Sampling Without Aliasing

The above examples suggest that the Nyquist frequency has some special significance with regard to sampling. Indeed, it is easy to believe that for any sinusoidal input signal that is known to have frequency lower than the Nyquist frequency, its frequency can be determined from its samples.

Since a sampler is a linear (though not time invariant) system, then if an input is a sum of sinusoids, the output will be a sum of sampled sinusoids. This suggests that if the input contains no frequencies above the Nyquist frequency, then it will be possible to reconstruct each of the sinusoidal components from the samples. This is an intuitive statement of the Nyquist-Shannon sampling theorem.

Before probing this further, let us examine what we mean by reconstruction.