# Fourier transform (math based question)

**URL:** <https://community.wolfram.com/t/fourier-transform-math-based-question/1458>\
**Category:** Questions\
**Tags:** engineering, image-processing, physics, mathematica\
**Created:** [February 7, 2014, 11:45pm UTC](https://community.wolfram.com/t/fourier-transform-math-based-question/1458 "2014-02-07T23:45:30Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![tx213](https://avatars.discourse-cdn.com/v4/letter/t/e480ec/32.png) [@tx213](https://community.wolfram.com/u/tx213)\
**Post date:** [February 7, 2014, 11:45pm UTC](https://community.wolfram.com/t/fourier-transform-math-based-question/1458/1 "2014-02-07T23:45:30Z")

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Hello all,

I am trying to take Fourier Transform of a function and I would love some pointers on how to best approach it.

My function is a function of (r,phi) and it is a piecewise function where:

```auto
f(r,phi) = 0 , r < r_inner
f(r,phi) = cos(phi).^2 + (-0.5)*sin(phi).^2 , r_inner <= r <= r_outter
f(r,phi) = 0 , r > r_outter

```

I’ve attached a figure here. Can I take the FT of the pieces individually and then sum? I realize that I should take the FT in polar coordinates; is there an efficient (clever) way to go about this given the the nature of the function, perhaps that it is symmetric?

Any suggestions/insight would be really appreciated. Thanks in advance!

 ![forupload.jpg](https://global.discourse-cdn.com/wolfram/original/3X/7/5/750f51b87715b9b0adfad32b7f7f60995439ae82.jpeg)

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<div class="post-metadata">

**Author:** ![bsimpson141421356](https://avatars.discourse-cdn.com/v4/letter/b/ac91a4/32.png) [@bsimpson141421356](https://community.wolfram.com/u/bsimpson141421356)\
**Post date:** [February 8, 2014, 5:16am UTC](https://community.wolfram.com/t/fourier-transform-math-based-question/1458/2 "2014-02-08T05:16:47Z")

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“Can I take the FT of the pieces individually and then sum?”

Search in this

[http://mathworld.wolfram.com/FourierTransform.html  
 ](http://mathworld.wolfram.com/FourierTransform.html)  
for the word linear

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<div class="post-metadata">

**Author:** ![fkampas](https://yyz1.discourse-cdn.com/wolfram/user_avatar/community.wolfram.com/fkampas/32/41217_2.png) [@fkampas](https://community.wolfram.com/u/fkampas)\
**Post date:** [February 8, 2014, 3:18pm UTC](https://community.wolfram.com/t/fourier-transform-math-based-question/1458/3 "2014-02-08T15:18:28Z")

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The Fourier transform of 0 is 0 so you just need to do the ring.  
It would probably be easier to advise if you tell us the goal of your calculation.