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Homework Set 3 Math/ECE 430 due Friday, Feb. 15, 2013 The page numbers below refer to the book by Gasquet and Witomski. 1. p. 56, # 6.1(a). For a linear function on the interval [0, a], expand in Fourier series the following extensions: (a) the odd periodic extension with period 2a (b) the even periodic extension with period 2a (c) the periodic extension with period a Note that these different Fourier series all represent the original function on the interval [0, a]. Hint: integrate by parts to compute the Fourier coefficients. 2. p 56, # 6.2. Use the Legendre polynomials P0 , P1 , P2 , P3 to compute the best approximations fi , i = 0, 1, 2, 3 to f (t) = |t| on [−1, 1] in sense of the L2 norm. Plot f, f1 , f2 on the same graph. 3. p. 62, # 7.2. Show that a real period signal has an amplitude spectrum that is even. 1