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Fourier Transform of cosine and rect

  • Thread starter vkl
  • Start date

vkl

2
0
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
 

vkl

2
0
bump
any takers?

V
 

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