HW4 - ELEN3801 - Fall 2009 Homework 4 Due Thursday October...

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ELEN3801 - Fall 2009 Homework 4 Due Thursday October 8th at the beginning of class (Mudd 227 9:10am) 1 Carefully justify ALL your answers 4.1 - Let H be a time-invariant (but not necessarily linear) system. Show that the system’s response to a constant input is also a constant, that is, if the input is f ( t ) = a for all t R , then H { f ( t ) } = b , where b R . 4.2 - Consider an LTI system that has impulse response h ( t ) = e - t u ( t ). Find the system response y ( t ) if the input is (a) u ( t ) (b) e - t u ( t ) (c) sin(3 t ) u ( t ) 4.3 - (CORRECTED) Let p ( t ) = u ( t + 1) - u ( t - 1). Compute and sketch ( p * p )( t ) and ( p * p * p )( t ). Comment on your results. 4.4 - Consider a system that has impulse response h ( t ) = - δ ( t ) + 2 e - t u ( t ). Compute the system’s response to input e t u ( - t ) and sketch both the input and output signals. 4.5 - (Optional) Prove the associativity property of the convolution. That is, prove that ( f 1 * ( f 2 * f 3 )) ( t ) = (( f
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HW4 - ELEN3801 - Fall 2009 Homework 4 Due Thursday October...

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