b09hwk4sol (1)

b09hwk4sol (1) - ECE2311 HOMEWORK 4 B09 Name S o(«Theirs...

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Unformatted text preview: ECE2311 _ HOMEWORK # 4 B09 Name : S o («Theirs ECE Box Number: Due date: This assignment is due Wednesday, December 2, bring to class. Make a photocopy for your reference for fast comparison to solution set. Put all answers on the lines provided! Attach any work sheets with a staple. Problem 1 ~ Fourier Transform Integral 1a) Obtain the Fourier transform of the function $(t) : te“u(t) by evaluating the intergral for the Fourier Transform (Le. do not use the table method). Show all work. {He 8 At : “(70 0 so - ‘t ‘6w+x\ mum M01 w- _ um _\ 0 l .i : .:.‘__. 3 l 1 mi) :_: «fl 4N »\ (w-J)‘ we lb) Obtain the Fourier transform of the function y(t) : te‘l‘l by evaluating the intergral for the Fourier Transform (ie. do not use the table method). Show all work. (>49 0 DD , ~ {:l j. t _ ft ~ .5 ' , 3/9“) ” t€ l e”) ‘t ~ jl; e 6"” J+ Jr te'te”wtot’l' ’90 mm o ‘- 41“) , ~‘b’v _ — 5w M "' “’“fl—T " , 2. (ta 1+ 13w -|\)(w1- 2y.) ‘1) (u +3)‘(w-A7‘ (gwqyzbwatfi Problem 2 —— Fourier Transform Tables 2a) Obtain the Fourier transform of the function :r(t) : te*‘u(t) by using the table on page 702 of the textbook, Show all work, (a f) m M 6,414,; at ’v Mot Myl’ J..— 2. ' (\+)W\ l x v» L g M w 2 L A0 (m k X(wl12 Pl) ’“l ' 2%», +L‘J 70“?! ) 2b) Obtain the Fourier transform of the function y(t )—— — lie—l" by using the table on page 702 of the textbook. Show all work t\ MLQ VLUM~L <0) 3(a): {e u(—tl+f/€;:é:’)/MV ‘40,”; ‘cM rig/:1 LAM M; 4'4 1 —( Fwy + (l 'fi/lq ,_-~~ 'M'i‘f’“ [/2 Y“): + !+ ’1‘“) : M /, 1 (l , 1w) ( J (1,)w)1(ll”gk}) / _ 5.1; K) _ \\\\fi '3 W t - L‘Iitg Y(w) : (iv-llzawfl)?’ \i (by-J) (my) (”b-010wflp q+ W Lang we, am‘ pm, 158' alt) 10¢ M9 3; lm revszmaQ so M? l ULURW 5.;«942/ prmgé +2 43“”:ng mcm be 7(a) : fefiaima'léa (jar-V4) ”WI/fl flafl‘lt): Ate c ( ml IT‘V‘J) W“ ”l :('/l"+‘l)) ~90 teal-606;“) Problem 3 — Basic Fourier Transform Properties Use the basic properties of the Fourier Transform to find the following transforms using the solutions you already obtained in Problems 1 and 2. (Where 33(t) and y(t) are as defined in the first two problems.) Provide the intermediate answers as requested. 3a)p(t)=3x(:—1)~2y(t+3) AWN“ ll‘neonlxg—f 41:4» sl/JA fwMMr —ju)'l 5w? —2\/{v)€ \/ W 39 W n 3‘? 3 (H0 P01): 3'. X(Lo\'€ —- «U _ CL/ : —e Z 6” f[;r(t— 1)} :- ‘U'L‘WW’\ (ManL (Eta-HY“ -u "3 PC1133 3‘ 8 J _, *"LMJE?J w _ 36:3“) 8’we 3,10 (Jw‘flll ()W’l31(l.