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Fourier Transform of cosine and rect

  1. Oct 11, 2008 #1


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    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
    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

  2. jcsd
  3. Oct 14, 2008 #2


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    any takers?

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