final07-ss1_solutions

final07-ss1_solutions - MAE 143A Signals and Systems Prof....

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Unformatted text preview: MAE 143A Signals and Systems Prof. M. Krstic FINAL August 3, 2007 NAME: SOLUTIONS • Open books and notes. • Present your reasoning and calculations clearly. Random or inconsistent etchings will not be graded. • Write only on the paper provided. If you run out of space for a given problem, continue on the pages at the end of the set and indicate “Continued on page X.” • The problems are not ordered by difficulty. • Total points: 75. • Time: 7:00–10:00. 1 Problem 1. (8 points) Find the Laplace transform of the “heartbeat” function: 1 2 3 4 5 6-1 1 f ( t ) t Solution: f ( t ) =- t 1( t ) + 3( t- 1)1( t- 1)- 3( t- 2)1( t- 2) + ( t- 3)1( t- 3) F ( s ) =- 1 s 2 + 3 s 2 e- s- 3 s 2 e- 2 s + 1 s 2 e- 3 s = (e- s- 1) 3 s 2 2 Problem 2. (8 points) The Laplace transform is often used to compute the sums of infinite series. This problem will teach you how to do it. Start with the definition of Laplace transform: F ( s ) = Z ∞ f ( t ) e- st dt. (a) (4 points) Compute ∞ X n =0 F ( n ) and ∞ X n =0 (- 1) n F ( n ) . Hint : Use the formula ∞ X n =0 q n = 1 1- q ,- 1 < q < 1 ....
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This note was uploaded on 04/30/2011 for the course MAE MAE 143b taught by Professor Callafon during the Winter '09 term at UCSD.

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final07-ss1_solutions - MAE 143A Signals and Systems Prof....

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