# HW12 - of this particular underlying signal x t we claim...

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ECE 301, Homework #12, due date: 11/30/2011 http://cobweb.ecn.purdue.edu/ chihw/11ECE301F/11ECE301F.html Question 1: [Advanced] We use the basic setting as stated in p. 632, Problem 8.24(a). But we only need to answer the following questions instead: 1. Find the expression of ω c as a function of T assuming Δ = 0. 2. Assuming Δ = 0, ﬁnd the maximum allowable value of ω M relative to T such that y ( t ) is proportional to x ( t )cos( ω c t ). Question 2: [Basic] p. 561, Problem 7.21(a,b,f,g). Question 3: [Basic] p. 561, Problem 7.22. Question 4: [Advanced] p. 564, Problem 7.26 but with the following modiﬁcation. Let ω 2 = 2 π × 2000 and ω 1 = 2 π × 1000. So basically the sampling theorem says that the sampling frequency ω s has to be larger than 2 ω 2 . However, due to the “bandpass” nature

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Unformatted text preview: of this particular underlying signal x ( t ), we claim that we can sample it at ω s = ω 2 instead and still be able to reconstruct x ( t ) perfectly provided we follow the system described in Figure p7.26(b). Explain why we can still have perfect reconstruction in this particular case by plotting the frequency spectrum X p ( ω ) of the impulse sampling x p ( t ). What are the values of ω a and ω b ? Question 5: [Advanced] p. 565, Problem 7.27. Question 6: [Basic] p. 566, Problem 7.29. Question 7: [Advanced] p. 567, Problem 7.31. Question 8: Do the following task. (The link is in the next page.) http://cobweb.ecn.purdue.edu/ ∼ chihw/11ECE301F/com/sampling.html...
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HW12 - of this particular underlying signal x t we claim...

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