Generalized Kravchenko-Kotel'nikov sampling theorem for interpolation of signals with complex shape

Kravchenko, Vladislav V.; Kravchenko, O. V.; Сафин, А. Р.

doi:10.1109/msmw.2010.5546004

Cited by 5 publications

(18 citation statements)

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“…The application of a rectangular window can lead to its negative spectrum. Then, this phenom enon is absent as in the case of WF (31).…”

Section: The Gibbs Phenomenon and Kravchenko Weighting Functions Basementioning

confidence: 96%

“…We ask the following question: What PDF does the RQ (36) have? To answer this question, we use the property of the PDF of a sum of two RQs [30][31][32][33][34][35][36][37][38][39][40]. Let RQ X (Y) have PDF ( ).…”

Section: A the Probabilistic Properties Of Parent Atomic Functionmentioning

confidence: 99%

“…According to the definition [30][31][32][33][34][35][36][37][38][39][40] the ratio of third central moment m 3 to the cubed RMSD is called asymmetry A of RQ X. In our case A = 0.…”

Section: The Asymmetry Excess and Entropy Of A Random Quantity Hmentioning

confidence: 99%

“…≤ and ≤ Let us compare these results for the Gaussian It is known [30][31][32] that RQs are statis tically independent when joint density function p x of these quantities equals the product…”

Section: In Our Case the Entropy Ismentioning

confidence: 99%

“…The coefficients of series (65) are such that As moments, these coefficients are characteristics of a probability distribution they are called cumulants or semiinvariants [30][31][32]. Cumulants unambiguously determine RQs if series (65) converges for all ξ.…”

Section: E Cumulant Analysis Of the Kravchenko-rvachev Atomic Distrimentioning

confidence: 99%

See 4 more Smart Citations

Atomic, WA-systems, and R-functions applied in modern radio physics problems: Part I

Кравченко

Kravchenko

Пустовойт

et al. 2014

J. Commun. Technol. Electron.

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The main physical applications of atomic, WA systems, and R functions are presented. The Whittaker-Kotelnikov-Shannon sampling theorem is generalized on the basis of atomic functions. Applica tions of atomic functions in the theory of probability and random processes, interpolation of stationary ran dom processes with atomic functions, and a new class of probabilistic weighting functions used in digital sig nal and image processing are considered.

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“…The application of a rectangular window can lead to its negative spectrum. Then, this phenom enon is absent as in the case of WF (31).…”

Section: The Gibbs Phenomenon and Kravchenko Weighting Functions Basementioning

confidence: 96%

Section: A the Probabilistic Properties Of Parent Atomic Functionmentioning

confidence: 99%

“…According to the definition [30][31][32][33][34][35][36][37][38][39][40] the ratio of third central moment m 3 to the cubed RMSD is called asymmetry A of RQ X. In our case A = 0.…”

Section: The Asymmetry Excess and Entropy Of A Random Quantity Hmentioning

confidence: 99%

Section: In Our Case the Entropy Ismentioning

confidence: 99%

Section: E Cumulant Analysis Of the Kravchenko-rvachev Atomic Distrimentioning

confidence: 99%

See 3 more Smart Citations

Atomic, WA-systems, and R-functions applied in modern radio physics problems: Part I

Кравченко

Kravchenko

Пустовойт

et al. 2014

J. Commun. Technol. Electron.

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Representation of multidimensional periodic functions by a finite weighted sum of sampled values

Slichenko

2014

J. Commun. Technol. Electron.

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A closed form analytic representation of multidimensional periodic functions with a finite Fou rier spectrum is obtained as a modified interpolation series with a finite number of terms. The corresponding theorem is formulated, and the multidimensional periodic kernel of the expansion is analyzed. It is shown that such a representation makes it possible to calculate values of the derivatives of an arbitrary order of a peri odic function with a finite spectrum from the samples of this function.

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Loss of Charged Particles as a Criterion for the Formation of a Highly Conductive Channel for the Protection of Electronic Equipment

Yasechko¹,

Smyrnova²

2020

Prospects and Priorities of Research in Science and Technology

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Generalized Kravchenko-Kotel'nikov sampling theorem for interpolation of signals with complex shape

Cited by 5 publications

References 0 publications

Atomic, WA-systems, and R-functions applied in modern radio physics problems: Part I

Atomic, WA-systems, and R-functions applied in modern radio physics problems: Part I

Representation of multidimensional periodic functions by a finite weighted sum of sampled values

Loss of Charged Particles as a Criterion for the Formation of a Highly Conductive Channel for the Protection of Electronic Equipment

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