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# HW7 - t Similarly let b k denote the Fourier series...

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ECE 301, Homework #7, due date: 10/16/2008 http://www.ece.purdue.edu/ chihw/ECE301 08F.html Question 1: [Basic] For a continuous time x ( t ) with period T , how many terms does the Fourier series of x ( t ) have? Write down the Fourier series (synthesis) formula. For a discrete time x [ n ] with period N , how many terms does the Fourier series of x [ n ] have? Write down the Fourier series (synthesis) formula. Question 2: [Basic] Consider a continuous time x ( t ) with period T x and a continuous time y ( t ) with period T y . Let a k denote the Fourier series coefficients of x
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Unformatted text preview: ( t ). Similarly, let b k denote the Fourier series coeﬃcients of y ( t ). 1. Suppose x ( t ) = y ( t ). Is a k = b k for all k ? Is T x = T y ? 2. Suppose a k = b k for all k . Is x ( t ) = y ( t )? (Hint: Consider two cases, T x = T y and T x 6 = T y .) Question 3: p. 255, Problem 3.22(c). Question 4: p. 256, Problem 3.23(a). (Hint: Use techniques similar to Example 3.6.) Question 5: p. 256, Problem 3.28(a) with Fig. P3.28(b). Problem 3.28(d). Question 6: p. 256, Problem 3.29(b,c)....
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