pset_VI-06-2 - MMAE 350 D. Rempfer Problem Set VI Page 1 of...

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Unformatted text preview: MMAE 350 D. Rempfer Problem Set VI Page 1 of 3 Due Date: November 06, 2006 1. You are given the following set of ( x,y ) pairs of values, describing (error-prone) measurements of some unknown function f ( x ): x i-1-0.8-0.6-0.4-0.2 0.2 0.4 0.6 0.8 1.0 y i 1.0 1.8 2.5 3.0 2.8 3.1 3.1 2.5 2.4 2.0 0.8 Find a least-squares approximation of the function f ( x ) that is of the form f ( x ) ≈ a log ( 1 + x 2 ) + a 1 exp (- x 2 ) + a 2 x 2 . (1) 2. Calculate the coe ffi cients of the Fourier expansion ˜ f ( t ) = a + 5 X j = 1 a j cos(2 πj t ) + 5 X i = j b j sin(2 πj t ) for the following two functions: a. f ( t ) = 1 2- 1 2 t, x ∈ [0 , 1) b. f ( t ) = 1 2 t- 1 2 t 2 , x ∈ [0 , 1] For each of the above, plot both the periodic extension of f and ˜ f in the interval [0 , 2]. Note that the integrals that give these coe ffi cients can be solved in closed form, so you do not have to integrate numerically....
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This note was uploaded on 05/04/2008 for the course MMAE 350 taught by Professor Rempher during the Spring '05 term at Illinois Tech.

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pset_VI-06-2 - MMAE 350 D. Rempfer Problem Set VI Page 1 of...

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