Limits of calculating the finite Hilbert transform from discrete samples

DOI10.1016/j.acha.2017.03.002zbMath1402.44003OpenAlexW2598720066MaRDI QIDQ1990968

Volker Pohl, Holger Boche

Publication date: 29 October 2018

Published in: Applied and Computational Harmonic Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.acha.2017.03.002

zbMATH Keywords

samplingHilbert transformapproximationstrong divergence

Mathematics Subject Classification ID

Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane (30E20) Special integral transforms (Legendre, Hilbert, etc.) (44A15) Numerical methods for integral transforms (65R10) Abstract approximation theory (approximation in normed linear spaces and other abstract spaces) (41A65)

Related Items (1)

Investigations on the approximability and computability of the Hilbert transform with applications

Cites Work

• Strong divergence for system approximations
• Approximating the finite Hilbert transform via a companion of Ostrowski's inequality for function of bounded variation and applications
• A method to evaluate the Hilbert transform on (\(0, +\infty \))
• Advanced topics in system and signal theory. A mathematical approach
• On the convergence of spline product quadratures for Cauchy principal value integrals
• Uniform approximations to finite Hilbert transform and its derivative.
• Numerical evaluation of Hilbert transforms for oscillatory functions: A convergence accelerator approach
• Strong divergence of reconstruction procedures for the Paley-Wiener space \(\mathcal{PW}_\pi^1\) and the Hardy space \(\mathcal{H}^1\)
• System Approximations and Generalized Measurements in Modern Sampling Theory
• Computing the Hilbert transform and its inverse
• Causality and dispersion relations for fixed momentum transfer
• On the Calculation of the Hilbert Transform From Interpolated Data
• Computing the Hilbert Transform on the Real Line
• An Automatic Quadrature for Cauchy Principal Value Integrals
• Applications of Hilbert Transform Theory to Numerical Quadrature
• On the strong divergence of Hilbert transform approximations and a problem of Ul'yanov
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