Assign6_Laplace - information above. There should be no...

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EE3210 Assignment 6: Laplace Transform Due: (before lecture) Nov 25, 2009 (Marks will be deducted for late submission.) 1. A causal LTI system with impulse response h ( t ) has the following properties: y When the input to the system is x ( t ) = e 2 t for all t , the output is y ( t ) = (1/6) e 2 t for all t . y The impulse response h ( t ) satisfies the differential equation ) ( ) ( ) ( 2 ) ( 4 t bu t u e t h dt t dh t + = + , where b is an unknown constant. a) Determine the system function H ( s ) of the system, consistent with the
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Unformatted text preview: information above. There should be no unknown constants in your answer; that is, the constant b should not appear in the answer. b) What is the ROC of H ( s )? c) Determine the impulse response h ( t ) of the system. 2. Consider the following signal, x ( t ): 2 4 1 3 2 a) Find the Laplace transform of ) ( ) ( t x dt d t y = . b) Hence, find the Laplace transform of x ( t )....
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