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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.
Download as PDF; Printable version ... move to sidebar hide. sampling theory may mean: Nyquist–Shannon sampling theorem, digital signal processing (DSP) Statistical ...
The following theorem is central to statistical learning of binary classification tasks. Theorem (Vapnik and Chervonenkis, 1968) [8] Under certain consistency conditions, a universally measurable class of sets is a uniform Glivenko-Cantelli class if and only if it is a Vapnik–Chervonenkis class.
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.
In probability theory, the optional stopping theorem (or sometimes Doob's optional sampling theorem, for American probabilist Joseph Doob) says that, under certain conditions, the expected value of a martingale at a stopping time is equal to its initial expected value. Since martingales can be used to model the wealth of a gambler participating ...
A visual representation of the sampling process. In statistics, quality assurance, and survey methodology, sampling is the selection of a subset or a statistical sample (termed sample for short) of individuals from within a statistical population to estimate characteristics of the whole population. The subset is meant to reflect the whole ...
An interactive proof session in CoqIDE, showing the proof script on the left and the proof state on the right. Coq is an interactive theorem prover first released in 1989. It allows for expressing mathematical assertions, mechanically checks proofs of these assertions, helps find formal proofs, and extracts a certified program from the constructive proof of its formal specification.
The graph of the Dirac comb function is an infinite series of Dirac delta functions spaced at intervals of T. In mathematics, a Dirac comb (also known as sha function, impulse train or sampling function) is a periodic function with the formula := = for some given period . [1]