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

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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) + δ ( 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 system’s 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 σ R does signal x with specification x ( t ) = e σt for all t R belong to D h ? For any such value of σ , find S ( x ). (c) For what values of σ R does signal x with specification x ( t ) = e σt u ( t ) for all t R belong to D h ? For any such value of σ , find S ( x ). Compare the S ( x ) you find with the S ( x ) you found in (b). For example, how do the signals compare for large t > 0? 3. A certain LTI system has impulse response h with specification h ( t ) = 5 e - 3 t u ( t ) for all t R .
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