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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.
Between samples no measurement of the signal is made; the sampling theorem guarantees non-ambiguous representation and recovery of the signal only if it has no energy at frequency f s /2 or higher (one half the sampling frequency, known as the Nyquist frequency); higher frequencies will not be correctly represented or recovered and add aliasing ...
sampling theory may mean: Nyquist–Shannon sampling theorem, digital signal processing (DSP) Statistical sampling; Fourier sampling This page was last edited on ...
Sampling is usually carried out in two stages, discretization and quantization. Discretization means that the signal is divided into equal intervals of time, and each interval is represented by a single measurement of amplitude. Quantization means each amplitude measurement is approximated by a value from a finite set.
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 ...
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He is credited with the introduction of sampling theorem, which he had derived as early as 1940, [60] and which is concerned with representing a continuous-time signal from a (uniform) discrete set of samples. This theory was essential in enabling telecommunications to move from analog to digital transmissions systems in the 1960s and later.
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.