Nyquist–Shannon sampling theorem

Sufficiency theorem for reconstructing signals from samples

The Nyquist–Shannon sampling theorem, or the sampling theorem, is a theorem in the field of signal processing which serves as a fundamental bridge between continuous-time signals and discrete-time signals. In the case of uniformly spaced (periodic) sampling, it establishes a sufficient condition on the sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth, such that the original signal can be reconstructed exactly from those samples. Strictly speaking, the theorem only applies to a class of mathematical functions having a Fourier transform that is zero outside of a finite region of frequencies.

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