HW6 - x t in each case 1 α k = δ k-3 δ k 3(1 2 α k =...

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ECE 301, Homework #6, due date: 2/24/2010 http://cobweb.ecn.purdue.edu/ chihw/10ECE301S/10ECE301S.html Question 1: p. 255, Problem 3.22(a). Do (e) and (f). Question 2: p. 255, Problem 3.22(b). Question 3: p. 255, Problem 3.22(c) and plot the x ( t ) in 3.22(c). Question 4: Consider two periodic signals x 1 ( t ) and x 2 ( t ). x 1 ( t ) has period 2 and its Fourier series coefficients are α 1 = α - 1 = 2 and α k = 0 for all k 6 = ± 1. x 2 ( t ) has period 3 and its Fourier series coefficients are α 1 = j, α - 1 = - j and α k = 1 for all k 6 = ± 1. Answer the following questions. 1. Plot x 1 ( t ) and x 2 ( t ). 2. Suppose y ( t ) = x 1 ( t ) + x 2 ( t ). Find out the Fourier series representation of y ( t ). Question 5: In each of the following, we specify the Fourier series coefficients of a con- tinuous time signal that is periodic with period 4. Determine the signal
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Unformatted text preview: x ( t ) in each case. 1. α k = δ [ k-3] + δ [ k + 3] . (1) 2. α k = e-2 | k | . (2) 3. Repeat the above two questions but consider the case that the period is 3 π instead of 4. Question 6: p. 256, Problem 3.23(a,b). Hint: You need to use the solution of Textbook Problem 3.5 and the time-shift property of Fourier series representation. Question 7: p. 256, Problem 3.23(c,d). Hint: For Problem 3.23(d), you need to use the solution of Textbook Problem 3.8 and the time-shift property of Fourier series representation. Question 8: p. 256, Problem 3.24 Question 9: p. 257, Problem 3.25. Question 10: p. 257, Problem 3.29(a,c). Question 11: p. 257, Problem 3.30(a,b)....
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