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 \(x_c(t)\)

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