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I am trying to grasp Fourier transform, I read few websites about it, and I think I don't understand it very good. I know how I can transform simple functions but there is few things that are puzzling to me.

Fourier transform takes a function from time domain to a frequency domain, so now I have $\widehat{f(\nu)}$, this is complex-valued function, so as I understand for every frequency I get an imaginary number.

  1. What does this number represent, what is an interpretation of real and imaginary part of $\widehat{f(\nu)}$?

  2. How can I graph $\widehat{f(\nu)}$? As I understand if function is not odd-function, $\widehat{f(\nu)}$ will have complex values and imaginary part will be different then 0. Do I need to plot it in 3d or do I just plot $|\widehat{f(\nu)}|$?. I am asking about plotting, because for example on wikipedia there is a plot of sinc function, which is fourier transform for square function. It is nice, because it is an odd-function in their case. And I am wondering about other functions.

I would be also very grateful for any useful links that can shed some light on the idea of fourier transform and some light theory behind it, preferably done step-by step.

  • 2
    To be pick<: You should better write $\hat{f}(\nu)$ instead of $\widehat{f(\nu)}$ because it is $f$ which is transformed, not $f(\nu)$.2012-04-13
  • 0
    See the [graph](http://math.stackexchange.com/questions/1665631/fourier-transform-of-simple-functions?rq=1)2017-03-18

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