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- Title
On Sharp Bounds for Remainders in Multidimensional Sampling Theorem.
- Authors
Olenko, A. Ya.; Pogány, T. K.
- Abstract
Sharp upper bounds for interpolation remainders of the multidimensional Paley--Wiener class functions by finite regular Whittaker--Kotel'nikov-- Shannon sampling sum are obtained. The extremal functions are given for which the derived bounds are attained. Truncation error analysis and convergence rate is provided in weak Cramér class random fields. The historical background, the development, and extensive reference list are given concerning truncation error upper bounds for deterministic and random signal functions. Finally, new research directions are posed and discussed.
- Subjects
INTERPOLATION; ERROR analysis in mathematics; MATHEMATICAL functions; RANDOM fields; STOCHASTIC convergence
- Publication
Sampling Theory in Signal & Image Processing, 2007, Vol 6, Issue 3, p249
- ISSN
1530-6429
- Publication type
Academic Journal
- DOI
10.1007/bf03549476