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Suppose signal $x(t)$ is periodic with period T. Then $x(t)$ can be represented by its Fourier series representation $$x(t)=\sum_{k=-\infty} ^\infty{} X_ke^{j2\pi kt/T}$$ Let the fourier series representation of $$y(t)=\hat x(t)=\sum_{k=-\infty} ^\infty{} Y_ke^{j2\pi kt/T}$$Where $\hat x(t)$ is Hilbert transform of $x(t)$.Express the Fourier series coefficients $Y_k$ in terms of the coefficient $X_k$

Can someone help me!!?Thanks a lot

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    How did you define the [Hilbert transform](https://en.wikipedia.org/wiki/Hilbert_transform#Table_of_selected_Hilbert_transforms) ? Note it is a linear operator so it is enough to look at how it acts on $e^{i \omega t}$ – 2017-02-13
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    $\hat x = x(t)*\frac{1}{\pi t}$ – 2017-02-13

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