{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 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 257 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 258 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 259 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 260 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 261 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 } {CSTYLE "" -1 262 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 263 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 264 "" 0 1 0 0 0 0 0 1 0 0 0 0 0 0 0 0 }{CSTYLE "" -1 265 "" 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 "Headi ng 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 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 "Helvetica" 1 10 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 1 0 0 3 3 3 0 3 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 "Author" -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 "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 13 "Seria Fourier" }}{PARA 18 "" 0 " " {TEXT -1 33 " Partea I: Seria Fourier Complexa" }}{PARA 19 "" 0 "" {TEXT -1 86 "Universitatea Tehnica \"Gh. Asachi\", Iasi, Facultatea de Electronica si Telecomunicatii" }}{PARA 19 "" 0 "" {TEXT -1 43 "Labor atorul de Semnale, Circuite si Sisteme" }}{PARA 19 "" 0 "" {URLLINK 17 "http://scs4.etc.tuiasi.ro" 4 "http://scs4.etc.tuiasi.ro/scslabs/Si mbolice/simbolice.htm" "" }{TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 16 "Breviar teoretic" }}{PARA 0 "" 0 "" {TEXT 259 16 "Scopul \+ lucrarii:" }}{PARA 0 "" 0 "" {TEXT -1 112 "Prezentarea conceptelor de \+ Serie Fourier Complexa (SFC) si Serie Fourier Reala (SFR). Semnificati a fizica a SFR." }}{PARA 0 "" 0 "" {TEXT 260 17 "Rezumat teoretic:" }} {PARA 0 "" 0 "" {TEXT -1 111 "Reprezentarea vectoriala a unui semnal s e bazeaza pe dezvoltarea acestuia \356ntr-o combinatie liniara de func tii " }{XPPEDIT 18 0 "\{phi[k](t), k = 1 .. N\};" "6#<$-&%$phiG6#%\"kG 6#%\"tG/F(;\"\"\"%\"NG" }{TEXT -1 1 " " }}{PARA 256 "" 0 "" {XPPEDIT 18 0 "sp(t) = sum(c[k]*phi[k](t),k = 1 .. N);" "6#/-%#spG6#%\"tG-%$sum G6$*&&%\"cG6#%\"kG\"\"\"-&%$phiG6#F/6#F'F0/F/;F0%\"NG" }}{PARA 0 "" 0 "" {TEXT -1 5 "unde " }{XPPEDIT 18 0 "N;" "6#%\"NG" }{TEXT -1 48 " est e dimensiunea spatiului vectorial (eventual " }{XPPEDIT 18 0 "N = infi nity;" "6#/%\"NG%)infinityG" }{TEXT -1 24 "), iar setul de functii " } {XPPEDIT 18 0 "phi[k](t);" "6#-&%$phiG6#%\"kG6#%\"tG" }{TEXT -1 54 " f ormeaza o baza a spatiului vectorial respectiv. Cei " }{XPPEDIT 18 0 " N;" "6#%\"NG" }{TEXT -1 13 " coeficienti " }{XPPEDIT 18 0 "c[k];" "6#& %\"cG6#%\"kG" }{TEXT -1 49 " constituie o reprezentare discreta a semn alului " }{XPPEDIT 18 0 "sp(t);" "6#-%#spG6#%\"tG" }{TEXT -1 52 " si f ormeaza ceea ce se numeste spectrul semnalului " }{XPPEDIT 18 0 "sp(t) ;" "6#-%#spG6#%\"tG" }{TEXT -1 29 " relativ la setul de functii " } {XPPEDIT 18 0 "phi[k](t);" "6#-&%$phiG6#%\"kG6#%\"tG" }{TEXT -1 71 ". \n\316n orice spatiu vectorial se defineste produsul scalar a doi vect ori " }{XPPEDIT 18 0 "x;" "6#%\"xG" }{TEXT -1 4 " si " }{XPPEDIT 18 0 "y;" "6#%\"yG" }{TEXT -1 11 ", notat cu " }{XPPEDIT 18 0 ";" "6#- %7rtable/ConstructColumnG6$%\"xG6#%\"yG" }{TEXT -1 39 " si pe baza ace stuia norma unui vector " }{XPPEDIT 18 0 "abs(x) = sqrt();" "6#/- %$absG6#%\"xG-%%sqrtG6#-%7rtable/ConstructColumnG6$F'6#F'" }{TEXT -1 27 ".\nBaza spatiului vectorial " }{XPPEDIT 18 0 "\{phi[k](t)\};" "6#< #-&%$phiG6#%\"kG6#%\"tG" }{TEXT -1 44 " se numeste ortogonala daca pro dusul scalar " }{XPPEDIT 18 0 ";" "6#-%7rtable/Co nstructColumnG6$-&%$phiG6#%\"kG6#%\"tG6#-&F(6#%\"mG6#F," }{TEXT -1 6 " este " }{XPPEDIT 18 0 "0;" "6#\"\"!" }{TEXT -1 8 " pentru " } {XPPEDIT 18 0 "k = m;" "6#/%\"kG%\"mG" }{TEXT -1 15 " si diferit de " }{XPPEDIT 18 0 "0;" "6#\"\"!" }{TEXT -1 15 " in rest.\nBaza " } {XPPEDIT 18 0 "\{phi[k](t)\};" "6#<#-&%$phiG6#%\"kG6#%\"tG" }{TEXT -1 67 " se numeste ortonormata daca \356n plus mai este satisfacuta condi tia " }{XPPEDIT 18 0 "abs(phi[k](t)) = 1;" "6#/-%$absG6#-&%$phiG6#%\"k G6#%\"tG\"\"\"" }{TEXT -1 22 " pentru orice functie " }{XPPEDIT 18 0 " phi[k](t);" "6#-&%$phiG6#%\"kG6#%\"tG" }{TEXT -1 2 ". " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT 261 3 "SFC" }}{PARA 0 "" 0 "" {TEXT -1 67 "Un exemplu de baza ortonormata pe spatiul vectorial L2 (T) cu norma " }{XPPEDIT 18 0 " = int(x(t)*conjugate(y(t)),t = c \+ .. c+T)/T;" "6#/-%7rtable/ConstructColumnG6$%\"xG6#%\"yG*&-%$intG6$*&- F'6#%\"tG\"\"\"-%*conjugateG6#-F)6#F1F2/F1;%\"cG,&F:F2%\"TGF2F2F " 0 "" {MPLTEXT 1 0 23 "restart:with(inttrans):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "libname:=\"../SCSlib\",libname:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "addtable(fourier,sg(t),Sg(omega),t, omega);" }{TEXT -1 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 33 "Pornind de la \+ semnalul generator " }{XPPEDIT 18 0 "sg(t);" "6#-%#sgG6#%\"tG" }{TEXT -1 48 " se poate scrie semnalul periodic de perioada T:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 46 "sp(t):=sum(sg(t-n*T),`n`=-infinity. .infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>-%#spG6#%\"tG-%$sumG6$ -%#sgG6#,&F'\"\"\"*&%\"nGF/%\"TGF/!\"\"/F1;,$%)infinityGF3F7" }}} {PARA 0 "" 0 "" {TEXT -1 72 "Semnalul periodic se poate descompune sub forma seriei Fourier complexe:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 42 "spsfc(t):=subs(T=2*Pi/Omega,SFC(sp(t),t));" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>-%&spsfcG6#%\"tG-%$sumG6$,$*&*(%&OmegaG\"\"\"-%#SgG6 #*&%\"nGF/F.F/F/-%$expG6#**^#F/F/F4F/F.F/F'F/F/F/%#PiG!