102_1_final_2010_fall

# 102_1_final_2010_fall - Systems and Signals Lee Fall...

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Unformatted text preview: Systems and Signals Lee, Fall 2010-11 EE102 Final Exam NAME: You have 3 hours for 6 questions. • Show enough (neat) work in the clear spaces on this exam to convince us that you derived, not guessed, your answers. • Put your final answers in the boxes at the bottom of the page. Closed notes, closed book, 1 letter sized handwritten sheets allowed. Problem Score 1 2 3 4 5 6 Total 1 Problem 1. Fourier Transforms (15 Points) Find the Fourier transform of the following signal f ( t ) t 1 2 3 4 5- 5- 4- 3- 2- 1 sinc 2 ( t / 3 ) rect ( t 2 ) This is an infinite sequence of rectangles, weighted by a sinc 2 (). Eliminate convolutions in your answer. F ( jω ) = 2 Problem 2. Laplace Transforms (15 Points) Find the Laplace transform of the following signal f ( t ) t p ( t ) p ( t- 2) p ( t- 4) 2 1 4 f ( t ) This is the sum of an infinite sequence of delayed causal subpulses f ( t ) = ∞ X n =0 p ( t- 2 n ) Assume p ( t ) = e- 7 t u ( t ) and indicate region of convergence. Hint: L{ p ( t- n ) } = e- sn P ( s ) . Also, recall that ∞ X n =0 a n = 1 1- a when simplyfing your answer. F ( s ) = 3 Problem 3. Discrete Time Fourier Transform (30 Points) An engineer purchased an expensive, finely-tuned discrete-time low-pass filter with an im- pulse response h [ n ] and frequency response H ( e jω ). Sadly, the filter did not exactly suit the needs of the application and need to be modified.needs of the application and need to be modified....
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102_1_final_2010_fall - Systems and Signals Lee Fall...

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