{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 }{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 Out put" -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 "Title" -1 18 1 {CSTYLE "" -1 -1 "Hel vetica" 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 "Heading 4" -1 20 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 128 0 0 1 1 2 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" -1 256 1 {CSTYLE "" -1 -1 "Helvetica" 1 10 0 0 0 1 2 2 2 2 2 2 1 1 1 1 }1 3 0 0 0 0 3 0 3 0 2 2 0 1 }{PSTYLE "Normal" -1 257 1 {CSTYLE "" -1 -1 "Hel vetica" 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 20 "Transformata Fourier" }}{PARA 19 "" 0 "" {TEXT -1 86 "Universitatea Tehnica \"Gh. Asachi\", Iasi, Fa cultatea 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://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 256 15 "Scopul lucrarii" }{TEXT -1 93 ": Transformata Fourier. Proprietati. C alculul si reprezentarea spectrului unor semnale reale." }}{PARA 0 "" 0 "" {TEXT 257 16 "Rezumat teoretic" }{TEXT -1 1 ":" }}{PARA 0 "" 0 " " {TEXT -1 34 "Transformata Fourier directa este:" }}{PARA 257 "" 0 " " {XPPEDIT 18 0 "S(omega) = int(s(t)*exp(-I*omega*t),t = -infinity .. \+ infinity);" "6#/-%\"SG6#%&omegaG-%$intG6$*&-%\"sG6#%\"tG\"\"\"-%$expG6 #,$*(%\"IGF0F'F0F/F0!\"\"F0/F/;,$%)infinityGF7F;" }}{PARA 0 "" 0 "" {TEXT -1 59 "Transformata Fourier inversa este (daca integrala exista! ):" }}{PARA 257 "" 0 "" {XPPEDIT 18 0 "s(t) = int(S(omega)*exp(I*omega *t),omega = -infinity .. infinity)/(2*pi);" "6#/-%\"sG6#%\"tG*&-%$intG 6$*&-%\"SG6#%&omegaG\"\"\"-%$expG6#*(%\"IGF1F0F1F'F1F1/F0;,$%)infinity G!\"\"F:F1*&\"\"#F1%#piGF1F;" }{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 247 "Transformata Fourier este o transformata liniara si se bazeaza pe reprezentarea unui semnal in raport cu un continuum de functii de \+ tip exponentiala complexa. Spectrul semnalului este ponderea fiecarei \+ exponentiale complexe din aceasta dezvoltare." }}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 12 "Mod de lucru" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "restart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 29 "libname:= \"../SCSlib\",libname:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 59 "F :=table([dir=inttrans[fourier],inv=inttrans[invfourier]]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 43 "S:=(omega)->simplify(F[dir](s(t),t, omega)):" }}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 7 "Exemple" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 14 "Semnal armonic" }}{SECT 0 {PARA 5 "" 0 " " {TEXT -1 14 "Semnal cosinus" }}{PARA 0 "" 0 "" {TEXT -1 57 "Semnalul de tip cosinus si transformata lui Fourier sunt:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "s:=(t)->cos(omega0*t):s(t);S(omega);" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#-%$cosG6#*&%'omega0G\"\"\"%\"tGF(" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#,&*&%#PiG\"\"\"-%&DiracG6#,&%&omegaGF& %'omega0G!\"\"F&F&*&F%F&-F(6#,&F+F&F,F&F&F&" 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Modulul are simetrie para iar argumentul este egal cu 0." }}}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 12 "Semnal sinus " }}{PARA 0 "" 0 "" {TEXT -1 55 "Semnalul de tip sinus si transformata lui Fourier sunt:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 36 "s:=(t) ->sin(omega0*t):s(t);S(omega);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#-%$s inG6#*&%'omega0G\"\"\"%\"tGF(" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,&*(^ #!