examII_s99 - EXAM 2 EE 350 16 March 1999 Name(Print ID...

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Unformatted text preview: EXAM 2 EE 350 16 March 1999 Name (Print): ID # : Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO TEST FORM A Instructions: 1. You have 2 hours (120 minutes total) to complete this exam. 2. This is a closed book exam. However, as told earlier, you are allowed 1 sheet of 8' 2” x 11” paper for notes, formulas, etc... 3. Solve each part only in the space following each question. Be sure to place your answers in the boxes (as appropriate) provided. If you need more space, continue on the reverse side and write the question number; for example, Question 4.2) continued..; NO credit will be given to a solution that does not meet this requirement. 4. DO NOT REMOVE ANY PAGES FROM THIS EXAM. Loose papers will NOT be accepted and a grade of ZERO will be assigned. thlem l: (25 points) Question 1.1 (2 points) For what section # of BBB 50 are you officially registered? Place yom' answer in the box provided. Question 1.2 (5 points) Given 133%1 10005(40t + 35°) - 55in(40t + 45°). Express fit) in phasor form, as a single exponential term, and place your answer in the box provided. Consider the following circuit. The input is the voltage f(t). R1219 Figure 1 Using y(t) as the output, the ODE system model is 03' — + 10 t = 5 t d, y( ) f( ) Question 1.3 (8 points) Find the frequency response function, 110w) : a;- , and express your result in the form . a? K How) = w = .,,, F 1+JAc Place your solution in the box provided. HUw) = Question 1.4 (10 points) Suppose fit) = 4cos{10t + 45°) is applied to the circuit in Figure 1. Find the sinusoidal steady-state current, i2(t). Place your answer in the box previded. i2(t) = nglgm 2; (25 points) Question 2.1 (10 points) Find the zero-state response to a unit-step input for the system modeled by em) = (D2 + SD + 4)y(t). Use the initial conditions y(0+) = 33(0”) 2 0. Place your answer in the box provided. Question 2.2 (10 points) The zero—state response to a unit-step input of a diffgent system is y(t) = (3 — 96‘t + 2e'3*)u(t). Find the impulse response, h(t), for the system. Justify, in a sentence or two, the process you used to find h(t). Place your answer in the b0x provided. h(t) = Question 2.3 (5 points) Consider a system, shown in Figure 2, composed from several subsystems. Find the impulse response, h(t), relating the input, {(t), to the output, y(t). Give your answer in terms of the subsystem impuise responses. Place your answer in the box provided. f(t) Figure 2 Proglgm 3: (25 points) Question 3.1 (10 points) Let f(t) = 36(t 4" 2) + 25(t — 1) and h(t) = 3e'31 u(t). Find y(t) for the system shown in Figure 3. Place your answer in the box provided. fa) ya) Figure 3 -— System for Problem 3. y(t) = Question 3.2 (15 points) Let Kt) = u(t + 3) — u(t u 1) and h(t) = e‘ u(— t). Using the graphical approach, determine y(t) = f(t) 1' h(t) for all values oft. Place your answer in the box provided. Problem 4: (25 points) Question 4.1 (5 points) Consider two, real-valued signals mm and xz(t) defined over the interval [t1 t2]. State the condition(s) for which these signals would be orthogonal. Question 4.2 (5 points) Give an example of two signals, x.(t) and x20), which are linearly independent but not onhogoual over the interval [0 2]. 10 Question 4.3 (15 points) Consider the signal fit) and its approximation Rt) shown in Figure 4. fit) Rt) Figure 4 Find the value of A that minimizes the energy of the error signal f(t) :56) over the interval —1t/2 s t s arc/2. Place your answer in the box provided. ll ...
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