HWV - ECE 3250 HOMEWORK ASSIGNMENT V Fall 2009 1. In each...

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Unformatted text preview: ECE 3250 HOMEWORK ASSIGNMENT V Fall 2009 1. In each case, h is the impulse response of a LTI system and x is an input signal. Your task is to find S ( x ). (a) h ( t ) = e- 3 t u ( t ) for all t R and x ( t ) = e- 5 t u ( t ) for all t R . (b) h ( t ) = e- 3 t u ( t ) for all t R and x ( t ) = e- 5 | t | for all t R . (c) h ( t ) = e- 3( t- 7) u ( t- 7) + ( t- 7) for all t R and x ( t ) = e- 5 t u ( t ) for all t R . (d) h ( t ) = e- 3 t u ( t ) for all t R and x ( t ) = u (- t ) for all t R . 2. A certain LTI system has impulse response h with specification h ( t ) = 7( e- 3 t- e- 5 t ) u ( t ) for all t R . (a) Find S ( u ) = Conv h ( u ), the systems step response. Express S ( u ) as follows: S ( u )( t ) = c o u ( t ) + ( c 1 e- 3 t + c 2 e- 5 t ) u ( t ) for all t R . (b) For what values of R does signal x with specification x ( t ) = e t for all t R belong to D h ? For any such value of , find S ( x ). (c) For what values of R does signal x with specification x ( t ) = e t u ( t ) for all t R belong to D h ? For any such value of , find S ( x ). Compare the S ( x ) you find with the S ( x ) you found in (b). For example, how do the signals compare) you found in (b)....
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HWV - ECE 3250 HOMEWORK ASSIGNMENT V Fall 2009 1. In each...

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