Fourier Transform of cosine and rect

[vkl]

Homework Statement

Just wanted to check if I did the Fourier transform of a somewhat long function correctly

Homework Equations

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

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:

\hat{F}(k) = (\delta(x)+(\delta(k-\frac{1}{W})+\delta(k+\frac{1}{W})))(w)sinc(\pikw)

where '\delta' stands for the delta function

Thanks in advance for the help

V

 

[vkl]

bump
any takers?

V