- #1
hadoque
- 43
- 1
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!"
Determine the Fourier transform of the following modern church function
http://www.apspektakel.com/bilder/churchf.svg
[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]
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]
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!"
Homework Statement
Determine the Fourier transform of the following modern church function
http://www.apspektakel.com/bilder/churchf.svg
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]
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]