hw5 - ECE 301, Homework #5, due date: 2/15/2012

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ECE 301, Homework #5, due date: 2/15/2012 https://engineering.purdue.edu/ chihw/12ECE301S/12ECE301S.html Question 1: [Basic] p. 141, Problem 2.21 (b,d). Question 2: [Basic] p. 141, Problem 2.22 (a,e). Question 3: [Basic] This question is to verify the following two properties of the convolu- tion sum / integral: Commutativity: (a) For an LTI system with h ( t ) = 2 U ( t + 1) - 2 U ( t ), find out the response y ( t ) when x ( t ) = U ( t + 1) - U ( t - 1). (b) For an LTI system with h ( t ) = U ( t +1) -U ( t - 1), find out the response y ( t ) when x ( t ) = 2 U ( t +1) - 2 U ( t ). Are your answers the same for the questions (a) and (b)? Distributivity: (a) For an LTI system with h ( t ) = 2 - 3 t U ( t ), find out the response y ( t ) when x ( t ) = 2 U ( t +1) - 2 U ( t ) by computing the convolution integral x ( t ) * h ( t ). (b) For an LTI system with h ( t ) = 2 - 3 t U ( t ), find out the response y 1 ( t ) when x 1 ( t ) = 2 U ( t + 1). Find out the response y 2 ( t ) when
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hw5 - ECE 301, Homework #5, due date: 2/15/2012

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