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# HW9 - a(1pt | | b ax f a x g = b(1pt ⎟ ⎠ ⎞ ⎜ ⎝...

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Homework #9 Due: Thursday, April 22, 2010 Note : Use of Matlab (or any other software) is not permitted. I. (see Exercise 3.9) Find the Fourier transform of each of the following functions: a. (1pt) Π = π x x x f ) cos( ) ( b. (1pt) ) 1 2 ( ) 1 2 ( ) ( Λ + Λ = x x x f c. (1pt) ) ( sinc ) ( | | 2 x e x f x π = d. (1pt) 2 2 1 ) ( 2 + + = x x x f e. (1pt) = ds e x f s isx 4 2 ) ( π f. (1pt) ( ) + = ds s sx x f 4 1 2 cos ) ( π II. Let F(s) denote the Fourier transform of f(x) . For any fixed real parameters a >0 and b , compute the Fourier transform of the following two functions
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Unformatted text preview: a. (1pt) ) ( | | ) ( b ax f a x g + = b. (1pt) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ − = a b x f a x g | | 1 ) ( in terms of F(s) . III. (2pts – see Exercise 3.16) Let a,b be real with a>0. Use your knowledge of Fourier analysis to evaluate the following definite integral: ∫ ∞ − 2 ) cos( dx e bx ax Total : 10 pts...
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