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The Nyquist–Shannon sampling theorem is an essential principle for digital signal processing linking the frequency range of a signal and the sample rate required to avoid a type of distortion called aliasing. The theorem states that the sample rate must be at least twice the bandwidth of the signal to avoid aliasing.
Nonuniform sampling is based on Lagrange interpolation and the relationship between itself and the (uniform) sampling theorem. Nonuniform sampling is a generalisation of the Whittaker–Shannon–Kotelnikov (WSK) sampling theorem. The sampling theory of Shannon can be generalized for the case of nonuniform samples, that is, samples not taken ...
The theorem of Petersen and Middleton can be used to identify the optimal lattice for sampling fields that are wavenumber-limited to a given set . For example, it can be shown that the lattice in ℜ 2 {\displaystyle \Re ^{2}} with minimum spatial density of points that admits perfect reconstructions of fields wavenumber-limited to a circular ...
The principle of sampling was developed during the 1930s in Bell Laboratories by Nyquist, after whom the sampling theorem is named. The first sampling oscilloscope was, however, developed in the late 1950s at the Atomic Energy Research Establishment at Harwell in England by G.B.B. Chaplin, A.R. Owens and A.J. Cole.
An analog-to-digital converter (ADC) can be modeled as two processes: sampling and quantization. Sampling converts a time-varying voltage signal into a discrete-time signal, a sequence of real numbers. Quantization replaces each real number with an approximation from a finite set of discrete values.
An early breakthrough in signal processing was the Nyquist–Shannon sampling theorem. It states that if a real signal's highest frequency is less than half of the sampling rate, then the signal can be reconstructed perfectly by means of sinc interpolation. The main idea is that with prior knowledge about constraints on the signal's frequencies ...
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The Whittaker–Shannon interpolation formula or sinc interpolation is a method to construct a continuous-time bandlimited function from a sequence of real numbers. The formula dates back to the works of E. Borel in 1898, and E. T. Whittaker in 1915, and was cited from works of J. M. Whittaker in 1935, and in the formulation of the Nyquist–Shannon sampling theorem by Claude Shannon in 1949.