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• Nyquist%E2%80%93Shannon_sampling_theorem abstract "In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous signals (analog domain) and discrete signals (digital domain). Strictly speaking, it only applies to a class of mathematical functions whose Fourier transforms are zero outside of a finite region of frequencies (see Fig 1). The analytical extension to actual signals, which can only approximate that condition, is provided by the discrete-time Fourier transform, a version of the Poisson summation formula. Intuitively we expect that when one reduces a continuous function to a discrete sequence (called samples) 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 bandlimited functions; no actual "information" is lost during the sampling process. It expresses the sample-rate in terms of the function's bandwidth. The theorem also leads to a formula for the mathematically ideal interpolation algorithm.The theorem does not preclude the possibility of perfect reconstruction under special circumstances that do not satisfy the sample-rate criterion. (See Sampling of non-baseband signals below, and compressed sensing.)The name Nyquist–Shannon sampling theorem honors Harry Nyquist and Claude Shannon. The theorem was also discovered independently by E. T. Whittaker, by Vladimir Kotelnikov, and by others. So it is also known by the names Nyquist–Shannon–Kotelnikov, Whittaker–Shannon–Kotelnikov, Whittaker–Nyquist–Kotelnikov–Shannon, and cardinal theorem of interpolation.".
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• Nyquist%E2%80%93Shannon_sampling_theorem wikiPageExternalLink pg=717.
• Nyquist%E2%80%93Shannon_sampling_theorem wikiPageExternalLink unser0001.html.
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• Nyquist%E2%80%93Shannon_sampling_theorem wikiPageExternalLink 1993_AdvancedTopicsOnShannon.pdf.
• Nyquist%E2%80%93Shannon_sampling_theorem wikiPageExternalLink 1999_IntroductionToShannonSamplingAndInterpolationTheory.pdf.
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• Nyquist%E2%80%93Shannon_sampling_theorem wikiPageExternalLink Sampling_Theory.pdf.
• Nyquist%E2%80%93Shannon_sampling_theorem wikiPageExternalLink sampling_theorem.
• Nyquist%E2%80%93Shannon_sampling_theorem wikiPageExternalLink G99_e.html.
• Nyquist%E2%80%93Shannon_sampling_theorem wikiPageExternalLink nyquist.pdf.
• Nyquist%E2%80%93Shannon_sampling_theorem wikiPageExternalLink shannonpaper.pdf.
• Nyquist%E2%80%93Shannon_sampling_theorem wikiPageExternalLink www.stsip.org.
• Nyquist%E2%80%93Shannon_sampling_theorem wikiPageExternalLink simusoft_nykvist.html.
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• Nyquist%E2%80%93Shannon_sampling_theorem hasPhotoCollection Nyquist–Shannon_sampling_theorem.
• Nyquist%E2%80%93Shannon_sampling_theorem subject Category:Articles_containing_proofs.
• Nyquist%E2%80%93Shannon_sampling_theorem subject Category:Claude_Shannon.
• Nyquist%E2%80%93Shannon_sampling_theorem subject Category:Digital_signal_processing.
• Nyquist%E2%80%93Shannon_sampling_theorem subject Category:Information_theory.
• Nyquist%E2%80%93Shannon_sampling_theorem subject Category:Mathematical_theorems_in_theoretical_computer_science.
• Nyquist%E2%80%93Shannon_sampling_theorem subject Category:Telecommunication_theory.
• Nyquist%E2%80%93Shannon_sampling_theorem subject Category:Theorems_in_Fourier_analysis.
• Nyquist%E2%80%93Shannon_sampling_theorem type Abstraction100002137.
• Nyquist%E2%80%93Shannon_sampling_theorem type Communication100033020.
• Nyquist%E2%80%93Shannon_sampling_theorem type MathematicalTheoremsInTheoreticalComputerScience.
• Nyquist%E2%80%93Shannon_sampling_theorem type Message106598915.
• Nyquist%E2%80%93Shannon_sampling_theorem type Proposition106750804.
• Nyquist%E2%80%93Shannon_sampling_theorem type Statement106722453.
• Nyquist%E2%80%93Shannon_sampling_theorem type Theorem106752293.
• Nyquist%E2%80%93Shannon_sampling_theorem type TheoremsInFourierAnalysis.
• Nyquist%E2%80%93Shannon_sampling_theorem comment "In the field of digital signal processing, the sampling theorem is a fundamental bridge between continuous signals (analog domain) and discrete signals (digital domain). Strictly speaking, it only applies to a class of mathematical functions whose Fourier transforms are zero outside of a finite region of frequencies (see Fig 1).".
• Nyquist%E2%80%93Shannon_sampling_theorem label "Bemonsteringstheorema van Nyquist-Shannon".
• Nyquist%E2%80%93Shannon_sampling_theorem label "Nyquist-Shannon-Abtasttheorem".
• Nyquist%E2%80%93Shannon_sampling_theorem label "Nyquist–Shannon sampling theorem".
• Nyquist%E2%80%93Shannon_sampling_theorem label "Shannonův teorém".
• Nyquist%E2%80%93Shannon_sampling_theorem label "Teorema de Nyquist".
• Nyquist%E2%80%93Shannon_sampling_theorem label "Teorema de mostreig de Nyquist-Shannon".
• Nyquist%E2%80%93Shannon_sampling_theorem label "Teorema de muestreo de Nyquist-Shannon".
• Nyquist%E2%80%93Shannon_sampling_theorem label "Teorema del campionamento di Nyquist-Shannon".
• Nyquist%E2%80%93Shannon_sampling_theorem label "Théorème d'échantillonnage de Nyquist-Shannon".
• Nyquist%E2%80%93Shannon_sampling_theorem label "Twierdzenie Kotielnikowa-Shannona".
• Nyquist%E2%80%93Shannon_sampling_theorem label "Теорема Котельникова".
• Nyquist%E2%80%93Shannon_sampling_theorem label "標本化定理".
• Nyquist%E2%80%93Shannon_sampling_theorem label "표본화 정리".
• Nyquist%E2%80%93Shannon_sampling_theorem sameAs m.09fvh.
• Nyquist%E2%80%93Shannon_sampling_theorem sameAs Nyquist–Shannon_sampling_theorem.
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• Nyquist%E2%80%93Shannon_sampling_theorem isPrimaryTopicOf Nyquist–Shannon_sampling_theorem.