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Applicable Analysis
An International Journal
Volume 50, 1993 - Issue 3-4
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Original Articles

Error analysis in regular and irregular sampling theory

, &
Pages 167-189 | Received 07 Jan 1992, Published online: 20 Jan 2011

References

  • Butzer , P.L. and Hinsen , L. 1989 . Two—dimensional nonuniform sampling expansions . I, 11. Appl. Anal. , 32 : 69 – 85 . 53–68 and
  • Butzer , P.L. , Splettstōber , W. and Stens , R. 1987 . The sampling theorem and linear prediction in signal analysis. . Jber.d. Dt. Math.—Verein. , 90 : 1 – 70 .
  • Clark , J.J. , Palmer , M.R. and Lawrence , P.D. 1985 . A transformation method for the reconstruction of functions from . nonuniforrnly spaced samples, IEEE Trans ASSP , 33 ( 4 ) : 1151 – 1165 .
  • Daubechies , L. 1990 . Daubechies. The wavelet transform, time-frequency localization and signal analysis. . IEEE Trans. Inform. Theory. , 36 : 961 – 1005 .
  • .Donohoe , D. and Stark , P. 1989 . Uncertainty principles and signal recovery. . SIAM J.Appl.Math. , 49/3 : 906 – 931 .
  • Duffin , R. and Schaeffer , A. 1952 . Schaeffer. A class of nonharmonic Fourier series. . Trans. Amer. Math. Soc. , 72 : 341 – 366 .
  • Feichtinger , H.G. Banach convolution algebras of Winner's type. Proc. Conf. 1980 , Budapest. Functions, Series, Operatorsn . Coll. Math. Soc. J.Bolyai, North Holland, Amsterdam—Oxford—New York.
  • Feīchtinger , H.G. 1981 . Banch spaces of distributions of Wiener' type and interpolation. Conf. 1981 , Basel, Birkhá. P. Butzer et al, eds., p. 153 – 165, ISNM Vol. 69, Proc. Conf. Oberwolfach
  • Feichtinger H.G. Discretization of convolution and reconstruction of bandlimited functions J. Approx. Th. 1991 To appear in
  • Feichtinger H.G. Grochenig K. terative Reconstruction of Multivariate Band- Limited Functions from Irregular Sampling Values 1991 Submitted
  • Feichtinger H.G. Grochenig K. Irregular sampling theorems and series expansions of band—limited functions J. Math. Anal. Appl. To appear in
  • Feichtinger , H.G. and Grōchening , K. Grochenig. Multidimensional irregular sampling of bandlimited functions in Lp-spaces. Proc. Conf. 1989 . Oberwolfach . Feb. ISNM 90, Birkhāuser, 1989, p.135–142.
  • Grōchenig , K. A new approach to irregular sampling of band—limited functions. NATO AS1 “Harmonic Analysis and Applications”, . 1989 , II Ciocco,Italy. J. Byrnes . ed., p. 251–260. Kluwer Publ.Comp.
  • Higgins , J .R. A sampling theorem for irregularly sampled points . IEEE Trans. Information Theory Sept . pp. 621 – 622 .
  • Jagerman , D. 1966 . Bounds for the truncation error of the sampling expansion. . SIAM J. Appl. Math. , 14 : 714 – 723 .
  • Jerri , A.J. 1977 . The Shannon sampling theorem—its various extensions and applications.A tutorial review. . Proc. IEEE , 65 : 1565 – 1596 .
  • Kadec , M.I. 1964 . The exact value of the Paley—Wiener constant. . Soviet Math. Dokl. , 5 : 559 – 561 .
  • Landau , H.L. 1967 . Sampling data transmission and the Nyquist rate. . Proc. IEEE , 55 : 1701 – 1706 .
  • Levinson , N. 1940 . “ Gap and Density Theorems. ” . In oll. Publ. 26, Amer. Math. Soc. New York
  • Marvasti , F.A. 1987 . “ A unified approach to zero—crossing and nonuniform sampling of single and multidimensional systems ” . In Encyclopedia of Mathematics and its Applications , Oak Park, IL 60304 : Nonuniform, P.0 .Box 1505 .
  • Marvasti , F. and Analoui , >F. May1989 . “ Recovery of signals from nonuniform samples using iterative methods ” . In in Proc.Int.Symp. Circuits Syst. Portland,, OR
  • Marvasti , F.A. 1989 . An iterative method to compensate for the interpolation distortion. . IEEE Trans. ASSP , 37 : 1619 – 1621 .
  • Papoulis , A. 1977 . “ Signal Analysis ” . New York : McGraw—Hill .
  • Papoulis , A. 1966 . Error analysis in sampling theory. . Proc. IEEE , 45/7 : 947 – 955 .
  • Reiter H. Classical Harmonic Analysis and Locally Compact Groups. Oxford Univ. Press 1968
  • Sauer , K.D. and Allebach , J.P. 1987 . Iterative reconstruction of band—limited images from nonuniformly spaced samples. . IEEE Trans. CAS , 34/2 : 1497 – 1506 .
  • Sezan , M.I. and Stark , H. 1988 . “ Recent analysis in signal processing in medical tomography ” . In Signal Processing Handbook , Edited by: Chen , C.H. Vol. 23 , 729 – 795 . Menlo Park, Calif. : Marcel Dekker .
  • Splettstöber W. Unregelmābige Abtastungen determinierter und zufälliger Signale to appear in the Quarterly of Applied Math. Gottingen 1981 In Kolloquium DFG—Schwerpunktprogramm Digit ale Signalverarbeitung , H.G. Zimmer, V. Neuhoff, Eds., , 1981, p. 1-4.
  • Thomas , J.B. and Liu , B. 1964 . Error problems in sampling representation. . IEEE Int. Cod. Rec. , 12 : 269 – 277 .
  • Triebel , H. 1983 . “ Theory of functions spaces ” . Calif. : Birkhauser Verlag .
  • Wiley , R.G. 1978 . ReRecovery of band—limited signals from unequally spaced samples. IEEE Trans. . Communications COM , 26 : 135 – 137 .
  • Yao , K. and Thomas , J.O. 1967 . On some stability and interpolatory properties of nonunifrom sampling expansions. . IEEE Trans. Circuit Theory , 14 : 404 – 408 .
  • Yen , S. and Stark , H. 1990 . Iterative and one—step reconstruction from nonuniform samples by convex projections. . J. Opt. Soc. Am. A, , 7 : 491 – 499 .
  • Young R. An Introduction to Nonharmonic Fourier Series. Academic Press New York 1980
  • Zwaan , M. Stability and error estimates for sinc interpolation . Report AMR8914, Centrum voor Wiskunde en Informatica. Vol. 75 ,
  • Zwaan , M. Approximation of the solution to the moment problem in a Hilbert space . Report AM-R8923, Centrum voor Wiskunde en Informatica . Vol. 75 , pp. 982 – 1008 .
  • Zwaan , M. Dynamic MRI reconstruction as a moment problem III . Report AM-R9002, Centrum voor Wiskunde en Informatica. Vol. 75 ,

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