\"\"#F/\"\"#/F4 ;,$%)infinityGF;FA" }}}{PARA 0 "" 0 "" {TEXT -1 5 "unde " }{XPPEDIT 18 0 "Omega = 2*Pi/T;" "6#/%&OmegaG*(\"\"#\"\"\"%#PiGF'%\"TG!\"\"" } {TEXT -1 47 " iar coeficientii seriei Fourier complexe sunt " } {XPPEDIT 18 0 "c[n] = Sg(n*Omega)/T;" "6#/&%\"cG6#%\"nG*&-%#SgG6#*&F' \"\"\"%&OmegaGF-F-%\"TG!\"\"" }{TEXT -1 1 "." }}{PARA 0 "" 0 "" {TEXT -1 60 "Pentru acelasi semnal se poate calcula transformata Fourier:" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 54 "Sp(omega)=subs(T=2*Pi/Omega ,FOURIER(sp(t),t,omega0));;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%#SpG 6#%&omegaG-%$sumG6$*(%&OmegaG\"\"\"-%#SgG6#*&%\"nGF-F,F-F--%&DiracG6#, &%'omega0GF-F1!\"\"F-/F2;,$%)infinityGF8F<" }}}}{SECT 0 {PARA 3 "" 0 " " {TEXT -1 12 "Mod de lucru" }}{PARA 0 "" 0 "" {TEXT -1 133 "In afara \+ de functiile incluse in libraria standard Maple, in aceasta lucrare vo r fi utilizate cateva functii din libraria aditionala " }{TEXT 262 7 " SCSlib." }}{PARA 0 "" 0 "" {TEXT -1 55 "Pentru calcularea transformate i Fourier a unor semnale:" }}{PARA 15 "" 0 "" {TEXT -1 8 "functia " } {TEXT 263 7 "FOURIER" }{TEXT -1 65 " \+ " }{HYPERLNK 17 "help" 1 "..\\Help\\Hel pfile.mws" "Functia FOURIER" }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 30 "Pentru trunchierea unor serii:" }}{PARA 15 "" 0 "" {TEXT -1 8 " functia " }{TEXT 264 2 "ts" }{TEXT -1 77 " \+ " }{HYPERLNK 17 "help " 1 "..\\Help\\Helpfile.mws" "Functia ts" }{TEXT -1 1 " " }}{PARA 0 " " 0 "" {TEXT -1 45 "Pentru reprezentarea spectrelor unor semnale:" }} {PARA 15 "" 0 "" {TEXT -1 8 "functia " }{TEXT 265 3 "rpa" }{TEXT -1 74 " \+ " }{HYPERLNK 17 "help" 1 "..\\Help\\Helpfile.mws" "Functia rpa " }{TEXT -1 1 " " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "libname:=\"../SCSlib\",libname:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "F:=table([dir=FOURIER,inv=inttrans[invfourier]]):" }} }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Sg:=(omega)->F[dir](sg(t),t ,omega):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 35 "Sp:=(omega)->F[ dir](sp(t),t,omega):" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 7 "Exemple " }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 57 "Semnal periodic dreptunghiula r cu puls generator simetric" }}{PARA 0 "" 0 "" {TEXT -1 17 "Pulsul ge nerator:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 49 "sg:=(t)->(Heavis ide(t+tau/2)-Heaviside(t-tau/2));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#> %#sgGR6#%\"tG6\"6$%)operatorG%&arrowGF(,&-%*HeavisideG6#,&9$\"\"\"*&#F 2\"\"#F2%$tauGF2F2F2-F.6#,&F1F2*&#F2F5F2F6F2!