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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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.
D. Ciulin, “Description of the sampling signals using functional analysis”, Telecommunication Review Nr 12, Bucharest, 1972.
D. Ciulin, “Sampling and quantizing signal reconstruction on the basis of generalized sampling functions”, SSCT, Prague, Czechoslovakia, 1974.
*** , “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.
S. Stoilov, “Theory of complex variables functions”, vol. 1, Bucharest 1953 (in Romanian).
E. Goursat, ‘Cours d’Analyse Mathématique’, tome II, Paris, Gauthier Villard, 1949.
V. Smirnov, ‘Cours de Mathématique Supérieure’, volume I, II et III, édition Mir Moscou, 1988.
D. Ciulin, “Sampling and quantizing signal reconstructions on the basis of generalized sampling functions”, SSCT 74, pp. 387-393, 1974, Prague, Czechoslovakia, 1974
D. Ciulin, “Sur l’operateur de quantification”, RTCL symphosium, Brest, 1998.
D. Ciulin, “Some tools for speech processing”,6th WORLD MULTICONFERENCE ON SYSTEMICS, CYBERNETICS AND INFORMATICS (SCI2002), Orlando, Florida, U.S.A 2002.
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.
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.
B. Chabat,” Introduction a l’analyse complexe”, tome 2, fonctions de plusieurs variables,MIR, Moscou, 1959.
D. Ciulin, ”Inverse Problem for a Car Headlight reflector”, Virtual Concept 2006 Symposium, Playa Del Carmen, Mexico, November–December 2006.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer Science+Business Media B.V.
About this paper
Cite this paper
Ciulin, D. (2008). About Sign Function and Some Extensions. In: Elleithy, K. (eds) Innovations and Advanced Techniques in Systems, Computing Sciences and Software Engineering. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-8735-6_28
Download citation
DOI: https://doi.org/10.1007/978-1-4020-8735-6_28
Publisher Name: Springer, Dordrecht
Print ISBN: 978-1-4020-8734-9
Online ISBN: 978-1-4020-8735-6
eBook Packages: Computer ScienceComputer Science (R0)