Squared Series Fourier

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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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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 $dv = \exp(i \xi x)$.