MIT6_003S10_assn03

MIT6_003S10_assn03 - 6.003 Homework 3 Due at the beginning...

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6.003 Homework 3 Due at the beginning of recitation on Wednesday, February 24, 2010 . Problems 1. Laplace Transforms Determine the Laplace transforms (including the regions of convergence) of each of the following signals: a. x 1 ( t ) = e 2( t 3) u ( t 3) b. x 2 ( t ) = (1 (1 t ) e 3 t ) u ( t ) c. x 3 ( t ) = t e −| t | | | d. 2 1 0 1 2 3 4 1 1 x 4 ( t ) t e. 2 1 0 1 2 3 4 1 x 5 ( t ) t 2. Inverse Laplace transforms Determine and sketch all possible signals with Laplace transforms of the following forms. For each signal, indicate the associated region of convergence. s + 2 a. X 1 ( s ) = ( s + 1) 2 1 b. X 2 ( s ) = s 2 ( s 1) s + 1 c. X 3 ( s ) = s 2 + 2 s + 2 d. X 4 ( s ) = ± 1 e s ² 2 s
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1 1 X 1 ( s ) 1 X 2 ( s ) 1 1 X 3 ( s ) 1 1 X 4 ( s ) 2 6.003 Homework 3 / Spring 2010 3. Symmetry Determine which of the following pole-zero 1 diagrams could represent Laplace transforms of even functions of time. Determine expressions
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This note was uploaded on 12/14/2011 for the course EECS 6.003 taught by Professor Dennism.freeman during the Spring '11 term at MIT.

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MIT6_003S10_assn03 - 6.003 Homework 3 Due at the beginning...

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