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Sampling Theorem for the Fourier Transform of a Distribution with Bounded Support

1968; Society for Industrial and Applied Mathematics; Volume: 16; Issue: 3 Linguagem: Inglês

10.1137/0116051

1095-712X

L. L. Campbell,

Stochastic processes and financial applications

Previous article Next article Sampling Theorem for the Fourier Transform of a Distribution with Bounded SupportL. L. CampbellL. L. Campbellhttps://doi.org/10.1137/0116051PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] E. T. Whittaker, On the functions which are represented by the expansions of interpolation theory, Proc. Roy. Soc. Edinburgh, 35 (1915), 181–194 CrossrefGoogle Scholar[2] R. W. Hamming, Numerical methods for scientists and engineers, International Series in Pure and Applied Mathematics, McGraw-Hill Book Co., Inc., New York, 1962xvii+411 MR0137279 0952.65500 Google Scholar[3] Moshe Zakai, Band-limited functions and the sampling theorem, Information and Control, 8 (1965), 143–158 10.1016/S0019-9958(65)90038-0 MR0174403 0127.10806 CrossrefGoogle Scholar[4] A. H. Zemanian, Distribution theory and transform analysis. An introduction to generalized functions, with applications, McGraw-Hill Book Co., New York, 1965xviii+371 MR0177293 0127.07201 Google Scholar[5] Hans Bremermann, Distributions, complex variables, and Fourier transforms, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1965xii+186 MR0208364 0151.18102 Google Scholar[6] H. D. Helms and , J. B. Thomas, Truncation error of sampling-theorem expansions, Proc. IRE, 50 (1962), 179–184 MR0148199 CrossrefISIGoogle Scholar[7] K. Yao and , J. B. Thomas, On truncation error bounds for sampling representations of band-limited signals, IEEE Trans. Aerospace and Electronic Systems, AES-2 (1966), 640–647 CrossrefISIGoogle Scholar[8] B. S. Tsybakov and , V. P. Iakovlev, On the accuracy of restoring a function with a finite number of terms of a Kotelnikov series, Radio Engrg. and Electronics, 4 (1959), 274–275 Google Scholar[9] D. Jagerman, Bounds for truncation error of the sampling expansion, SIAM J. Appl. Math., 14 (1966), 714–723 10.1137/0114060 MR0213816 0221.65200 LinkISIGoogle Scholar[10] E. W. Cheney, Introduction to approximation theory, McGraw-Hill Book Co., New York, 1966xii+259 MR0222517 0161.25202 Google Scholar[11] A. V. Balakrishnan, A note on the sampling principle for continuous signals, IRE Trans. Information Theory, IT-3 (1957), 143–146 10.1109/TIT.1957.1057404 CrossrefISIGoogle Scholar[12] M. J. Lighthill, Introduction to Fourier analysis and generalised functions, Cambridge Monographs on Mechanics and Applied Mathematics, Cambridge University Press, New York, 1958viii+79 MR0092119 0078.11203 CrossrefGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Uniform and non-uniform sampling of bandlimited functions at minimal density with a few additional samples28 October 2022 | Sampling Theory, Signal Processing, and Data Analysis, Vol. 21, No. 1 Cross Ref Bernstein Inequality in $$L^p$$ on the Line with Power Weight for $$p>0$$24 February 2022 | Mathematical Notes, Vol. 111, No. 1-2 Cross Ref О неравенстве Бернштейна в $L^p$ на оси со степенным весом при $p>0$31 January 2022 | Математические заметки, Vol. 111, No. 2 Cross Ref On the Reversibility of Discretization17 April 2020 | Mathematics, Vol. 8, No. 4 Cross Ref On Inverses of the Dirac Comb6 December 2019 | Mathematics, Vol. 7, No. 12 Cross Ref Generalized Poisson Summation Formulas for Continuous Functions of Polynomial Growth24 May 2016 | Journal of Fourier Analysis and Applications, Vol. 23, No. 2 Cross Ref Influence of Unknown Exterior Samples on Interpolated Values for Band-Limited ImagesLoïc Simon and Jean-Michel Morel4 February 2016 | SIAM Journal on Imaging Sciences, Vol. 9, No. 1AbstractPDF (5559 KB)Boas’ Formula and Sampling Theorem26 January 2015 | Axioms, Vol. 4, No. 1 Cross Ref System Approximations and Generalized Measurements in Modern Sampling Theory Cross Ref SAMPLING EXPANSION OF BANDLIMITED FUNCTIONS OF POLYNOMIAL GROWTH ON THE REAL LINECommunications of the Korean Mathematical Society, Vol. 29, No. 2 Cross Ref Uniqueness and reconstruction theorems for pseudodifferential operators with a bandlimited Kohn-Nirenberg symbol10 March 2013 | Advances in Computational Mathematics, Vol. 40, No. 1 Cross Ref Upper bounds for Fourier transforms of exponential functionsComplex Variables and Elliptic Equations, Vol. 57, No. 10 Cross Ref Synchrosqueezing-Based Recovery of Instantaneous Frequency from Nonuniform SamplesGaurav Thakur and Hau-Tieng Wu1 September 2011 | SIAM Journal on Mathematical Analysis, Vol. 43, No. 5AbstractPDF (1527 KB)System Representations for the Zakai Class With ApplicationsIEEE Transactions on Information Theory, Vol. 56, No. 8 Cross Ref Comments on Nyquist rate in engineering application Cross Ref Interconnections Between Multiplier Methods and Window Methods in Generalized Sampling1 January 2010 | Sampling Theory in Signal and Image Processing, Vol. 9, No. 1-3 Cross Ref Sampling-Type Representations of Signals and Systems1 January 2010 | Sampling Theory in Signal and Image Processing, Vol. 9, No. 1-3 Cross Ref Behavior of Shannon’s Sampling Series for Hardy Spaces22 May 2008 | Journal of Fourier Analysis and Applications, Vol. 15, No. 3 Cross Ref Sampling and Ergodic Theorems for Weakly Almost Periodic SignalsIEEE Transactions on Information Theory, Vol. 55, No. 4 Cross Ref Global and Local Approximation Behavior of Reconstruction Processes for Paley-Wiener Functions1 January 2009 | Sampling Theory in Signal and Image Processing, Vol. 8, No. 1 Cross Ref There Exists No Globally Uniformly Convergent Reconstruction for the Paley–Wiener Space ${{\cal PW}}_{\pi}^{1}$ of Bandlimited Functions Sampled at Nyquist RateIEEE Transactions on Signal Processing, Vol. 56, No. 7 Cross Ref Reconstruction of polyharmonic functions from samplesJournal of Approximation Theory, Vol. 148, No. 1 Cross Ref Interpolation of entire functions of finite orderIntegral Transforms and Special Functions, Vol. 17, No. 4 Cross Ref Localization of the generalized sampling series and its numerical applicationLiwen Qian and Dennis B. 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