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

DOI10.3390/e14112192zbMath1314.94034OpenAlexW2062052611MaRDI QIDQ406211

Gerhard Schmeisser, Rudolf L. Stens, Paul L. Butzer

Publication date: 8 September 2014

Published in: Entropy (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3390/e14112192

zbMATH Keywords

Hilbert transformsBernstein's inequalityderivative-free error estimatesformulae with remaindersnon-bandlimited functionssampling formulaealiasing errordifferentiation formulae

Mathematics Subject Classification ID

Sampling theory in information and communication theory (94A20)

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Cites Work

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• Numerical differentiation inspired by a formula of R.P. Boas
• Heaviside's operational calculus and the attempts to rigorise it
• Norm inequalities for derivatives and differences
• On the error in reconstructing a non-bandlimited function by means of the bandpass sampling theorem
• A sampling theorem for duration-limited functions with error estimates
• Cardinal-Type Approximations of a Function and Its Derivatives

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