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This is the classical sampling theorem. When you sample a continuous signal $x(t)$, you are basically multiplying it by a sample train $s(t) = \sum_{-\infty}^{+\infty}\delta(t-kT_s)$, the value at consecutive $T_s$ being your samples. In frequency domain, it effect is to convolve $X(\omega)$ and $S(\omega)$ $$S(\omega) = \sum_{-\infty}^{+\infty}\delta(\...


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