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exam2_sol - VIRGINIA TECH ECE 2704 Signals 85 Systems Fhll...

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Unformatted text preview: VIRGINIA TECH ECE 2704: Signals 85 Systems Fhll 2007 - Morning Section Exam 2, 10/24 NA SILUT (ms SIGNATURE: Instructions: 1. Print and sign your name above. Note that the Virginia Tech Honor System applies. 2. In accordance with class policy, you are allowed to use two sheets (both sides) of notes, where one sheet is from exam 1, plus a calculator. You are NOT allowed to use your text- book or any other references. 3. The exam consists of 4 questions, with multiple parts. The number of points per question is indicated. The maximum score is 100. 4. Circle your final answer! (I’m not kidding!) 5. 6(t) and u(t) refer to the unit impulse function and unit step function, respectively, as defined in your textbook. All other notation similarly follows conventions used in your text- book. 6. You may leave factors of j, 7r, powers of 10 and e, and ratios of integers in your answer, but all other constants must be multiplied through. 7. If you run out of space while working on a particular problem, please use the back of the previous page and clearly identify the number of the problem being worked there. Some friendly suggestions: Don’t get stalled on any one question or part of a question. Always take a moment to consider the possible ways to do the problem, and seek the easiest method. Do the parts you understand & seem easy first, and save the parts that seem more difficult for last. The questions are in no particular order, and certainly not in order of difficulty, Check your answer using an independent technique if you can. 1. Consider the differential equation dy(t)/dt — y(t) = —-8e‘3t and let y(0‘) = 2. (a) [15] Transform this problem into a single equation in the s (Laplace) domain. (b) [5] Solve for Y(s). (c) [5] Determine y(t). 2. Consider an electrical circuit consisting of a 2 Q resistor, a 3 H inductor, and a 4 Q resistor in series. Let m(t) be the voltage measured across all three components, and the input to this system. Let y(t) be the voltage measured across the 4 Q resistor, and the output of this system. (a) [10] Determine the system transfer function, H (s). (b) [5] Determine the impulse response h(t). (c) [5] Indicate the location of the poles of this system using a plot in the s—domain. (d) [5] Is this system BIBO stable? 257.. 3H- 1— ° -+ 9:15 ‘ln “0 (a) 1’er 04M Mn WM W5 '2 3: °’JWV"’VW‘*T-‘ * ‘l' L] 3N5 [H0919 m A “5) '*= N6) 2+35+ll , L] ‘ . .. [risk 55:; ”MMWI‘NM‘ 3. Consider the system H (s) = [2/ (3 + 3)] + [4/ (3 —- 6)]. (a) [20] Implement H (s) using only integrators, multipliers, and adders (it is not necessary to use a minimum number of components). (b) [5] Is this system BIBO stable? HB)‘ ;&,*'§:@ W‘JWJ H, +3 sum ..L to 4751 + ———4> a... \ H1 1 6......— = E I’i—g 35" WW W ‘0'“ - W MW MW”; 4. Let the impulse response h(t) = 2e‘tu(t) for some system. Let the output y(t) be the response when :1:(t) = u(t)/2. (a) [5] Determine the system transfer function, H (s). (b) [5] Determine the Laplace transform of :1:(t). (c) [15] Determine y(t). 70th M; ———v( H65) 19—43%) m): 25m (a) H15): 135m} = a» 55%} E W ‘ 19” 5% —> ._..__—/ ’- S 54- s(s+\) (”I K‘: \) K\+kl:0 —;> K2:-\ v _L., \((S) = E ,, SH .1: ”t ...
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