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 ( j ) = 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 j ). 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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