shannon-nyquist theorem

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

1. \(x_c(t)\) is a bandlimited signal

2. 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 \(x_c(t)\)