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.

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