# Fourier Transform of cosine and rect

#### vkl

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($$\frac{2pix}{w}$$))rect2($$\frac{x}{w}$$)
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:

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

where '$$\delta$$' stands for the delta function

Thanks in advance for the help

V

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V

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