The Summation Formulae of Euler–Maclaurin, Abel–Plana, Poisson, and their Interconnections with the Approximate Sampling Formula of Signal Analysis (original) (raw)

The sampling theorem, Poisson's summation formula, general Parseval formula, reproducing kernel formula and the Paley–Wiener theorem for bandlimited signals – their interconnections

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The Euler-MacLaurin summation formula, the sampling theorem, and approximate integration over the real axis

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Shannon’s Sampling Theorem for Bandlimited Signals and Their Hilbert Transform, Boas-Type Formulae for Higher Order Derivatives—The Aliasing Error Involved by Their Extensions from Bandlimited to Non-Bandlimited Signals

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Irregular sampling theorems and series expansions of band-limited functions

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The Exponential Sampling Theorem of Signal Analysis and the Reproducing Kernel Formula in the Mellin Transform Setting

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A generalization of the exponential sampling series and its approximation properties

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Approximation of bandlimited functions

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Approximation error of the Whittaker cardinal series in terms of an averaged modulus of smoothness covering discontinuous signals

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A Whittaker-Shannon-Kotel’nikov sampling theorem related to the Askey-Wilson functions

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Finite sampling approximations for non-band-limited signals

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