HW6 - ∞<< ∞ βˆ’ = βˆ’ ∠∞ ∞ βˆ’ x x f du u x f...

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Homework #6 Due: Tuesday, March 23, 2010 1. (2pts) Find the Fourier transform of the function f:R R = 2 / 1 2 / 1 ) ( 2 ) ( du e x f u x π 2. (2pts) Let f 0 ,f 1 :R R be functions defined by 2 2 ) ( , ) ( 1 0 x x xe x f e x f = = Compute the following convolutions: i) f 0 *f 0 ii) f 0 *f 1 . 3. (3pts) Find a non-zero function f on R that satisfies the following equation:
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Unformatted text preview: ∞ < < ∞ βˆ’ = βˆ’ ∫ ∞ ∞ βˆ’ x x f du u x f u f , ) ( ) ( ) ( 4. (3pts) Find a continuous function f:R R that satisfies x , , ) ( ) ( ' ⎩ ⎨ ⎧ < > = + βˆ’ βˆ’ x e x f x f x Total: 10pts....
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