\"\"\"\"\"%#PiGF'-%&DiracG6#,&%&omegaGF'%'omega0GF&F'F'*(^#F'F'F(F'- F*6#,&F-F'F.F'F'F'" }}}{PARA 0 "" 0 "" {TEXT -1 51 "Reprezentarea graf ica a semnalului si a spectrului:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 90 "plot(eval(s(t),omega0=1),t=-3*Pi..3*Pi,color=black,ti tle=\"s(t)\",view=[DEFAULT,-1.1..1.1]);" }}{PARA 13 "" 1 "" {GLPLOT2D 399 206 206 {PLOTDATA 2 "6'-%'CURVESG6#7gt7$$!3^***H>%zxC%*!#<$!3)Q)G8 ?!QR)=!#D7$$!3#*F*$!3)*3(=M B9*R?F37$$!3qF(\\_$zi;\"*F*$!3PPEIEK'H.$F37$$!3N/jNm7\"R,*F*$!35zjo;// %*RF37$$!3ObSf<[;N))F*$!3ck>;i_RgbF37$$!3;3=$)o$=kl)F*$!3O(3m2Om&\\pF3 7$$!3_s6p#H*Rb%)F*$!3K3-#\\:V`C)F37$$!3mQ0b;-Qa#)F*$!3XROxaq04#*F37$$! 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10 3 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" }}}}{PARA 0 "" 0 "" {TEXT -1 95 "Pentru toate semnalele, faza are simetrie impara (semnale reale ) si este dependenta de defazaj." }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 28 "Puls dreptunghiular unipolar" }}{SECT 0 {PARA 5 "" 0 "" {TEXT -1 44 "Puls dreptunghiular simetric fata de origine" }}{PARA 0 "" 0 " " {TEXT -1 51 "Semnalul si transformata Fourier a semnalului sunt:" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 68 "s:=(t)->1/tau*(Heaviside(t+t au/2)-Heaviside(t-tau/2)):s(t);S(omega);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#*&,&-%*HeavisideG6#,&%\"tG\"\"\"*&#F*\"\"#F*%$tauGF*F*F*-F&6#,&F )F**&#F*F-F*F.F*!\"\"F4F*F.F4" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,$*&- %$sinG6#,$*&%$tauG\"\"\"%&omegaGF+#F+\"\"#F+*&F*F+F,F+!\"\"F." }}} {PARA 0 "" 0 "" {TEXT -1 51 "Reprezentarea grafica a semnalului si a s pectrului:" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 102 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Intrebari" }} {PARA 0 "" 0 "" {TEXT -1 62 "1. Sa se calculeze spectrul unui semnal t riunghiular deplasat." }}{PARA 0 "" 0 "" {TEXT -1 71 "2. Sa se calcule ze spectrul unui semnal format dintr-un puls de forma: " }{XPPEDIT 18 0 "PIECEWISE([cos(t), abs(t) < 1/2*Pi],[0, 1/2*Pi <= abs(t)]);" "6#-%* PIECEWISEG6$7$-%$cosG6#%\"tG2-%$absG6#F**(\"\"\"F0\"\"#!\"\"%#PiGF07$ \"\"!1*(F0F0F1F2F3F0-F-6#F*" }}{PARA 0 "" 0 "" {TEXT -1 109 "3. Sa se \+ calculeze spectrul unui semnal obtinut din convolutia a doua, a trei, \+ patru semnale dreptunghiulare." }}{PARA 0 "" 0 "" {TEXT -1 45 "4. Care este spectrul exponentialei complexe " }{XPPEDIT 18 0 "s(t) = e^(-I*o mega0*t);" "6#/-%\"sG6#%\"tG)%\"eG,$*(%\"IG\"\"\"%'omega0GF-F'F-!\"\" " }{TEXT -1 2 "? " }}{PARA 0 "" 0 "" {TEXT -1 34 "5. Se presupune cuno scut semnalul " }{XPPEDIT 18 0 "p(t);" "6#-%\"pG6#%\"tG" }{TEXT -1 17 " si spectrul sau " }{XPPEDIT 18 0 "P(omega);" "6#-%\"PG6#%&omegaG" } {TEXT -1 32 ". Care este spectrul semnalului " }{XPPEDIT 18 0 "s(t) = \+ p(t)*cos(omega0*t);" "6#/-%\"sG6#%\"tG*&-%\"pG6#F'\"\"\"-%$cosG6#*&%'o mega0GF,F'F,F," }{TEXT -1 33 " ? Care este spectrul semnalului " } {XPPEDIT 18 0 "s(t) = p(t)*e^(-I*omega0*t);" "6#/-%\"sG6#%\"tG*&-%\"pG 6#F'\"\"\")%\"eG,$*(%\"IGF,%'omega0GF,F'F,!\"\"F," }{TEXT -1 2 " ?" }} }}{MARK "0 0" 0 }{VIEWOPTS 1 1 1 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }