fa2003_exam3soln

fa2003_exam3soln - ECE 210 Analeg Signal Precessing Fall...

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Unformatted text preview: ECE 210 Analeg Signal Precessing Fall 2003 University,' ef Illineis Sarwate, Mitefsky. Kedeki Exam 3 Thursday. December 4, EUDB +— T:[l[l--8:15 PM Name: ' Sectien : [circle ene] Please PRINT yeur NAME and CIRCLE yeur SECTION in the beaes abeve. This is a clesed-beek, clesed-netes eaare except fer eue 3.5"}:11” sheet ef netes. beth sides ef which may be used. Calculaters. laptep ceruputers, PDAs. iPODs. etc. are net allewed. Please shew all yeur werk. Backs ef pages matr he used fer scratch werk if necessary. All answers sheuld include uuits wherever apprepriate. Geed luck! Preblem 1 (40 peiuts) Preblem 2 (2O peiuts) Preblcm 3 [20 peints) Preblem 4 [20 peints] _ {r 315 —— : r. 2-H» If f? 6( JE7§MT é) ) Prnblem 1 (40 points): .,-——...~_ P var? 1. Sketch H (rs) en the graph below. Be sure te indieate the values corresponding tn the hashrnarks en the axes. 2. Is this a. causal filter? Circle nne answer: YES @ 3. Which ef the fellewing names best deserihes this filter? Cirele ONE answer: anpass filter Highness filter fiend-pass filter Nene nf the previens 3 names 4. 1Lqfiul'hat is the lflfi% bandwidth ef this filter? 6 flag! 5 b) (10 peints} Let Mt) = fit) at Mt) where fit) and Mt] are as shewn below. Find the value of e) [10 peims) The impulse respense Mt} ef e LT] *1 stem sstisfies the relstien “(35) 1* hft] = u(t — 2}. 1. What is the system sere—stete respense fit] if the system input is fit} 2 4u(t — 2]? MUS ({(tr-Z) ——-‘3— F H) 4u(+.-q): (6:) __ I; 4:5“ F I hm “MW; 2.W'hstisyfijifflQZflt)? £2,- Hwe :eefMJe/LM Li + r 9L [44004: £(t)=w(+-1)j :) 30¢) {filt- L?) $(‘Er?> *‘a(i): £(i'1) d) [1!] peinte} Given the Feurier Transform pair fre= 1 e-‘Efltr‘rHawker“? U2’fl' use the properties 01‘ the Feurier treneferm to determine the eenvelutien eitJ=f(t]rf(t}- <97 @(m) : Fm) W": 1! h .3 Fart" _____-__-:__-:“'———-:M t _ _ #q-lpJ-L wart“? 6—:2 4(w)r€ . 11 “gm t. z: "27 ii ) Problem 2 (2!) points}: 3) Determine the Feurier Treneferm F{w} ef the signal fit) shewn belew frem first prteetpiee i“ (i.e., perferm the Feurier treneferm integral eitplieitl}r te determine PM”. fin .. r j: if '0 Hun—A (n-(-+)):l ’k ,, Prnblem 3 (20 paints): fit} Pit) c05{fit] misfit) .3) Sketch IF(m}|, |G(w]|, |P(w}l, and |Y{w}|. Be sure t0 label all the axes. w. any!) :lmwl‘l Ix _ - 1" :3 -9 3-! a 5 P(H}:fPh-J)| 1,31 J? _., flu” r "* '3' m r -Hfl l ..-h I 1 I} “I”; ,lTlHtt-um F’ may} Iéfi b) Find Mt}. _ I ' - w :1: 1: “'J-~g\('t a{m):fimH(w)flin> ‘3: at) 1 J Prnblem 4 [2|] paints): —i Let at) = ream * fa) where Ht) = { r g t a 0: —e , t a: D. a) Sketeh the signal ffir) aa a fnnetien af 1 M ,F (“L \J m Gr f... WEI b) Write but [in not evaluate integral fermnlaa fer 33H} far all t, -ne c: t a: an. Each integrand must be of the farm ieii and the limits ef eaeh integral must be clearly epeeified. Yen niiht net need tn use all the lines helnw, but if an need niere, yen are in deep trnnble ...
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fa2003_exam3soln - ECE 210 Analeg Signal Precessing Fall...

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