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.
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