Reconstruction of signals inLp(ℝ)-space by generalized sampling series based on linear combinations ofB-splines†

DOI10.1080/10652460701511285zbMath1146.41002OpenAlexW2007012640MaRDI QIDQ5458007

Rudolf L. Stens, Paul L. Butzer

Publication date: 10 April 2008

Published in: Integral Transforms and Special Functions (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/10652460701511285

zbMATH Keywords

order of approximationB-splinesgeneralized sampling series

Mathematics Subject Classification ID

Signal theory (characterization, reconstruction, filtering, etc.) (94A12) Rate of convergence, degree of approximation (41A25) Approximation by operators (in particular, by integral operators) (41A35) Spline approximation (41A15) Approximation by other special function classes (41A30) Sampling theory in information and communication theory (94A20)

Related Items (11)

Uniform approximation by multivariate quasi-projection operators ⋮ Approximation properties of the sampling Kantorovich operators: regularization, saturation, inverse results and Favard classes in \(L^p\)-spaces ⋮ Some applications of modular convergence in vector lattice setting ⋮ Modular filter convergence theorems for abstract sampling type operators ⋮ Approximation by multivariate quasi-projection operators and Fourier multipliers ⋮ Band-limited scaling and wavelet expansions ⋮ Rates of approximation for general sampling-type operators in the setting of filter convergence ⋮ Approximation of differentiable and not differentiable signals by the first derivative of sampling Kantorovich operators ⋮ On Window Methods in Generalized Shannon Sampling Operators ⋮ Quantitative estimates for Durrmeyer-sampling series in Orlicz spaces ⋮ Multivariate sampling-type approximation

Cites Work

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• Approximation error of the Whittaker cardinal series in terms of an averaged modulus of smoothness covering discontinuous signals
• Optimal kernels for a general sampling theorem
• Spline Functions
• Prediction of Non-Bandlimited Signals from Past Samples in Terms of Splines of Low Degree
• Central factorial numbers; their main properties and some applications.
• Error estimates for sampling sums based on convolution integrals
• The Shannon Sampling Series and the Reconstruction of Signals in Terms of Linear, Quadratic and Cubic Splines
• Linear Combinations of Bernstein Polynomials

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