examIII_s99 - EXAM 3 EE 350 13 April 1999...

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Unformatted text preview: EXAM 3 EE 350 13 April 1999 Name (Print): _—-——.—-——_.....—_ ID#: Section: DO NOT TURN THIS PAGE UNTIL YOU ARE TOLD TO DO SO “Hm 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'/:” 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 4.21 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. Problem 1: (25 points) Question 1.1 (15 points) Compute the trigonometric Fourier series coefficients for the function g(t) shown in Figure 1. Assume that A = 4 and T = 4. Figure l - Triangle wave for question 1.1. Question 1.2 (10 points) Let y(t) be the output of the system shown in Figure 2. Compute the power of the signal y(t) using Parseval's theorem. Assume that the input to the system in Figure 2 is on 1 ' 1m: f(t)=9921—4n2 eJ2 . Place your answer in the box provided. 1, 91: <|w|<177c 0, otherwise f(t) y(t) HGm){ Figure 2 - The system for question 1.2. Power of y(t) = Problem 2: (25 points) Figure 3. | The discrete-frequency magnitude spectrum, I D,I i vs. 03, for some real-valued periodic signal, f(t), is given be10w in i | Dn I | Figure 3 - Magnitude spectrum for {(t). Question 2.1 (5 points) Determine the fundamental period of f0). Place your answer in the box provided. Question 2.2 (5 points) Determine the hannonics present in f(t). Place your answcr(s) in the box provided. Question 2.3 (5 points) Determine the bandwidth, in Hz, of ftt). Place your answer in the box provided. Bandwidth (Hz) = Question 2.4 (to points) Suppose it was known that f(l) has even symmetry. In Figure 4 below. sketch :1 possible phase spectrum. 4D,. vs. to, which coincides with the magnitude spectrum given in Figure 3. 4D,. Figure 4 - Blank graph for sketching the phase spectrum when f0) has even symmetry. Problem 3: (25 points) Question 3.1 (10 points) Use the system diagram in Figure 5 to find y(t) in terms of ftt). Place your answer in the box provided. f(t) Figure 5 - The system for question 3.1. W) = Question 3.2 (7 points) Find the energy of the function f(t) = 12 sinc(3t + 411:). Place your answer in the be): provided. Energy of f(t) = Question 3.3 (8 points) Using direct integration, find the Fourier transform of f(t) = 62‘ u(t + 3). Place your answer in the box provided. F003} = Problem 4: (25 points) Consider the standard amplitude modulation CDSB-LC) system in Figure 6. The message. m(t), is 200sinc2(100m). A cos(1000m) Figure 6 — Standard AM System to transmit m(t) II2t)(lsiue’(100m). Question 4.1 (5 points) Find the minimum bias value A so that envelope detection will be possible at the receiver. Place your answer in the box provided. Question 4.2 ([0 points) Sketch and clearly label the spectrum of w(t) in Figure 7 below, in terms of the parameter A (i.e.. do NOT substitute in a value for A). W003) Figure 7 — Blank graph for sketchlng the spectrum of w(t), Le., wow). Question 4.3 (10 points) Consider the low-pass filter system given in Figure 8. YO) Figure 8 - Low-pass filter with cutofl' frequency m... = 1000 radsfs. For the input f(t) = 4cos(101) — 12cos(35t — 40°). the output was found to he y(t) = 5cos(10t —. 40') - Scos(35t — 80°). Determine if the filter exhibits distortion and if so, specify the nature of this distortion. 10 ...
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