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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 ...
Statistical proof is the rational demonstration of degree of certainty for a proposition, hypothesis or theory that is used to convince others subsequent to a statistical test of the supporting evidence and the types of inferences that can be drawn from the test scores.
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.
Theorem 2 : A Tutte matrix determinant is not a 0-polynomial if and only if there exists a perfect matching. A subset D of E is called a matching if each vertex in V is incident with at most one edge in D. A matching is perfect if each vertex in V has exactly one edge that is incident to it in D. Create a Tutte matrix A in the following way:
Through a series of rigorous arguments employing deductive reasoning, a statement that is proven to be true becomes a theorem. A specialized theorem that is mainly used to prove another theorem is called a lemma. A proven instance that forms part of a more general finding is termed a corollary. [98]
A general proof of this was given by Halmos and Savage [6] and the theorem is sometimes referred to as the Halmos–Savage factorization theorem. [7] The proofs below handle special cases, but an alternative general proof along the same lines can be given. [ 8 ]
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 ...