The Euler-MacLaurin summation formula, the sampling theorem, and approximate integration over the real axis
P.L. Butzer,R.L. Stens +1 more
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TLDR
In this article, the Euler-MacLaurin summation formula is used to deduce the Whittaker-Shannon sampling theorem for not necessarily band-limited functions, as well as to study numerical integration over the real axis.About:
This article is published in Linear Algebra and its Applications.The article was published on 1983-07-01 and is currently open access. It has received 29 citations till now. The article focuses on the topics: Borel summation & Poisson summation formula.read more
Citations
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Journal ArticleDOI
Five short stories about the cardinal series
TL;DR: In this article, the cardinal series and LCA groups were derived from the L 2 and L p theory and extended to higher dimensions, and the cardinal and allied series were derived.
Book ChapterDOI
An Introduction to Sampling Analysis
TL;DR: The Lagrangian interpolation formula is used in this paper to determine the polynomial P n (t v ) of degree n which possesses the property that it is unique and can be determined by its values at an arbitrary given set of n + 1 distinct points t 0, t 1, etc.
Book
Handbook of Fourier Analysis & Its Applications
TL;DR: In this article, Fourier Transforms in Probability, Random Variables and Stochastic Processes are used for time-frequency representation of signal and image synthesis in the context of Fourier analysis.
Journal ArticleDOI
The Summation Formulae of Euler–Maclaurin, Abel–Plana, Poisson, and their Interconnections with the Approximate Sampling Formula of Signal Analysis
TL;DR: In this paper, it was shown that these four fundamental propositions are all equivalent, in the sense that each is a corollary of any of the others, and the first three summation formulae of Euler-Maclaurin (EMSF) and Abel-Plana (APSF) of numerical analysis, the PSF of Fourier analysis and the approximate sampling formula (ASF) of signal analysis, were all equivalent.
References
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Journal ArticleDOI
Methods of Numerical Integration.
Book
An introduction to nonharmonic Fourier series
TL;DR: Bases in Banach Spaces - Schauder Bases Schauder's Basis for C[a,b] Orthonormal Bases in Hilbert Space The Reproducing Kernel Complete Sequences The Coefficient Functionals Duality Riesz Bases The Stability of Bases of Complex Exponentials as mentioned in this paper.