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EL611 Laplace

# EL611 Laplace - directly and by using the convolution...

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EL611 Laplace Practice Fall 2008 1. State whether the Laplace transforms of the following functions exist and, where they do exist, find the Laplace transforms and the regions of convergence. a) ) ( 5 ) ( 2 ) ( 3 t U e t U e t f t t b) ) ( 5 ) ( 4 ) ( 2 t U e t U e t f t t c) ) ( ) ( 7 3 t U e t t f t 2. For the Laplace transform 3 2 3 ) 5 . 0 )( 1 ( 5 2 3 ) ( s s s s s s F a) Find the Partial Fraction expansion of ) ( s F . b) Find all possible inverse transforms ) ( t f . 3. Determine whether the following LTI systems are BIBO stable. Do it two ways, first by calculating dt t h ) ( , and then by checking the region of convergence of ) ( s H . a) ) ( ) ( 2 t U e t t h t b) ) ( 5 ) ( 2 ) ( 3 t U e t U e t h t t 4. Find ) ( * ) ( t x t h directly and by using the convolution theorem.

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Unformatted text preview: directly and by using the convolution theorem. a) elsewhere t t h ; 2 ; 1 ) ( elsewhere t t x ; 4 ; 1 ) ( b) ) ( ) ( 2 t U e t h t ) ( ) ( 5 t U e t x t c) ) ( ) ( 2 t U e t h t ) ( ) ( 5 t U e t x t 5. The system function and input to a stable LTI system are: 2 ) 1 )( 1 ( 2 ) ( s s s s H ) ( ) ( 3 / 5 ) ( 9 / 24 ) ( 2 2 5 t U e t t U e t U e t x t t t . Find the output, ) ( t y ....
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