FinalExamSP14Soln
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Clemson University *
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Electrical Engineering
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Nov 24, 2024
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Col© Tioe N Name: - Final Exam ECE301 mignals and Systems Tuesday, May 6, 2014 Cover Sheet Write your name on this page and every page to be safe. Test Duration: 120 minutes. | Coverage: Comprehensive Open Book but Closed Notes. Three two-sided handwritten sheets. Calculators NOT allowed. This test contains four problems, each with multiple parts. You have to draw your own plots. You must show all work for each problem to receive full credit. Good luck! It was great having you in class this semester! Have a great Summer!
Problem 1. : (a) (b) (e) (£) For the signal s(t) below, plot the Fourier Transform S(w) which is purely real-valued: 7 {sin(2.5t) S(t) - é—g i }22 cos(5t) (1) An AM signal r(t) is formed from s(¢) above as prescribed below, where k£ = 0.1 and ¢ r(£) = [1 4+ k s(t)] cos (35t + o) ' (2) The signal r(t) above is applied to a square-law device, followed by amplification, to form z(t) = 1072(¢t) p(t) = 10 {[1+k s(t)] cos (35t + ¢)}> 10 [14+k s(t)]z‘cos2 (35t + ¢) (3) Plot the magnitude of the Fourier Transform of z(t) denoted |X(w)|, IGNORE as negligible any term which is scaled by &% = 0.01. Recall cos*(0) = £ + £ cos(26). Consider an LTI system with impulse response h(t) = {_ZT_ sin(15¢) Sin(25t)} 15 7t 7t (4) Determine and plot the frequency response, H(w), the Fourier Transform of h(%). For the LTI system with this impulse response, determine the output y(t) for the input z(t) above. Plot |Y(w)|. Again, ignore any term which is amplitude-scaled by k* = 0.01 as negligible. | y(t) = z(t) * h(t) Would your answer to part (d) change if the phase shift in the sinewave was changed from ¢ = 7 to ¢ = Z7 Does the value of the phase shift ¢ have any impact on the recovery of s(t) via the method above? Explain your answer. In the scheme above, a strong DC component is added before the signal is multiplied by the cosine wave. Determine the final output y(¢) via the same sequence of steps with the DC component removed: (1) Form r(t) = 2s(¢) cos (35t + ¢), (2) Multiply by - cosine at the same frequency z(t) = r(t) cos (35¢t), and (3) y(t) = z(¢) * h(t). Recall: 2 cos(0) cos(p) = cos(0 + ¢) + cos(@ — ¢). How does the output y(¢) depend on the value of gb7 What is the output When the phase is gb =T / 2‘7 N Prast
Sy OV S€ 0€ S¢ Oc G+ OF & 0 G—0L-G1-0c¢-5¢065C0v-Gi—- I I ] | | [ . . . . . . f . . . . . . . . . . B . . . . f P . . . . . . . . . . . . . . . . f . . . . . . . . f . . . . . . . P . . . f . . . . f . . . . . . . . . . . . . . . . . . . . . . f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . f . . . . . . . . . . . f . . . . f . . . . . . . ’ . . . . . . . . . f . . . . . P PR S . . M - . . . f . . . . . . . . . . . . . . f f . . . . . . . . f . . . . . . . . . f . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . f . . . f . . . f . . . . . . . . f . . . . . . . . . . . f . . . . . . . . . . . . . . f . . . . . f . . . . f . . . . . . B . . . f . . 3 ¢ . B e et : . PR O e e . - . : 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . f f . . . . . . . . . . . . . . . . . . . . . . . . . . . N . f . . . . . . . . . . . . . . . . f . . . f . . . . . . . . P . . . . . . . . . . . f . . f . f . . f . . . f . . . . . . . . . . B . . . . . . . . . . . f . . . . . . . . . . . . . . . . . . . . . . . f . . . . . . f . . f . . . . . . . f . . . . . . . . . . . . f . . . . . . . . . . . . . . . . . . . . . f . . . . . . . . . . . . . . . . . . . . . . . . f . . . . . . . . . . . [ . . . . . : . . . . . . . . . . . . P . . . . . . . . . . . . . f . . . . . f . . f . . . . . f . . . . . . . . . . . . . f . . . . . . . P . . . . . . . f . . . . . . . . . . f . . . . . . B . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . f . . . . . . . . . . . . . . . f . . . . f . . . . . . . . . . . . . . .. X K s e e e : P " K . : * . . . . . . . . f . f . . . . . . . . . . f f . . f f . . . . . . . . . . f . . . . . . . . . . . . . . . . . . . . \ . . . . f . . . . . . . . . . . f . . . . . . . . . . f . . . . . . . f . . . . . . . . f . . . . . . . . . . . . . . . . B PN . e R e . . . . ‘("e) T we[qOoadg 103 j0[d puUE NIoM [[e MOUS
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Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:9780134746968
Author:James W. Nilsson, Susan Riedel
Publisher:PEARSON
Engineering Electromagnetics
Electrical Engineering
ISBN:9780078028151
Author:Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:Mcgraw-hill Education,