Generalized classical and quantum signal theories / Rundblad E., Labunets V., Novak P. // Proceedings of SPIE - The International Society for Optical Engineering. - 2005. - V. 5815, l. . - P. 235-246.

ISSN:
0277786X
Type:
Conference Paper
Abstract:
In this paper we develop two topics and show their inter- and cross-relation. The first centers on general notions of the generalized classical signal theory on finite Abelian hypergroups. The second concerns the generalized quantum hyperharmonic analysis of quantum signals (Hermitean operators associated with classical signals). We study classical and quantum generalized convolution hypergroup algebras of classical and quantum signals.
Author keywords:
Classical and quantum Fourier transforms; Generalized classical and quantum convolutions; Hypergroups; Signals; Systems; Weyl quantization
Index keywords:
Algebra; Fourier transforms; Harmonic analysis; Signal processing; Signal theory; Classical and quantum Fourier transforms; Generalized classical and quantum comvolutions; Hypergroups; Signals; System
DOI:
10.1117/12.603954
Смотреть в Scopus:
https://www.scopus.com/inward/record.uri?eid=2-s2.0-27644561219&doi=10.1117%2f12.603954&partnerID=40&md5=488efadbd51bd96fca272cbea33f836d
Соавторы в МНС:
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Поле Значение
Art. No. 35
Link https://www.scopus.com/inward/record.uri?eid=2-s2.0-27644561219&doi=10.1117%2f12.603954&partnerID=40&md5=488efadbd51bd96fca272cbea33f836d
Affiliations EnerSoft Inc., Florida, NY, United States
Author Keywords Classical and quantum Fourier transforms; Generalized classical and quantum convolutions; Hypergroups; Signals; Systems; Weyl quantization
References Marty, F., Sur une generalization de la notion de groupe (1934) Sartryck ur Forhandlingar via Altonde Skandinavioka Matematiker Kongressen i Stockholm, pp. 45-49; Wall, H.S., Hypergroups (1934) Bulletin of the American Mathematical Socity, 41, pp. 36-40. , Presented at the annual meeting of the American Mathematical Socity, Pittsburgh, December 27-31, 1934; Levitan, B.M., The application of generalized displacement operators to linear differential equations of second order (1949) Uspechi Math. Nauk, 4 (1-29), pp. 3-112; (1962) Amer. Mat. Soc. Transl. (1), 10, pp. 408-541. , English transl., MR 11, 116; Labunets-Rundblad, E.V., Labunets, V.G., Astola, J., Algebraic frames for commutative hyperharmonic analysis of signals and images (2000) Algebraic Frames for the Perception-action Cycle, pp. 294-308. , Second Inter. Workshop, AFPAC 2000, Kiel, Germany, September 2000. Lectures Notes in Computer Science, 1888, Berlin, 2000; Creutzburg, R., Labunets, E.V., Labunets, V.G., Algebraic foundations of an abstract harmonic analysis of signals and systems (1998) Workshop on Transforms and Filter Banks, pp. 30-68. , Tampere International Center for Signal Processing; Labunets, E., Labunets, V., Creutzburg, R., Towards an "Erlangen program" for general linear systems theory (1991) Second International Workshop on Computer Aided Systems Theory (EUROCAST-91), pp. 108-112. , Krems (Wachau), Austria, April; Wigner, E.R., On the quantum correction for thermo-dynamic equilibrium (1932) Physics Review, 40, pp. 749-759; Ville, J., Theorie et applications de la notion de signal analytique (1948) Gables et Transmission, 2 A, pp. 61-74; Woodward, P.M., Information theory and design of radar receivers (1951) Proceedings of the Institute of Radio Engineers, 39, pp. 1521-1524; Weyl, H., (1932) The Theory Group and Quantum Mechanics, 236p. , London: Methuen
Correspondence Address EnerSoft Inc., Florida, NY, United States; email: krundblad@enersoft.com
Editors Donkor E.J.Pirich A.R.Brandt H.E.
Sponsors SPIE - The Intenational Society for Optical Engineering
Conference name Quantum Information and Computation III
Conference date 29 March 2005 through 30 March 2005
Conference location Orlando, FL
Conference code 65968
CODEN PSISD
Language of Original Document English
Abbreviated Source Title Proc SPIE Int Soc Opt Eng
Source Scopus