sample exam 3

sample exam 3 - 1 0 N ovember 2 011 E XAM I II E E 3 50 L...

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EE 350 EXAM III 10 November 2011 Last Name (Print): .sold::.; onS First Name (Print): ID number (Last 4 digits): _ Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO -- Problem Weight Score 1 I------ 25 2 3 4 Total 100 Test Form A INSTRUCTIONS 1. You have 2 hours to complete this exam. 2. This is a closed hook exam. You may use one 8.5" x 11" note sheet. 3. Calculators are not allowed. 4. Solve each part of the problem in the space following the question. If you need more space, continue your solution on the reverse side labeling the page with the question number; for example, Problem 1.2 Continued. NO credit will be given to solutions that do not meet this requirement. 5. DO NOT REMOVE ANY PAGES FROM THIS EXAM. Loose papers will not be accepted and a grade of ZERO will be assigned. 6. The quality of your analysis and evaluation is as important as your answers. Your rea.<;oning must be precise and clear; your complete English sentences should convey what you are doing. To receive credit, you must show your wo~
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Problem 1: (25 points) 1. J(1(2)points) ~ig.ure 1 shows a periodic signal J(t). Determine the trigonometric Fourier series representation of t by speclfymg the parameters (a o ' an, b n ). f(t} To.::: 2:tT ~ WIQ::: ~ ::=. J rD Figure 1: Periodic signal J(t). Bect<l. .v~e. .f(-t:)::. - f(--t:') IS afl oJl.J- -{")L~On I .f:,me J i:J,e. . <A.V"-,"~ .,. ... I_a. [~o - 01 <frtJ)L fin ~OJ f<r f)~I)L,~,--. f. T", ~o I: +(",).1' /. (nwot) -= ¥: r t-(.f;) S If) {_.-t )£L -;: 0 v~ P.>.7-7 1J V - - ~ J.2. '!: Sl~ (n -/;).P.b ~ .;,:- [s''ICOt) - n~co5(n-l.) L 2
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2. (13 points) Consider the periodic signal f(t) in Figure 2. As indicated in the figure, the shape of in the interval -n/4 < t < n/4 is cos(at). J(f) SJr 4 3Jr 4 Jr 4 o cos( at) ,/ 4 4 rr 5Jr 4 Figure 2: Periodic signal f(t). (a) (2 points) Determine the fundamental frequency of the periodic signal To = 11' => tV€) = ~::::. "2. . .,.-i.t~e;. .. of (f:.) = fC-t:) (a) (b) (3 points) What is the average value of f(t)? (c) (8 points) Determine the complex exponential Fourier series coefficients D n for 4
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VSlif &.7- b C.O~ "f. C OSJ = "i: COJ(7'~) -4- ~ C¢~ (;<~)) Do":: ;n: of f 1 ~ co> fc IM)<." ] J-! () + +
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Problem 2: (25 Points) 1. (6 points) Consider the following three periodic si n I . gas represented uSlllg an exponential TO" " rouner senes 100 k JklOt Xl(t) ~(D e X2(t) 2: cos(kJr) t?k20t k=-lOO X3(t) = Jsin (k1r) eJk30t. k=-IOO 2 (a) (3 points) Which signals, if any, are real-valued? Justify yOU . . r answer III one or two short sentences ')«(:1:.) rec.Q-.,-~ ~ ~~ - (b!n)~ . D~' ::: (1:.)' orJL ~o &, l-t:.) IS not rf2j)-v~ToJ((J~.) (D~()'Z. .)~:= (Co~ (-I)1r»)~:= CDSVJ.,,-).= D:~ (b) (3 points) Which sigr I of sentenceso la s, r any, are an even function of time? J ustify your answer in one or two short fl (.0 j c..o~ en (1-) an Q-<!n .c. . .. ~.["u\ I "J C:<.{) '0 t~·":r;. .·I-h,(r'Q. J Cl,,{l ro SI" ("'E) ~" () Q~ {...,. ~t'W'\ 6
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2. (10 points) A periodic signal f(t) with fundamental frequency W o and the exponential Fourier series represen- tation JA f D = - [1 - cos(mr)] n n7T is passed through a linear time-invariant system with frequency response representation 27T WQ < Iwi < 4w o { o otherwise W .".
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sample exam 3 - 1 0 N ovember 2 011 E XAM I II E E 3 50 L...

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