An Irregular Sampling Theorem for Functions Bandlimited in a Generalized Sense (1987)

Previous article Next article An Irregular Sampling Theorem for Functions Bandlimited in a Generalized SenseKristian SeipKristian Seiphttps://doi.org/10.1137/0147073PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAboutAbstractIt is shown that a well-known irregular sampling formula for ordinary bandlimited functions is also valid for functions bandlimited in a generalized sense, except for some necessary modifications.[1] J. R. Higgins, A sampling theorem for irregularly spaced sample points, IEEE Trans. Information Theory, IT-22 (1976), 621–622 10.1109/TIT.1976.1055596 54:4805 0342.94007 CrossrefISIGoogle Scholar[2] Lars Hörmander, Linear partial differential operators, Springer-Verlag, Berlin, 1964 CrossrefGoogle Scholar[3] Alan J. Lee, Characterization of bandlimited functions and processes, Information and Control, 31 (1976), 258–271 53:9366 0332.60022 CrossrefGoogle Scholar[4] Norman Levinson, Gap and Density Theorems, American Mathematical Society Colloquium Publications, v. 26, American Mathematical Society, New York, 1940viii+246 2,180d 0026.21601 CrossrefGoogle Scholar[5] Robert M. Young, An introduction to nonharmonic Fourier series, Pure and Applied Mathematics, Vol. 93, Academic Press Inc. [Harcourt Brace Jovanovich Publishers], New York, 1980x+246 81m:42027 0493.42001 Google ScholarKeywordsgeneralized bandlimited functionsirregular sampling Previous article Next article FiguresRelatedReferencesCited byDetails A sampling theorem by perturbing the zeros of a sine-type function14 January 2020 | Applicable Analysis, Vol. 100, No. 14 Cross Ref Sampling and Average Sampling in Quasi Shift-Invariant Spaces6 April 2020 | Numerical Functional Analysis and Optimization, Vol. 41, No. 10 Cross Ref Arbitrarily slow convergence of reconstruction from nonuniform sampleSignal Processing, Vol. 171 Cross Ref Multichannel interpolation of nonuniform samples with application to image recoveryJournal of Computational and Applied Mathematics, Vol. 367 Cross Ref On Send-on-Delta sampling of bandlimited functions Cross Ref Classical Sampling Series of Band Limited Functions: Oversampling and Non-existence1 January 2016 | Sampling Theory, Signal Processing, and Data Analysis, Vol. 15, No. 1 Cross Ref Cardinal sine series: Oversampling and non-existence Cross Ref Sampling Formulas for Groups of Operators in Banach Spaces1 January 2015 | Sampling Theory in Signal and Image Processing, Vol. 14, No. 1 Cross Ref Cardinal Sine Series: Convergence and Uniqueness1 January 2014 | Sampling Theory, Signal Processing, and Data Analysis, Vol. 13, No. 1 Cross Ref Towards a general theory of reconstruction of bandlimited signals from sine wave crossingsSignal Processing, Vol. 92, No. 3 Cross Ref New Formulas for Irregular Sampling of Two-Bands SignalsJournal of Signal and Information Processing, Vol. 02, No. 04 Cross Ref Non-equidistant sampling for bounded bandlimited signalsSignal Processing, Vol. 90, No. 7 Cross Ref Convergence behavior of non-equidistant sampling seriesSignal Processing, Vol. 90, No. 1 Cross Ref About Bi-periodic Samplings1 September 2009 | Sampling Theory in Signal and Image Processing, Vol. 8, No. 3 Cross Ref Signal reconstruction by random sampling in chirp space12 August 2008 | Nonlinear Dynamics, Vol. 56, No. 3 Cross Ref The Ghost Sampling Sequence Method1 January 2009 | Sampling Theory in Signal and Image Processing, Vol. 8, No. 1 Cross