Nyquist rate

In signal processing, the Nyquist rate, named after Harry Nyquist, is twice the bandwidth of a bandlimited function or a bandlimited channel. This term means two different things under two different circumstances:

Nyquist rate relative to sampling

When a continuous function, x(t), is sampled at a constant rate, f_ssamples/second, there is always an unlimited number of other continuous functions that fit the same set of samples. But only one of them is bandlimited to ½ f_scycles/second (hertz), which means that its Fourier transform, X(f), is 0 for all |f| ≥ ½ f_s.  The mathematical algorithms that are typically used to recreate a continuous function from samples create arbitrarily good approximations to this theoretical, but infinitely long, function. It follows that if the original function, x(t), is bandlimited to ½ f_s, which is called the Nyquist criterion, then it is the one unique function the interpolation algorithms are approximating. In terms of a function's own bandwidth (B), as depicted above, the Nyquist criterion is often stated as f_s > 2B.  And 2B is called the Nyquist rate for functions with bandwidth B. When the Nyquist criterion is not met (B > ½ f_s), a condition called aliasing occurs, which results in some inevitable differences between x(t) and a reconstructed function that has less bandwidth. In most cases, the differences are viewed as distortion.