Fourier transform of hat function

captainjack2000

1. Homework Statement
obtaining the fourier transform of the hat function
h(x) = 1 if modulus of x</= 1
=0 otherwise

2. Homework Equations
F(k)=1/sqrt(2*PI) *integral from -1 to 1 of exp(ikx)

3. The Attempt at a Solution
I've carried through the transform and got an answer of
sqrt(2/PI)*sinc(k)
could someone tell me if this is correct please?

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tiny-tim

Homework Helper
obtaining the fourier transform of the hat function
h(x) = 1 if modulus of x</= 1
=0 otherwise

F(k)=1/sqrt(2*PI) *integral from -1 to 1 of exp(ikx)
Hi captainjack2000! (have a pi: π and a ≤ and a √ and an ∫ and try using the X2 tag just above the Reply box )

Yes, that looks good … see http://en.wikipedia.org/wiki/Rectangular_function Physics Forums Values

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