Editing Nyquist frequency (section)

{{Use American English|date = March 2019}}
{{Short description|Maximum frequency of non-aliased component upon sampling}}
{{distinguish|Nyquist rate}}
[[File:Nyquist frequency & rate.svg|thumb|Typical example of Nyquist frequency and rate. To avoid aliasing, the sampling rate must be no less than the Nyquist rate of the signal; that is, the Nyquist rate of the signal must be under double the Nyquist frequency of the sampling.]]
In [[signal processing]], the '''Nyquist frequency''' (or '''folding frequency'''), named after [[Harry Nyquist]], is a characteristic of a [[Sampling (signal processing)|sampler]], which converts a continuous function or signal into a discrete sequence. For a given [[Sampling (signal processing)|sampling rate]] (''samples per second''), the Nyquist frequency ''([[cycles per second]]'') is the frequency whose cycle-length (or period) is twice the interval between samples, thus ''0.5 cycle/sample''.  For example, audio [[compact disc|CDs]] have a sampling rate of 44100 ''samples/second''.  At ''0.5 cycle/sample'', the corresponding Nyquist frequency is 22050 ''cycles/second'' ([[hertz|Hz]]).  Conversely, the Nyquist rate for sampling a 22050 Hz signal is 44100 ''samples/second''.<ref name="Grenlander" /><ref name="Leis" />{{efn-ua
|When the function domain is distance, as in an image sampling system, the sample rate might be dots per inch and the corresponding Nyquist frequency would be in cycles per inch.
}} 

When the highest frequency ([[Bandwidth (signal processing)|bandwidth]]) of a signal is less than the Nyquist frequency of the sampler, the resulting [[discrete-time]] sequence is said to be free of the distortion known as [[aliasing]], and the corresponding sample rate is said to be above the [[Nyquist rate]] for that particular signal.<ref name="Condon" /><ref name="Stiltz" />

In a typical application of sampling, one first chooses the highest frequency to be preserved and recreated, based on the expected content (voice, music, etc.) and desired fidelity. Then one inserts an [[anti-aliasing filter]] ahead of the sampler. Its job is to attenuate the frequencies above that limit. Finally, based on the characteristics of the filter, one chooses a sample rate (and corresponding Nyquist frequency) that will provide an acceptably small amount of [[aliasing]].  In applications where the sample rate is predetermined (such as the CD rate), the filter is chosen based on the Nyquist frequency, rather than vice versa.