+7%$\"+O9Gc7F/F+F+7%$\" +R>Qw7F/F+F+7%$\"+UC['H\"F/F+F+7%$\"+XHe;8F/F+F+7%$\"+[MoO8F/F+F+7%$\" +^Ryc8F/F+F+7%$\"+aW)oP\"F/F+F+7%$\"+d\\)pR\"F/F+F+7%$\"+ga3<9F/F+F+7% $\"+jf=P9F/F+F+7%$\"+mkGd9F/F+F+7%$\"+ppQx9F/F+F+7%$\"+su[(\\\"F/F+F+7 %$\"+vze<:F/F+F+7%$\"+y%)oP:F/F+F+7%$\"+\")*)yd:F/F+F+7%$\"+%[*)yd\"F/ F+F+7%$\"+()**)zf\"F/F+F+7%$\"+!\\!4=;F/F+F+7%$\"+$*4>Q;F/F+F+7%$\"+' \\\"He;F/F+F+7%$\"+**>Ry;F/F+F+7%$\"+-D\\)p\"F/F+F+7%$\"+0If==F/F+F+7%$\"+Bg>R=F/F+F+7%$\"+ElHf=F/F+F+7%$\"+HqRz=F/F+F+7% $\"+Kv\\**=F/F+F+7%$\"+N!)f>>F/F+F+7%$\"+Q&)pR>F/F+F+7%$\"+T!*zf>F/F+F +7%$\"+W&**)z>F/F+F+7%$\"+Z+++?F/F+F+-%&COLORG6&%$RGBGF*F*F*-%*THICKNE SSG6#\"\"\"-%*LINESTYLEGFdam-F$6&7$7%$!+++++!)F]uF+F+7%F\\bm$\"+e&)[uF !#7$!+e&)[uFFabm-Fcam6#\"\"#FfamF^am-F$6&7$7%$\"+++++!*F]uF+F+7%F[cm$! 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Spre deosebire de situatia clasica can d defazajul este nul (" }{XPPEDIT 18 0 "phi = 0;" "6#/%$phiG\"\"!" } {TEXT -1 60 "), componentele spectrale sunt acum defazate suplimentar \+ cu " }{XPPEDIT 18 0 "phi;" "6#%$phiG" }{TEXT -1 89 ". Altfel spus, fie care componenta spectrala este defazata suplimentar cu acelasi defazaj " }{XPPEDIT 18 0 "phi;" "6#%$phiG" }{TEXT -1 95 ".(spre deosebire de \+ exemplul anterior unde defazajul crestea cu ordinul componentei spectr ale)." }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 8 "Probleme" }}{PARA 0 "" 0 "" {TEXT -1 146 "Pentru semnalele MF/MP de mai jos cere sa se reprez inte grafic forma de unda, sa se calculeze si sa se reprezinte grafic \+ spectrul acestor semnale:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "sMF:=Ap*sin(wp*t+beta*sin(wm*t)):sMP:=Ap*sin(wp*t+alpha*sin(wm*t)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "sMF:=Ap*cos(wp*t+beta*cos (wm*t)):sMP:=Ap*cos(wp*t+alpha*cos(wm*t)):" }}}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 69 "sMF:=-Ap*sin(wp*t+beta*sin(wm*t)):sMP:=-Ap*sin(wp*t +alpha*sin(wm*t)):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 67 "sMF:= Ap*sin(wp*t-beta*sin(wm*t)):sMP:=Ap*sin(wp*t-alpha*sin(wm*t)):" }}} {PARA 0 "" 0 "" {TEXT -1 74 "Pentru reprezentarile grafice se vor util iza urmatoarele valori numerice: " }{XPPEDIT 18 0 "wp = 1;" "6#/%#wpG \"\"\"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "wm = .1;" "6#/%#wmG$\"\"\"!\" \"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "beta = 4.0;" "6#/%%betaG$\"#S!\" \"" }{TEXT -1 2 ", " }{XPPEDIT 18 0 "alpha = .1;" "6#/%&alphaG$\"\"\"! \"\"" }{TEXT -1 1 "." }}}}{MARK "5 8 0" 0 }{VIEWOPTS 1 1 1 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }