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Theorem If the Fourier transform $\hat{f}(w)$ of a signal function $f(x)$ is zero for all frequencies ouside the interval $-w_c\leq w \leq w_c$, then $f(x)$ can be uniquely determined from its sampled values: $$f_n=f(nT),$$ $-\infty\leq n \leq \infty$ if $T=\dfrac{1}{2w_c}$.

How I will be able to generalize the Sampling Theorem for the cases $T < 1/2w_c$ e $T > 1/2w_c$ using the Poisson’s sum formula?. Any of two cases please ...

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