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 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 for the time functions of those that can represent even functions of time. For those that cannot, explain why they cannot.
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