# shannon-nyquist theorem

One can recover a continuous signal \(x_c(t)\) from sampled signal \(x[n]\) exactly when

- \(x_c(t)\) is a bandlimited signal
The sampling rate is greater than twice the frequency, or

\begin{equation} \frac{2\pi}{T} > 2\Omega_{max} \end{equation}Where \(T\) is the sampling period (how long between samples) and \(\Omega{max}\) is the maximum frequency in the frequency response of \(x_c(t)\)