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  2. Nyquist–Shannon sampling theorem - Wikipedia

    en.wikipedia.org/wiki/Nyquist–Shannon_sampling...

    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.

  3. Whittaker–Shannon interpolation formula - Wikipedia

    en.wikipedia.org/wiki/Whittaker–Shannon...

    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.

  4. Nyquist rate - Wikipedia

    en.wikipedia.org/wiki/Nyquist_rate

    And it turns out that one can directly achieve the same result by sampling the bandpass function at a sub-Nyquist sample-rate that is the smallest integer-sub-multiple of frequency A that meets the baseband Nyquist criterion: f s > 2B. For a more general discussion, see bandpass sampling.

  5. Central limit theorem - Wikipedia

    en.wikipedia.org/wiki/Central_limit_theorem

    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 ...

  6. Poisson summation formula - Wikipedia

    en.wikipedia.org/wiki/Poisson_summation_formula

    The Poisson summation formula may be used to derive Landau's asymptotic formula for the number of lattice points inside a large Euclidean sphere. It can also be used to show that if an integrable function, s {\displaystyle s} and S {\displaystyle S} both have compact support then s = 0. {\displaystyle s=0.} [ 2 ]

  7. Hoeffding's inequality - Wikipedia

    en.wikipedia.org/wiki/Hoeffding's_inequality

    The proof of Hoeffding's inequality follows similarly to concentration inequalities like Chernoff bounds. [9] The main difference is the use of Hoeffding's Lemma : Suppose X is a real random variable such that X ∈ [ a , b ] {\displaystyle X\in \left[a,b\right]} almost surely .

  8. Inverse transform sampling - Wikipedia

    en.wikipedia.org/wiki/Inverse_transform_sampling

    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.

  9. Noisy-channel coding theorem - Wikipedia

    en.wikipedia.org/wiki/Noisy-channel_coding_theorem

    In information theory, the noisy-channel coding theorem (sometimes Shannon's theorem or Shannon's limit), establishes that for any given degree of noise contamination of a communication channel, it is possible (in theory) to communicate discrete data (digital information) nearly error-free up to a computable maximum rate through the channel.