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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.
Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, or the Smirnov transform) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given its cumulative distribution function.
Download as PDF; Printable version ... move to sidebar hide. sampling theory may mean: Nyquist–Shannon sampling theorem, digital signal processing (DSP) Statistical ...
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]
Papoulis's generalization of the sampling theorem [6] unified many variations of the Nyquist–Shannon sampling theorem into one theorem. [7] [8] The Papoulis–Gerchberg algorithm [9] [10] [11] is an iterative signal restoration algorithm that has found widespread use in signal and image processing. [12] [13]
The misconceived belief that the theorem applies to random sampling of any variable, rather than to the mean values (or sums) of iid random variables extracted from a population by repeated sampling. That is, the theorem assumes the random sampling produces a sampling distribution formed from different values of means (or sums) of such random ...
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.
According to the de Moivre–Laplace theorem, as n grows large, the shape of the discrete distribution converges to the continuous Gaussian curve of the normal distribution. In probability theory , the de Moivre–Laplace theorem , which is a special case of the central limit theorem , states that the normal distribution may be used as an ...