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I am wondering if the function $\mathrm{sinc}(x)=\frac{\sin x}{x}$ can be represented in terms of Fourier series?

Thank you.

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    I did not understand about the cosing sing. Could you elaborate, please. thank you!2011-12-17

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Well, in order to compute the Fourier series of any function, you need to specify the interval $(-\ell,\ell)$. But once you do, sure you can find the Fourier series of $f(x)={\sin x\over x}$ in the usual way.

For example, taking $\ell=\pi$, here is a plot of $f(x)$ (black) and the first three terms of its Fourier series (blue):

Mathematica graphics