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Kramer's sampling theorem for multidimensional signals and its relationship with Lagrange-type interpolations (1992)

Zayed, Ahmed I.

Springer

Multidimensional systems and signal processing 3 (1992), S. 323-340

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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

URL: http://dx.doi.org/10.1007/BF01940228

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Synthesis of Uridine with Methylene-2-thiohydantoin as 5-Substituent (1994)

El-Barbary, Ahmed A. ; Khodair, Ahmed I. ; Pedersen, Erik B. ; [et al.]

Weinheim : Wiley-Blackwell

Liebigs Annalen 1994 (1994), S. 619-621

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ISSN: 0170-2041

Keywords: Uridine, methylene-2-thiohydantoin derivative ; Nucleosides ; 2-Thiohydantoin ; Herpes simplex virus ; Chemistry ; Organic Chemistry

Source: Wiley InterScience Backfile Collection 1832-2000

Topics: Chemistry and Pharmacology

Notes: 5-Formyl-1-(2,3,5-tri-O-acetyl-β-D-ribofuranosyl)uracil (4) was synthesized from 5-formyluracil (2) and 1,2,3,5-tetra-O-acetyl-β-D-ribofuranose (3) and condensed with 2-thiohydantoin derivatives 5 by using piperidine as the catalyst to give 5-(uridin-5-ylmethylene)-2-thiohydantoin (8a) and 3-phenyl-5-(uridin-5-ylmethylene)-2-thiohydantoin (8b) after deprotection with sodium methoxide in methanol. Compound 8a was also obtained in an inversed reaction sequence from 5-formyluracil starting with condensation with 2-thiohydantoin and then with 3. The compounds 8a and 8b did not show any activity against HSV-1 or HIV-1.