Editing Aliasing (section)

=== Sample frequency ===

[[File:Aliasing.gif|thumb|300px|Illustration of 4 waveforms reconstructed from samples taken at six different rates. Two of the waveforms are sufficiently sampled to avoid aliasing at all six rates. The other two illustrate increasing distortion (aliasing) at the lower rates.]]

When the condition {{math|''f''{{sub|s}}/2 > '' f ''}} is met for the highest frequency component of the original signal, then it is met for all the frequency components, a condition called the [[Nyquist–Shannon sampling theorem|Nyquist criterion]]. That is typically approximated by filtering the original signal to attenuate high frequency components before it is sampled. These attenuated high frequency components still generate low-frequency aliases, but typically at low enough amplitudes that they do not cause problems. A filter chosen in anticipation of a certain sample frequency is called an [[anti-aliasing filter]].

The filtered signal can subsequently be reconstructed, by interpolation algorithms, without significant additional distortion.  Most sampled signals are not simply stored and reconstructed.  But the fidelity of a theoretical reconstruction (via the [[Whittaker–Shannon interpolation formula]]) is a customary measure of the effectiveness of sampling.