1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Fourier Transform of cosine and rect

  1. Oct 11, 2008 #1

    vkl

    User Avatar

    1. The problem statement, all variables and given/known data
    Just wanted to check if I did the Fourier transform of a somewhat long function correctly


    2. Relevant equations

    f(x) = (1+cos([tex]\frac{2pix}{w}[/tex]))rect2([tex]\frac{x}{w}[/tex])
    they're not convolutions, just a modulation equation used in imaging studies
    'rect' is rectangle function

    3. The attempt at a solution
    Euler's formula used to substitute in for cos(ax) with ((e^(iax) + e^(-iax)))/2
    i=imaginary
    the resultant Fourier Transform:

    [tex]\hat{F}[/tex](k) = ([tex]\delta[/tex](x)+([tex]\delta[/tex](k-[tex]\frac{1}{W}[/tex])+[tex]\delta[/tex](k+[tex]\frac{1}{W}[/tex])))(w)sinc([tex]\pi[/tex]kw)

    where '[tex]\delta[/tex]' stands for the delta function

    Thanks in advance for the help

    V
     
  2. jcsd
  3. Oct 14, 2008 #2

    vkl

    User Avatar

    bump
    any takers?

    V
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Fourier Transform of cosine and rect
Loading...