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Fourier 1st step?

How to find fourier transform of a series of the such form: $$y_k=\left[f(x) \right]^{2},$$ but I am not sure of the step by step for going about this computation.

how is the first step??

thank you very much!!

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marked as duplicate by mixedmath, Zhen Lin, Arturo Magidin, Jyrki Lahtonen, anon Jun 20 '12 at 7:29

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

What is $k$? You don't take Fourier transform of a series. – Thomas Andrews Jun 18 '12 at 21:23
to be specfic, it states $y_{k} = [k-\frac{n-1}{2}]^{2}$ thank you very much!! – nanme Jun 18 '12 at 21:28
Wait, where is $x$ in that definition of $y_k$? – Thomas Andrews Jun 18 '12 at 21:33
my error. the true problem is stated with $y_K$ and i wrote question as f(x)...does this answer? i am really lost here!! how do you know when to use integral vs when to use sum to find the transform? – nanme Jun 18 '12 at 21:54
up vote 2 down vote accepted

Integration by parts. You're doing an integral of the form $$ \int (f(x))^2 \exp(i\xi x) dx $$

Let $u = (f(x))^2$ and $dv = \exp(i \xi x)$.

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Based on nanme's comment and previous question, I find it likely OP means the discrete transform. – anon Jun 18 '12 at 21:32
i think so too!but how to go about this? – nanme Jun 18 '12 at 22:06

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