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Unformatted text preview: ECE 301, Homework #4, due date: 9/30/2008 http://www.ece.purdue.edu/ ∼ chihw/ECE301 08F.html Question 1: p. 61, Problem 1.27 (d,e,f). Question 2: p. 62, Problem 1.28 (a,d,e,g). Question 3: Consider a linear time-invariant system. Suppose we know that when the input is x [ n ] = δ [ n ], the output y [ n ] = (1- e- n ) U [ n ]. Solve the following questions in order. 1. If the input is x [ n ] = δ [ n- 1], what is the output y [ n ]? (Hint: Use the time-invariance property.) 2. If the the input is x [ n ] = U [ n ]-U [ n- 2], what is the output y [ n ]? (Hint: First plot the signal, and see what x [ n ] looks like. Then use the linearity of the system and the result of the previous sub-question.) Question 4: p. 62, Problem 1.31. Question 5: p. 141, Problem 2.21 (b,d). Question 6: p. 141, Problem 2.22 (b,c). Question 7: Confirm the two properties of the convolution sum / integral: • Commutativity: (a) For an LTI system with h ( t ) = 2 U ( t )- 2 U ( t- 1), find out the response y (...
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- Spring '06
- Digital Signal Processing, LTI system theory, Impulse response