# 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.