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($$\pi$$kw)

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

Thanks in advance for the help

V

 

[vkl]

bump
any takers?

V