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- Nyquist–Shannon_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. And it expresses the sample-rate in terms of the function's bandwidth. Thus no actual "information" is lost during the sampling process. 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.".
- Nyquist–Shannon_sampling_theorem thumbnail Bandlimited.svg?width=300.
- Nyquist–Shannon_sampling_theorem wikiPageID "37864".
- Nyquist–Shannon_sampling_theorem wikiPageRevisionID "605293132".
- Nyquist–Shannon_sampling_theorem subject Category:Articles_containing_proofs.
- Nyquist–Shannon_sampling_theorem subject Category:Digital_signal_processing.
- Nyquist–Shannon_sampling_theorem subject Category:Information_theory.
- Nyquist–Shannon_sampling_theorem subject Category:Mathematical_theorems_in_theoretical_computer_science.
- Nyquist–Shannon_sampling_theorem subject Category:Theorems_in_Fourier_analysis.
- Nyquist–Shannon_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–Shannon_sampling_theorem label "Bemonsteringstheorema van Nyquist-Shannon".
- Nyquist–Shannon_sampling_theorem label "Nyquist-Shannon-Abtasttheorem".
- Nyquist–Shannon_sampling_theorem label "Nyquist–Shannon sampling theorem".
- Nyquist–Shannon_sampling_theorem label "Teorema de Nyquist".
- Nyquist–Shannon_sampling_theorem label "Teorema de muestreo de Nyquist-Shannon".
- Nyquist–Shannon_sampling_theorem label "Teorema del campionamento di Nyquist-Shannon".
- Nyquist–Shannon_sampling_theorem label "Théorème d'échantillonnage de Nyquist-Shannon".
- Nyquist–Shannon_sampling_theorem label "Twierdzenie Kotielnikowa-Shannona".
- Nyquist–Shannon_sampling_theorem label "Теорема Котельникова".
- Nyquist–Shannon_sampling_theorem label "مبرهنة الاستعيان".
- Nyquist–Shannon_sampling_theorem label "標本化定理".
- Nyquist–Shannon_sampling_theorem label "采样定理".
- Nyquist–Shannon_sampling_theorem sameAs Nyquist%E2%80%93Shannon_sampling_theorem.
- Nyquist–Shannon_sampling_theorem sameAs Shannonův_teorém.
- Nyquist–Shannon_sampling_theorem sameAs Nyquist-Shannon-Abtasttheorem.
- Nyquist–Shannon_sampling_theorem sameAs Teorema_de_muestreo_de_Nyquist-Shannon.
- Nyquist–Shannon_sampling_theorem sameAs Théorème_d'échantillonnage_de_Nyquist-Shannon.
- Nyquist–Shannon_sampling_theorem sameAs Teorema_del_campionamento_di_Nyquist-Shannon.
- Nyquist–Shannon_sampling_theorem sameAs 標本化定理.
- Nyquist–Shannon_sampling_theorem sameAs 표본화_정리.
- Nyquist–Shannon_sampling_theorem sameAs Bemonsteringstheorema_van_Nyquist-Shannon.
- Nyquist–Shannon_sampling_theorem sameAs Twierdzenie_Kotielnikowa-Shannona.
- Nyquist–Shannon_sampling_theorem sameAs Teorema_de_Nyquist.
- Nyquist–Shannon_sampling_theorem sameAs Q679800.
- Nyquist–Shannon_sampling_theorem sameAs Q679800.
- Nyquist–Shannon_sampling_theorem wasDerivedFrom Nyquist–Shannon_sampling_theorem?oldid=605293132.
- Nyquist–Shannon_sampling_theorem depiction Bandlimited.svg.
