Nyquist–Shannon sampling theorem Fig. 1: Hypothetical spectrum of a bandlimited signal as a function of frequency The Nyquist–Shannon sampling theorem , after Harry Nyquist and Claude Shannon , in the literature more commonly referred to as the Nyquist sampling theorem or simply as the sampling theorem , is a fundamental result in the field of information theory , in particular telecommunications and signal processing . Sampling is the process of converting a signal (for example, afunction of continuous time or space) into a numeric sequence (a function of discrete time or space). Shannon's version of the theorem states: [ 1 ] If a function x ( t ) contains no frequencies higher than B hertz , it is completely determined by giving its ordinates at a series of points spaced 1/(2 B ) seconds apart. Since the theorem was also discovered independently by E. T. Whittaker , by Vladimir Kotelnikov , and by others, it's also known as the Nyquist–Shannon–Kotelnikov , Whittaker–Shannon–Kotelnikov , Whittaker–Nyquist–Kotelnikov–Shannon , WKS , as well as the cardinal theorem of interpolation theory . In essence, the theorem shows thata bandlimited analog signal can be perfectly reconstructed from an infinite sequence of samples if the sampling rate exceeds 2 B samples per second, where B is the highest frequency of the original signal. If a signal contains a component at exactly B hertz, then samples spaced at exactly 1/(2 B ) seconds do not completely determine the signal, Shannon's statement notwithstanding. This sufficient condition can be weakened, as discussed at Sampling of non-baseband signals below. More recent statements of the theorem are sometimes careful to exclude the equality condition; that is, the condition is if x ( t ) contains no frequencies higher than or equal to B ; this condition is equivalent to Shannon's except when the function includes a steady sinusoidal component at exactly frequency B . The theorem assumes an idealization of any real-world situation, as it only applies to signals that are sampled for infinite time; any time-limited x ( t ) cannot beperfectly bandlimited . Perfect reconstruction is mathematically possible for the idealized model but only an approximation for real-worldsignals and sampling techniques, albeit in practice often a very good one. The theorem also leads to a formulafor reconstruction of the original signal. The constructive proof of the theorem leads to an understanding of the aliasing that can occur when a sampling system does not satisfy the conditions of the theorem. The sampling theorem provides a sufficient condition, but not a necessary one, for perfect reconstruction. The field of compressed sensing provides a stricter sampling condition when theunderlying signal is known to be sparse. Compressed sensing specifically yields a sub-Nyquist sampling criterion.