ece366-06ex1 - Name: SDI UVH {305 Student ID: ECE 366 EXAM...

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Unformatted text preview: Name: SDI UVH {305 Student ID: ECE 366 EXAM 1 October 13, 2006 No textbooks, notes or HW solutions. One page of hand—written notes. Calculators are allowed. Exam is 50 minutes. To maximize your score on this exam, read the questions carefully and write legibly. For those problems that allow partial credit, show your work clearly. - Good luck. 1. [30] State whether the following statements are true or false. Please give a brief explanation to justify your answers. a) The system with the input output relationship y(t) = x(ar) is non—causal for all values of 05,0: i O. lfalSB- H is. causal for txri ‘\ notes . IL b) The signal given by x(t) = cos(7rt) + 2 + e 4 is periodic with period equal to 8 seconds. Ti : é-ZJL :2— Nafi-e «v A C 3 W5 True «rt pun 001A C . M T; :- 2:qu :— 8 Wat ‘11 = J— ‘12; : 8 c) x(t) = m0) + ru(—r) + u(t + 2) + u(—t — 2) is an odd signal. “l (1H3 HUFU] “Ft *2) file—e 3&0 false. 4.. = X([),a i 0 is given d) It is known that the response of the system yo!) = (5 + 36"“ )u(r) . Therefore, a must be equal to m2. ez-(é %S:#z st imp/(S3 =0 Wage SVufi—(Xro 15$:"2‘W V e) Ice—2’66 —2)d1' = e‘4 —03 mm. 93'“ mic—2:) _.._.—---' f) x(t) = e""' is a power signal. “Mke 2. [35} Given the frequency spectrum for a periodic signal, i.e. the Fourier series coefficients, Magnitude of Ck 3 wwr . - If. m; 7 fl . l ‘7 ' i l i l 1 «it ‘. .2 0 L W : in a: : ism . . .. l —3 —2 -‘I 0 1 2 3 0) Phase of CR 1 ; mm « ! WW.” —1 l (“5.1” g '- 0.5'. lq' 4‘: ll 0 [u _......_._.g...._....._ ._._. .i-.- __ _ MT ___________ ig _____________ m: -05;- ~ \T/G l 1 ...___.4 i { I mm... —3 —2 —'1 0 '1 2 3 0) a) [5] Determine the fundamental frequency of this signal. b) [10] Write the signal x0) with the given Fourier series coefficients. Simplify your answer in terms of sines/cosines. c) [8] Determine Whether this signal is even or odd, energy or power signal. c) [12] If the signal found in part b) goes through a LTI system with transfer function 2 H = (S) 5+4 , what is the steady—state response, y(t)? 9""? +6”? 005(6) = — . 2 Hint: .6 _.6 J _6 J . e sm(6) = — 2} 0x3Wg‘: imci [SEC me figure, C033/CE38- C250 ‘3‘ ,_ «J / -- ‘51 - -‘ it fit Xkflc 3 'i‘ e‘m/‘l eJWGt .4; ram/‘te’QJC +0.: 9‘ Me + OS €"Jfi/6 thgt Xk‘i\: :5 + 52005 [I 4;, «qt/Q Jrcosb‘f +T‘/e)/ WMWWWWWWwww-———WWWMWWWWWWWWMMMAWMWWWMmem Extra Page for Question 2: C} ?0W , gmcg H’s @a'viodig, Me‘iflrflr odd {Caner} (hm—e \Hnod fine cosine/am ~3wj'kd and are mahoga— mm) W03: 1 i U 2. k p "A J'- ij); 2 15> [Hg)\=2 [Jim—*W" (Q 3'“! m: “ nag—#2 ~ \\«1g“):—3~~:='0-q HM) 33“! J) a; 3. [35] Consider two LTI systems connected in series with impulse response h, (I) and I120!) , respectively with kl (t) = t[u(t + 2) — u(r — 2)] and hz (t) = 5(3 — 2). H] (n a) [8] Determine whether each one of the systems, MG) and 11220), are causal and stable. Justify your answers. b) [10] Determine the impulse response of the composite system and state whether it is stable and causal. c) [12] Assume that an input signal x(t) : u(t) is applied to this composite system. What is the output, y(t)? Sketch y(t). d) [5] Find a simple relationship between the output y(t) found in part c) and the impulse response of the composite system, i.e. your answer to part b). CR3 hA\iy\.:JtYul‘\'+23~ulJc—'Z)j __>_)no‘i rwgqi/ a, mute raffle a: $1 = 3: 11: q <06 Slfabie “'2’ a 7, O : SC'E“Z> ‘JISCCLLLSOLL jmeouc : .t <01» stable. hm - imUcl a heft) m 6 mm we SW13 3 pmwgtfim we :“hfi KIC'ZB can « lie-M) as H = imitate u 1 a; cmmfl "l’Slfiuaifl \fl * Ltlixtlhfi) [5:0 C.) :QliB '— JC<O gang OVGFia/i’: L/ mess SWIM OW” ’ : L; k/\f\= Z -){ «Z O 7- t F“ t1 flit :js/l‘7z 5 % ,QT\O.— :9:— t 7L\ J; 3cm overlap fl VLQ: 05in~1)€1'€- O z E mmmmmmnmmww‘ 3 mummen-m W.memmmWWWMWM-v_ 4 OD Extra Page for Question 3: wt) .—. Shkédt _OQ W4u.%mfidmwww smmmmmmmmmmwwmmmwmwammwww ‘ ‘..,...HWWWXWMW ...
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This note was uploaded on 06/08/2009 for the course ECE 366 taught by Professor Staff during the Spring '08 term at Michigan State University.

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ece366-06ex1 - Name: SDI UVH {305 Student ID: ECE 366 EXAM...

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