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**Fourier transform of "church" function**

This is an old examn question that I'm trying to solve. There is a solution, but I'm having a hard time getting it since there is only some kind of graphic equation with no explanation. To only test in the solution is "Derivate!"

**1. Homework Statement**

Determine the Fourier transform of the following modern church function

http://www.apspektakel.com/bilder/churchf.svg

**2. Homework Equations**

[tex]

F(s) = \int ^\infty _{-\infty} f(x) e ^ {-i2\pi xs} dx[/tex]

[tex]

i2\pi sF(s) = \int ^\infty _{-\infty} f'(x) e ^ {-i2\pi xs} dx

[/tex]

**3. The Attempt at a Solution**

This is what I think the derivative of the church function would be. I coloured the impulses red, so that their origins are visible. Is the derivative correct?

http://www.apspektakel.com/bilder/churchfd.svg

So, the next step, would it be adding the transform of the first impulse to the transform of the first square, to the second impulse and so on?

I mean would the correct way be something like:

[tex]

i2\pi sF(s) = 2 + \text{sinc}_{something} - 2 \cdots

[/tex]