Fourier transform of hat function

  • #1
captainjack2000
99
0

Homework Statement


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


Homework Equations


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


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?
 

Answers and Replies

  • #2
tiny-tim
Science Advisor
Homework Helper
25,838
255
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! :smile:

(have a pi: π and a ≤ and a √ and an ∫ and try using the X2 tag just above the Reply box :wink:)

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

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