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  • 1
    Book
    Book
    Boston :Birkhäuser,
    Title: Sampling, wavelets, and tomography /
    Contributer: Benedetto, John , Zayed, Ahmed I.
    Publisher: Boston :Birkhäuser,
    Year of publication: 2003
    Pages: p. cm
    Series Statement: Applied and computational harmonic analysis
    ISBN: 0-8176-4304-4 , 3-7643-4304-4
    Type of Medium: Book
    Language: English
    Keywords: Hamonic analysis ; Wavelets (Mathematics) ; Fourier analysis ; Sampling (Statistics) ; Tomography
    Library Location Call Number Volume/Issue/Year Availability
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Multidimensional systems and signal processing 3 (1992), S. 323-340 
    ISSN: 1573-0824
    Keywords: Shannon and Kramer sampling theorems inN dimensions ; anN-dimensional Paley-Wiener interpolation theorem for band-limited signals and multidimensional Lagrange interpolation
    Source: Springer Online Journal Archives 1860-2000
    Topics: Electrical Engineering, Measurement and Control Technology
    Notes: Abstract Kramer's sampling theorem, which is a generalization of the Whittaker-Shannon-Kotel'nikov (WSK) sampling theorem, enables one to reconstruct functions that are integral transforms of types other than the Fourier one from their sampled values. In this paper, we generalize Kramer's theorem toN dimensions (N ≥ 1) and show how the kernel function and the sampling points in Kramer's theorem can be generated. We then investigate the relationship between this generalization of Kramer's theorem andN-dimensional versions of both the WSK theorem and the Paley-Wiener interpolation theorem for band-limited signals. It is shown that the sampling series associated with this generalization of Kramer's theorem is nothing more than anN-dimensional Lagrange-type interpolation series.
    Type of Medium: Electronic Resource
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  • 3
    Electronic Resource
    Electronic Resource
    Springer
    The journal of Fourier analysis and applications 2 (1995), S. 303-314 
    ISSN: 1531-5851
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics
    Notes: Abstract In this article a generalized sampling theorem using an arbitrary sequence of sampling points is derived. The sampling theorem is a Kramer-type sampling theorem, but unlike Kramer's theorem the sampling points are not necessarily eigenvalues of some boundary value problems. The theorem is then used to characterize a class of entire functions that can be reconstructed from their sample values at the points tn = an + b if n = 0, 1, 2, ... and tn = an + c if n = 0, -1, -2, ..., where a, b, c are arbitrary constants. The reconstruction formula is derived explicitly in the form of a sampling series expansion. When a = 1, b = 0 = c, the famous Whittaker-Shannon-Kotel'nikov sampling theorem is obtained as a special case.
    Type of Medium: Electronic Resource
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