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THEOREM

Nyquist theorem; Shannon sampling theorem; Nyquist sampling theorem; Nyquist's theorem; Shannon-Nyquist sampling theorem; Nyquist-Shannon Sampling Theorem; Nyqvist-Shannon sampling theorem; Sampling theorem; Nyquist Sampling Theorem; Nyquist-Shannon sampling theorem; Nyquist–Shannon theorem; Nyquist–Shannon Theorem; Nyquist Theorem; Shannon-Nyquist theorem; Nyquist sampling; Nyquist's law; Nyquist law; Coherent sampling; Nyqvist limit; Raabe condition; Nyquist-Shannon Theorem; Nyquist-Shannon theorem; Nyquist noise theorem; Shannon–Nyquist theorem; Kotelnikov-Shannon theorem; Kotelnikov–Shannon theorem; Nyquist-Shannon; Kotelnikov theorem; Nyquist's sampling theorem; Sampling Theorem; Nyquist Shannon theorem; Nyquist–Shannon–Kotelnikov sampling theorem; Whittaker–Shannon–Kotelnikov sampling theorem; Whittaker–Nyquist–Kotelnikov–Shannon sampling theorem; Nyquist-Shannon-Kotelnikov sampling theorem; Whittaker-Shannon-Kotelnikov sampling theorem; Whittaker-Nyquist-Kotelnikov-Shannon sampling theorem; Cardinal theorem of interpolation; WKS sampling theorem; Whittaker–Kotelnikow–Shannon sampling theorem; Whittaker-Kotelnikow-Shannon sampling theorem; Nyquist–Shannon–Kotelnikov; Whittaker–Shannon–Kotelnikov; Whittaker–Nyquist–Kotelnikov–Shannon; Nyquist-Shannon-Kotelnikov; Whittaker-Shannon-Kotelnikov; Whittaker-Nyquist-Kotelnikov-Shannon; Whittaker–Shannon sampling theorem; Whittaker–Nyquist–Shannon sampling theorem; Whittaker-Nyquist-Shannon sampling theorem; Whittaker-Shannon sampling theorem

Nyquist Theorem

<communications> A theorem stating that when an analogue waveform is digitised, only the frequencies in the waveform below half the sampling frequency will be recorded. In order to reconstruct (interpolate) a signal from a sequence of samples, sufficient samples must be recorded to capture the peaks and troughs of the original waveform. If a waveform is sampled at less than twice its frequency the reconstructed waveform will effectively contribute only noise. This phenomenon is called "aliasing" (the high frequencies are "under an alias"). This is why the best digital audio is sampled at 44,000 Hz - twice the average upper limit of human hearing. The Nyquist Theorem is not specific to digitised signals (represented by discrete amplitude levels) but applies to any sampled signal (represented by discrete time values), not just sound. {Nyquist (http://geocities.com/bioelectrochemistry/nyquist.htm)} (the man, somewhat inaccurate). (2003-10-21)

Nyquist–Shannon sampling theorem

The Nyquist–Shannon 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. 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.

https://en.wikipedia.org/wiki/Nyquist–Shannon_sampling_theorem

Nyquist frequency

IN SIGNAL PROCESSING, THE FREQUENCY WHOSE CYCLE-LENGTH IS TWICE THE INTERVAL BETWEEN SAMPLES

Nyquist Frequency; Folding frequency; Nyquist limit

<DSP> The highest frequency that can be represented in a digital signal of a specified sampling frequency. It is equal to one-half of the sampling rate. See Nyquist Theorem. (2001-06-06)

ويكيبيديا

Nyquist–Shannon sampling theorem

The Nyquist–Shannon 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. 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. It expresses the sufficient sample rate in terms of the bandwidth for the class of functions. The theorem also leads to a formula for perfectly reconstructing the original continuous-time function from the samples.

Perfect reconstruction may still be possible when the sample-rate criterion is not satisfied, provided other constraints on the signal are known (see § Sampling of non-baseband signals below and compressed sensing). In some cases (when the sample-rate criterion is not satisfied), utilizing additional constraints allows for approximate reconstructions. The fidelity of these reconstructions can be verified and quantified utilizing Bochner's theorem.

The name Nyquist–Shannon sampling theorem honours Harry Nyquist and Claude Shannon, but the theorem was also previously discovered by E. T. Whittaker (published in 1915), and Shannon cited Whittaker's paper in his work. The theorem is thus also known by the names Whittaker–Shannon sampling theorem, Whittaker–Shannon, and Whittaker–Nyquist–Shannon, and may also be referred to as the cardinal theorem of interpolation.

https://en.wikipedia.org/wiki/Nyquist–Shannon sampling theorem