Nyquist frequency
The Nyquist frequency, named after electronic engineer Harry Nyquist, is half of the sampling rate of a discrete signal processing system. It is sometimes known as the folding frequency of a sampling system. An example of folding is depicted in Figure 1, where fs is the sampling rate and 0.5 fs is the corresponding Nyquist frequency. The black dot plotted at 0.6 fs represents the amplitude and frequency of a sinusoidal function whose frequency is 60% of the sample-rate (fs). The other three dots indicate the frequencies and amplitudes of three other sinusoids that would produce the same set of samples as the actual sinusoid that was sampled. The symmetry about 0.5 fs is referred to as folding.
The Nyquist frequency should not be confused with the Nyquist rate, which is the minimum sampling rate that satisfies the Nyquist sampling criterion for a given signal or family of signals. The Nyquist rate is twice the maximum component frequency of the function being sampled. For example, the Nyquist rate for the sinusoid at 0.6 fs is 1.2 fs, which means that at the fs rate, it is being undersampled. Thus, Nyquist rate is a property of a continuous-time signal, whereas Nyquist frequency is a property of a discrete-time system.
When the function domain is time, sample rates are usually expressed in samples/second, and the unit of Nyquist frequency is cycles/second (hertz). 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/inch.
Referring again to Figure 1, undersampling of the sinusoid at 0.6 fs is what allows there to be a lower-frequency alias, which is a different function that produces the same set of samples. That condition is usually described as aliasing. The mathematical algorithms that are typically used to recreate a continuous function from its samples will misinterpret the contributions of undersampled frequency components, which causes distortion. Samples of a pure 0.6 fs sinusoid would produce a 0.4 fs sinusoid instead. If the true frequency was 0.4 fs, there would still be aliases at 0.6, 1.4, 1.6, etc., but the reconstructed frequency would be correct.
...
Wikipedia