The

Nyquist frequency is the

minimum sampling frequency of a band-limited

signal that ensures no loss in

information. The Nyquist frequency

happens to be twice the highest frequency contained in the signal to be sampled. Sampling at a frequency above the Nyquist frequency means that the

aliases of the signal's

spectrum will be far enough that no spectral

aliasing will occur. One can

recover without any error the original signal by

interpolating the samples with the

sinc function. Filtering a signal before sampling it with a

low-pass filter, and then sampling it at a frequency that is twice the

cut-off of the

filter is called

anti-aliasing filtering, and should always be used prior to sampling.

For example, my digital answering machine do not use a proper anti-aliasing filtering before sampling. When I listen to my messages, I always hear strange noises, like wind in a forest or something like this. This is because ambient noise contains high frequencies (above one half the sample frequency used) that are folded back into the audible frequency range.

*Note: in this writeup, the "Nyquist frequency" refers to the sampling frequency, or sampling rate. Sometimes, the term "Nyquist frequency" refers to the highest signal frequency that can be sampled using the "Nyquist rate", the "Nyquist rate" being twice the "Nyquist frequency" in this context.*