\"\"F " 0 "" {MPLTEXT 1 0 48 "sp:=(t)->sum(sg(t-n*T),`n`=- infinity..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#spGR6#%\"tG 6\"6$%)operatorG%&arrowGF(-%$sumG6$-%#sgG6#,&9$\"\"\"*&%\"nGF4%\"TGF4! \"\"/F6;,$%)infinityGF8F " 0 " " {MPLTEXT 1 0 10 "Sg(omega);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&- %$sinG6#,$*&%$tauG\"\"\"%&omegaGF+#F+\"\"#F+F,!\"\"F." }}}{PARA 0 "" 0 "" {TEXT -1 49 "Seria Fourier Complexa a semnlului periodic este:" } }{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "SFC(sp(t),t);" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#-%$sumG6$*&*&-%$sinG6#*&*(%$tauG\"\"\"%\"nGF.%#P iGF.F.%\"TG!\"\"F.-%$expG6#*&**^#\"\"#F.F/F.F0F.%\"tGF.F.F1F2F.F.*&F/F .F0F.F2/F/;,$%)infinityGF2F?" }}}{PARA 0 "" 0 "" {TEXT -1 42 "Spectrul semnalului periodic este discret:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Sp(omega);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$sumG 6$,$*&*&-%$sinG6#*&*(%$tauG\"\"\"%\"nGF/%#PiGF/F/%\"TG!\"\"F/-%&DiracG 6#,&%&omegaGF/*&*(\"\"#F/F0F/F1F/F/F2F3F3F/F/F0F3F;/F0;,$%)infinityGF3 F?" }}}{PARA 0 "" 0 "" {TEXT -1 104 "Reprezentarea grafica a pulsului \+ generator si a semnalului periodic dreptunghiular cu factor de umplere " }{TEXT 256 3 "1/4" }{TEXT -1 1 ":" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 197 "plot(eval([sg(t),ts(sp(t),n=-20..20)],[tau=Pi/2,T=2* Pi]),t=-5.25*Pi..5.25*Pi,numpoints=1000,color=[black,red],title=\"sg(t ) (negru) si sp(t) (rosu)\",view=[DEFAULT,-1..2], style=LINE, thicknes s = 2);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6)-%'CU RVESG6$7jjn7$$!37++%)RhL\\;!#;$\"\"!F,7$$!3#pOI]S\")ek\"F*F+7$$!3^r[ue a(Gk\"F*F+7$$!3!Rskx&\\\\R;F*F+7$$!3!orH'[?4O;F*F+7$$!3mAy#HJ0Fj\"F*F+ 7$$!3B?)*Rv`cH;F*F+7$$!3B`='>:9ji\"F*F+7$$!3(\\QJ?t^Hi\"F*F+7$$!3*pFCa 4+'>;F*F+7$$!3/g`?DD:;;F*F+7$$!3Y')*zM!f68;F*F+7$$!3G:\"RmQ(p4;F*F+7$$ !3&4lRI$[E1;F*F+7$$!3Q_)4;$p&Hg\"F*F+7$$!3ku*3-/`**f\"F*F+7$$!3WM2zA6Q 'f\"F*F+7$$!3s0$3-CbLf\"F*F+7$$!39*pC%>a$)*e\"F*F+7$$!3]F0i\"y>ne\"F*F +7$$!3]Bt9L9I$e\"F*F+7$$!3uO=.dj/!e\"F*F+7$$!3MM_eE+lw:F*F+7$$!3+Lc,N6 `t:F*F+7$$!39--6*)p;q:F*F+7$$!3mT/*pesmc\"F*F+7$$!3ukFn*pIOc\"F*F+7$$! 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Factorul de umplere a celor doua semnale este " }{TEXT 257 3 "1/2" }{TEXT -1 11 " respectiv " }{TEXT 258 3 "1/3" }{TEXT -1 186 ". Spectrul semnalul ui periodic este discret cu pas de discretizare dependent de perioada \+ T a semnalului infasuratoarea raminind de fiecare data transformata Fo urier a pulsului generator." }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 389 "PLOT(rpa(ts(eval(T/(2*Pi)*Sp(omega),[tau=Pi,T=2*Pi]),n=-20..20),o mega,interval=-5..5,tipgrafic=modul,culoare=[1,0,0]),rpa(ts(eval(T/(2* Pi)*Sp(omega),[tau=Pi,T=3*Pi]),n=-20..20),omega,interval=-5..5,tipgraf ic=modul,culoare=[0,0,1]),rpa(eval(Sg(omega),tau=Pi),omega,interval=-5 ..5,tipgrafic=modul),AXESSTYLE(NORMAL),AXESLABELS(\"omega\",\"\"),TITL E(\"|Sp(omega)| (rosu) si |Sg(omega)| (negru)\"));" }}{PARA 13 "" 1 " " {GLPLOT2D 400 300 300 {PLOTDATA 2 "6L-%'CURVESG6&7dw7$$!