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Sampling Theorem:

Let $x(t)\$ be a BAND-LIMITED signal with $X(\omega) = 0\$ for $|\omega| > \omega_m\$. Then $x(t)\$ is uniquely determined by its samples $x(nT)\$, n=-2,-1,0,1,2... IF $\omega_s > 2\omega_m\$, where $\omega_x = 2 \frac{\pi}{T}$.

Given these samples, we can reconstruct $x(t)\$ through an impulse train where amplitudes are successive sample values.

THIS DEFINITION IS EXTRACTED FROM THE TEXTBOOK.

Signals & Systems Second Edition Alan V. Oppenheim, Alan S. Willsky, with S. Hamid Nawab

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