‘d*l)t Ti—l-‘(+‘——l—Tl/ Z ’0‘?) (ID—Q CWT“ P<w>=__. _________________ Jud —I“" Eu) 2. 1,2.) “Xe lgje ow‘F 3Q a.) -82’we ‘ (ijV'UNhV .. (‘41 \f“) '2‘) 3;“ - Ze wégwe’ —2w‘e +53%”: «(HA 9’ [‘gl Xh‘» ”Me SPEC/‘55)]: ijgwwl) _ ( 45%) gut-t0 =7(a(+—2)) fimkhm fact/(9. (7(2Jc)4—>mWW/a)* \ - ‘_2 “ z 1 Cjw.2):1(jw+z)’¢ flxwgfl : (”IQ—1L 0 W” ‘ M M» «WM» __l'5,'w 6,520) f[y(2t — 4)] :2 4139*?) L(1%" +331 U‘)‘ g’b*‘ 004) L3 QW‘f’fi / jud+ W m (120 fl‘bQU/M W 2 S‘ _ 2‘ _ ‘léjwe 4’” _ [Arafat ( 310$!th jWhSK)?’ H —7—' -110 3 55'” 39 +l£5w1+zluqvllojcae 2'04”“sz ’ +64%) 9 L (aw—131(k) 1231(25w +|\ Problem 4 —~ Basic Fourier Transform Properties Use the basic properties of the Fourier Transform and the Fourier tables to find the following function. Provide the intermediate results requested 3a) 7"(t) : 6‘3(“1)u(t— 1) * te‘2tu(t) 3P 6‘3“")auvq : e‘J‘J- f «Rm .2 (5“). ”-1—“ jg) 1- 3 e 4: l 1': e l : ‘(h— 39 u (+\ CW ”)1 67’“) .7:[e’3(‘“1)'u(t— 1)] : _ 10+} l l, 1 7113841240] : (1‘4"? Z) ._—— Bo mewbm M \Q(.‘,\ ;; m pwhd“ ’6 ’(LL +wo {LowL Wrfirm c 8' jw : f 9r l -i ”I‘d __.__' 5 . L '1, — ¥ . 1 f , 6 R(w):f[r(t)]: (“WWW”) ‘” : 604,3 ‘v 3: v5 «1) k 00%“me :1 f. comforni'fakmgl ffilufl .4, rlf) ,xtvs 4* *1 -2++2 :( I rm: [5: +8 -ze ode—B 4/ R60) Rio flora am Wéfiwbrlo do PMIHJ ’me ES {Masha}; ‘QLJTW \ x 2 . , tarrmPW-‘t’mf “9 . > r‘r V ’ ‘4) l P \j B/w) '— ‘x’ _ Q} 6’1 , 1 E '2‘) 1:)..‘7—1‘1'” (7') [m+3)()zan) (w—zij45) w-zj («2,201 (0-; NW; >41!an imarliwm QIwL W’fl MS 4'13” ”(”JM Mg rfiruljl‘“ L?) l “Louuwfl beau?" "0/ ell” VT Problem 5"— Matlab Fourier Transform Plot Construction Look at the example C51 in the textbook on page 536 to get an idea about how to use the abs() and angle() functions in Matlab to plot the magnitude and phase of a complex function (Ignore the second and third lines which are not relevant to your problem, just use the same methods you have used before to sample the function you wish to plot over a. range of frequencies defined by a linspace command). (a) Plot the magnitude and phase functions for X (w) in problem 1a over the range from —20 rad/sec to 20 rad/sec. Attach the resulting plots. (b) Plot the magnitude and phase functions for Y(w) in problem 1b over the range from —20 rad/sec to 20 rad / sec. Attach the resulting plots. NM 4 X[m] [deg] 0.8 0.6 0.4 0.2 -20 -15 -1O 10 15 2O 200 , 100 -100 -200 MM 4 Y[(1)] [deg] -20 1.5 0.5 -20 100 50 100 ~20 -15 -10 m rad/s 2O ...
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