\"&\"\"!$F*F *7$$!3MV([(\\RUZ\\!#Rycw6*p%F/F+7$$!3'oNrUvQ'\\YF/ F+7$$!3!Gc7Dgn%)f%F/F+7$$!3=KkGd0YZXF/F+7$$!3#Ha3Rycd<%H%F/F+7 $$!3uBZ%*))3Y[UF/F+7$$!3OOsW*[,T>%F/F+7$$!3Y$pQx%>0[TF/F+7$$!3M&3RG#Q*QF/F+7$$!3i\"Ryc$yNYQF/F+7$$!3;Fa3u 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}}}}}} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 57 "Semnal periodic dreptunghiular cu puls generator deplasat" }}{PARA 0 "" 0 "" {TEXT -1 17 "Pulsul genera tor:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 41 "sg:=(t)->(Heaviside( t)-Heaviside(t-tau));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#sgGR6#%\"t G6\"6$%)operatorG%&arrowGF(,&-%*HeavisideG6#9$\"\"\"-F.6#,&F0F1%$tauG! \"\"F6F(F(F(" }}}{PARA 0 "" 0 "" {TEXT -1 47 "Transformata Fourier a p ulsului generator este:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "S g(omega);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,(^#!\"\"\"\"\"*&^#F'F' -%$cosG6#*&%$tauGF'%&omegaGF'F'F'-%$sinGF,F'F'F/F&" }}}{PARA 0 "" 0 " " {TEXT -1 41 "Semnalul periodic este definit sub forma:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 48 "sp:=(t)->sum(sg(t-n*T),`n`=-infinit y..infinity);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#spGR6#%\"tG6\"6$%) operatorG%&arrowGF(-%$sumG6$-%#sgG6#,&9$\"\"\"*&%\"nGF4%\"TGF4!\"\"/F6 ;,$%)infinityGF8F " 0 "" {MPLTEXT 1 0 13 "SFC(sp(t),t);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$s umG6$,$*&*&,(^#!\"\"\"\"\"*&^#F,F,-%$cosG6#,$*&*(%$tauGF,%\"nGF,%#PiGF ,F,%\"TGF+\"\"#F,F,-%$sinGF1F,F,-%$expG6#*&**^#F9F,F6F,F7F,%\"tGF,F,F8 F+F,F,*&F6F,F7F,F+#F,F9/F6;,$%)infinityGF+FH" }}}{PARA 0 "" 0 "" {TEXT -1 37 "Spectrul acestui semnal este discret:" }}{EXCHG {PARA 0 " > " 0 "" {MPLTEXT 1 0 10 "Sp(omega);" }}{PARA 11 "" 1 "" {XPPMATH 20 " 6#-%$sumG6$,(*&*&^#!\"\"\"\"\"-%&DiracG6#,&%&omegaGF+*&*(\"\"#F+%\"nGF +%#PiGF+F+%\"TGF*F*F+F+F4F*F+*&*(^#F+F+-%$cosG6#,$*&*(%$tauGF+F4F+F5F+ F+F6F*F3F+F,F+F+F4F*F+*&*&-%$sinGF " 0 "" {MPLTEXT 1 0 197 "plot(eval([sg(t),ts(sp(t),n=-20..20)],[tau=Pi/2,T=2*Pi]),t=-5 .25*Pi..5.25*Pi,numpoints=1000,color=[black,red],title=\"sg(t) (negru) si sp(t) (rosu)\",view=[DEFAULT,-1..2], style=LINE, thickness = 2);" }}{PARA 13 "" 1 "" {GLPLOT2D 400 300 300 {PLOTDATA 2 "6)-%'CURVESG6$7j jn7$$!37++%)RhL\\;!#;$\"\"!F,7$$!3#pOI]S\")ek\"F*F+7$$!3^r[uea(Gk\"F*F +7$$!3!Rskx&\\\\R;F*F+7$$!3!orH'[?4O;F*F+7$$!3mAy#HJ0Fj\"F*F+7$$!3B?)