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Unformatted text preview: Systems and Signals Lee, Fall 201011 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, finelytuned discretetime lowpass 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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 Fall '08
 Levan
 Laplace, Lowpass filter, Dirac delta function, Time Fourier Transform

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