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## Homework Statement

Find Fourier coefficients of the periodic function whose template is x(t) where the Fourier Transform of x(t) is [tex]X(f) = (1-f^2)^2[/tex] where [itex]\left|f\right|<1[/itex] and period [itex]T_0= 4[/itex].

## Homework Equations

[tex]FC=\hat x_T(k,T_0)=\sum_{k=-\infty}^\infty\frac{1}{T_0}X\left(k/T_0\right)[/tex]

## The Attempt at a Solution

I know the expression for FC only applies with the Fourier transform X(f) has no limit on bandwidth, so something different needs to be done. We've had nothing in lectures about finding the Fourier series for this situation (i.e. where FT is zero outside of a specific frequency range), so I'm not sure where to go from here.

There is a short section in the book about waveform sampling stating that for [itex]T=1/(2f_c)[/itex]:

[tex]x(t) = T\sum_{k=-\infty}^\infty x(kT) \frac{sin 2 \pi f_c (t-kT)}{\pi(t-kT)}[/tex] which I think is just saying:

[tex]T\sum_{k=-\infty}^\infty x(kT) \frac{sin 2 \pi f_c (t-kT)}{\pi(t-kT)} <==> (1-f^2)^2[/tex] where [itex]|f|<1[/itex] and [itex]f_c=1[/itex], but I don't immediately see how that's useful. Any tips or suggestions?