* 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"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" }}}}} {SECT 0 {PARA 4 "" 0 "" {TEXT -1 55 "Semnal periodic triunghiular cu p uls generator simetric" }}{PARA 0 "" 0 "" {TEXT -1 17 "Pulsul generato r:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 86 "sg:=(t)->1/tau^2*((t+t au)*Heaviside(t+tau)-2*t*Heaviside(t)+(t-tau)*Heaviside(t-tau));" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%#sgGR6#%\"tG6\"6$%)operatorG%&arrowG F(*&,(*&,&9$\"\"\"%$tauGF1F1-%*HeavisideG6#F/F1F1*(\"\"#F1F0F1-F46#F0F 1!\"\"*&,&F0F1F2F:F1-F46#F " 0 "" {MPLTEXT 1 0 24 "convert(Sg(omega),trig);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&,&-%$cosG6#*&%$tauG\"\"\"%&omegaGF +F+F+!\"\"F+*&)F*\"\"#F+)F,F0F+F-!\"#" }}}{PARA 0 "" 0 "" {TEXT -1 41 "Semnalul periodic este definit sub forma:" }}{EXCHG {PARA 0 "> " 0 " " {MPLTEXT 1 0 48 "sp:=(t)->sum(sg(t-n*T),`n`=-infinity..infinity);" } }{PARA 11 "" 1 "" {XPPMATH 20 "6#>%#spGR6#%\"tG6\"6$%)operatorG%&arrow GF(-%$sumG6$-%#sgG6#,&9$\"\"\"*&%\"nGF4%\"TGF4!\"\"/F6;,$%)infinityGF8 F " 0 "" {MPLTEXT 1 0 13 "SFC(sp(t),t) ;" }{TEXT -1 0 "" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%$sumG6$,$*&*(% \"TG\"\"\",&-%$cosG6#,$*&*(%$tauGF+%\"nGF+%#PiGF+F+F*!\"\"\"\"#F+F+F6F +-%$expG6#*&**^#F7F+F4F+F5F+%\"tGF+F+F*F6F+F+*&)F4F7F+)F5F7F+F6#F6F7/F 4;,$%)infinityGF6FFF+*$)F3F7F+F6" }}}{PARA 0 "" 0 "" {TEXT -1 37 "Spec trul acestui semnal este discret:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 10 "Sp(omega);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&-%$su mG6$,&*&*(%\"TG\"\"\"-%$cosG6#,$*&*(%$tauGF+%\"nGF+%#PiGF+F+F*!\"\"\" \"#F+-%&DiracG6#,&%&omegaGF+*&*(F6F+F3F+F4F+F+F*F5F5F+F+*&)F3F6F+F4F+F 5F5*&*&F*F+F7F+F+*&F?F+F4F+F5F+/F3;,$%)infinityGF5FFF+*$)F2F6F+F5" }}} {PARA 0 "" 0 "" {TEXT -1 68 "Reprezentarea grafica a pulsului generato r si a semnalului periodic:" }}{EXCHG {PARA 0 "> " 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Pentru semnalul nedeplasat, faza este constanta si egala cu 0. 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Intrebar" }}{PARA 0 "" 0 "" {TEXT -1 110 "1. 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Sa se refaca calculele \+ pentru semnal periodic dreptunghiular nesimetric fata de origine." }} {PARA 0 "" 0 "" {TEXT -1 123 "4. Sa se calculeze pe baza Seriei Fourie r Complexe, Seria Fourier Reala pentru semnalele discutate in exemplel e anterioare." }}{PARA 0 "" 0 "" {TEXT -1 65 "5. Ce legatura exista in tre coeficientii Seriei Fourier Complexe " }{XPPEDIT 18 0 "c[k];" "6#& %\"cG6#%\"kG" }{TEXT -1 4 " si " }{XPPEDIT 18 0 "c[-k];" "6#&%\"cG6#,$ %\"kG!\"\"" }{TEXT -1 37 " ? Cum sunt modul si argumentul lor ?" }}}} {MARK "8 1 1" 0 }{VIEWOPTS 1 1 1 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }