Abstract

Starting from the well.known definition (1) of the Sign function, a different compact definition has the advantage that leads also to compact definitions for other useful functions as, for example, the Dirac impuls and the unity step function. Extensions using single periodical functions leads to compact relations for some test periodical signals, the Ladder function and its derivative, the periodical Dirac impulse and then, to a ‘quantized’ operator. An extension for double (and/or multiple) periodical functions is also presented. It may find out applications in image and/or field theory.

Keywords

Milton 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    D. Ciulin, “Signal representation by methods of functional analysis”, Proceeding of the Telecommunication Conference, Bucharest 15-17 November 1971 and also in Telecommunication Review Nr. 5, Bucharest, 1972.Google Scholar
  2. [2]
    D. Ciulin, “Description of the sampling signals using functional analysis”, Telecommunication Review Nr 12, Bucharest, 1972.Google Scholar
  3. [3]
    D. Ciulin, “Sampling and quantizing signal reconstruction on the basis of generalized sampling functions”, SSCT, Prague, Czechoslovakia, 1974.Google Scholar
  4. [4]
    *** , “Handbook of Mathematical functions with formulas, graphs, and mathematical tables”, edited by Milton Abramovitz and Irene A. Stegun, National Bureau of Standards, Applied Mathematics Series. 55, June, 1964.Google Scholar
  5. [5]
    S. Stoilov, “Theory of complex variables functions”, vol. 1, Bucharest 1953 (in Romanian).Google Scholar
  6. [6]
    E. Goursat, ‘Cours d’Analyse Mathématique’, tome II, Paris, Gauthier Villard, 1949.Google Scholar
  7. [7]
    V. Smirnov, ‘Cours de Mathématique Supérieure’, volume I, II et III, édition Mir Moscou, 1988.Google Scholar
  8. [8]
    D. Ciulin, “Sampling and quantizing signal reconstructions on the basis of generalized sampling functions”, SSCT 74, pp. 387-393, 1974, Prague, Czechoslovakia, 1974Google Scholar
  9. [9]
    D. Ciulin, “Sur l’operateur de quantification”, RTCL symphosium, Brest, 1998.Google Scholar
  10. [10]
    D. Ciulin, “Some tools for speech processing”,6th WORLD MULTICONFERENCE ON SYSTEMICS, CYBERNETICS AND INFORMATICS (SCI2002), Orlando, Florida, U.S.A 2002.Google Scholar
  11. [11]
    D. Ciulin, “Bandwidth-compression theorem, a new tool in signal processing,”,10th International, Signal Processing Conference on Concurrent Enginring: Research and Application, Madeira, Portugal, 2003.Google Scholar
  12. [12]
    D. Ciulin, “New improved blocks for signal processing,”,DECOM-TT 2004, AUTOMATIC SYSTEMS FOR BUILDING THE INFRASTRUCTURE IN DEVELOPING COUNTRIES, Bansko, Bulgaria, 3-5 October 2004.Google Scholar
  13. [13]
    B. Chabat,” Introduction a l’analyse complexe”, tome 2, fonctions de plusieurs variables,MIR, Moscou, 1959.Google Scholar
  14. [14]
    D. Ciulin, ”Inverse Problem for a Car Headlight reflector”, Virtual Concept 2006 Symposium, Playa Del Carmen, Mexico, November–December 2006.Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Dan Ciulin
    • 1
  1. 1.E-I-ALausanneSwitzerland

Personalised recommendations