The Nyquist—Shannon sampling theorem is a theorem in the field of digital signal processing which serves as a fundamental bridge between continuous-time signals and discrete-time signals. It establishes a sufficient condition for a sample rate that permits a discrete sequence of samples to capture all the information from a continuous-time signal of finite bandwidth. 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. Intuitively we expect that when one reduces a continuous function to a discrete sequence and interpolates back to a continuous function, the fidelity of the result depends on the density or sample rate of the original samples. The sampling theorem introduces the concept of a sample rate that is sufficient for perfect fidelity for the class of functions that are band-limited to a given bandwidth, such that no actual information is lost in the sampling process.
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Category:Nyquist Shannon theorem
In communications, the Nyquist ISI criterion describes the conditions which, when satisfied by a communication channel including responses of transmit and receive filters , result in no intersymbol interference or ISI. It provides a method for constructing band-limited functions to overcome the effects of intersymbol interference. This causes intersymbol interference because the previously transmitted symbols affect the currently received symbol, thus reducing tolerance for noise. The Nyquist theorem relates this time-domain condition to an equivalent frequency-domain condition. The Nyquist criterion is closely related to the Nyquist—Shannon sampling theorem , with only a differing point of view. The Nyquist theorem says that this is equivalent to:.
Nyquist ISI criterion
Nyquist–Shannon sampling theorem