Ref Nonuniform Sampling of Bandlimited FunctionsIEEE Transactions on Information Theory, Vol. 54, No. 8 Cross Ref A criterion for the uniform convergence of sinc-approximations on a segment6 August 2008 | Russian Mathematics, Vol. 52, No. 6 Cross Ref Estimates for the Lebesgue functions and the Nevai formula for the sinc-approximations of continuous functions on an intervalSiberian Mathematical Journal, Vol. 48, No. 5 Cross Ref Reconstruction of polyharmonic functions from samplesJournal of Approximation Theory, Vol. 148, No. 1 Cross Ref On Sharp Bounds for Remainders in Multidimensional Sampling Theorem1 September 2007 | Sampling Theory in Signal and Image Processing, Vol. 6, No. 3 Cross Ref Критерии поточечной и равномерной сходимости синк-приближений непрерывных функций на отрезкеМатематический сборник, Vol. 198, No. 10 Cross Ref General sampling theorem using contour integralJournal of Mathematical Analysis and Applications, Vol. 291, No. 1 Cross Ref Irregular Sampling of Generalized Harmonizable ProcessesStochastic Analysis and Applications, Vol. 22, No. 5 Cross Ref A Brief Walk Through Sampling Theory Cross Ref Nonuniform Sampling and Reconstruction in Shift-Invariant SpacesAkram Aldroubi and Karlheinz Gröchenig4 August 2006 | SIAM Review, Vol. 43, No. 4AbstractPDF (855 KB)An Introduction to Sampling Analysis Cross Ref Lagrange Interpolation and Sampling Theorems Cross Ref Sampling-50 years after ShannonProceedings of the IEEE, Vol. 88, No. 4 Cross Ref A Sampling Theorem with Nonuniform Complex NodesJournal of Approximation Theory, Vol. 90, No. 2 Cross Ref A New Interpretation of the Sampling Theorem and Its Extensions Cross Ref Statistical estimation of the bandwidth from irregularly spaced dataSignal Processing, Vol. 54, No. 1 Cross Ref Irregular sampling theorems and series expansions of band-limited functionsJournal of Mathematical Analysis and Applications, Vol. 167, No. 2 Cross Ref Iterative Reconstruction of Multivariate Band-Limited Functions from Irregular Sampling ValuesHans G. Feichtinger and Karlheinz Gröchenig1 August 2006 | SIAM Journal on Mathematical Analysis, Vol. 23, No. 1AbstractPDF (2128 KB)Irregular Sampling and Frames Cross Ref On Kramer's Sampling Theorem Associated with General Sturm-Liouville Problems and Lagrange InterpolationAhmed I. Zayed5 July 2006 | SIAM Journal on Applied Mathematics, Vol. 51, No. 2AbstractPDF (2321 KB)Sampling theorems and the contour integral methodApplicable Analysis, Vol. 41, No. 1-4 Cross Ref A note on sampling of bandlimited stochastic processesIEEE Transactions on Information Theory, Vol. 36, No. 5 Cross Ref On Lagrange Interpolation and Kramer-Type Sampling Theorems Associated with Sturm–Liouville ProblemsAhmed I. Zayed, Guido Hinsen, and Paul L. Butzer10 July 2006 | SIAM Journal on Applied Mathematics, Vol. 50, No. 3AbstractPDF (1589 KB)Reconstruction of bounded signals from pseudo-periodic, irregularly spaced samplesSignal Processing, Vol. 17, No. 1 Cross Ref A scheme of discretization and reconstruction of signals Cross Ref Volume 47, Issue 5| 1987SIAM Journal on Applied Mathematics History Submitted:09 July 1986Accepted:16 January 1987Published online:11 July 2006 InformationCopyright © 1987 Society for Industrial and Applied MathematicsKeywordsgeneralized bandlimited functionsirregular samplingMSC codes94A0541A05PDF Download Article & Publication DataArticle DOI:10.1137/0147073Article page range:pp. 1112-1116ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics