Algebraic frames for commutative hyperharmonic analysis of signals and images / Rundblad E., Labunets V., Astola J., Egiazarian K. // Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). - 2000. - V. 1888, l. . - P. 294-308.

ISSN:

03029743

Type:

Conference Paper

Abstract:

Integral transforms and the signal representations associated with them are important tools in applied mathematics and signal theory. The Fourier transform and the Laplace transform are certainly the best known and most commonly used integral transforms. However, the Fourier transform is just one of many ways of signal representation and there are many other transforms of interest. In the past 20 years, other analytical methods have been proposed and applied, for example, wavelet, Walsh, Legendre, Hermite, Gabor, fractional Fourier analysis, etc. Regardless of their particular merits they are not as useful as the classical Fourier representation that is closely connected to such powerful concepts of signal theory as linear and nonlinear convolutions, classical and high–order correlations, invariance with respect to shift, ambiguity and Wigner distributions, etc. To obtain the general properties and important tools of the classical Fourier transform for an arbitrary orthogonal transform we associate to it generalized shift operators and develop the theory of abstract harmonic analysis of signals and linear and nonlinear systems that are invariant with respect to these generalized shift operators. © Springer-Verlag Berlin Heidelberg 2000.

Author keywords:

Index keywords:

Algebra; Fourier analysis; Integral equations; Integrodifferential equations; Laplace transforms; Mathematical transformations; Signal theory; Analysis of signal; Applied mathematics; Fractional fouri

DOI:

нет данных

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https://www.scopus.com/inward/record.uri?eid=2-s2.0-84937397171&partnerID=40&md5=f2c98c71cb5df94af1241601434fa713

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Другие поля

Поле	Значение
Link	https://www.scopus.com/inward/record.uri?eid=2-s2.0-84937397171&partnerID=40&md5=f2c98c71cb5df94af1241601434fa713
Affiliations	Tampere University of Technology, Signal Processing Laboratory, Tampere, Finland
References	Labunets, V.G., (1984) Algebraic Theory of Signals and Systems, , (Russian), KrasnojarskSta te University, Krasnojarsk; Labunets, V.G., (1986) Double Orthogonal Functions in Generalized Harmonic Analysis, pp. 4-15. , (Digital methods in control, radar and telecommunication systems). (Russian), Urals State Technical University, Sverdlovsk; Weyl, H., (1931) The Theory Group and Quantum Mechanics, , London: Methuen; 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; Volterra, V., (1959) Theory of Functionals and of Integral and Integro–Differential Equations, , Dover Publications. New York
Editors	Zeevi Y.Y.Sommer G.
Publisher	Springer Verlag
Conference name	2nd International Workshop on Algebraic Frames for the Perception-Action Cycle, AFPAC 2000
Conference date	10 September 2000 through 11 September 2000
Conference code	121239
ISBN	3540410139; 9783540410133
Language of Original Document	English
Abbreviated Source Title	Lect. Notes Comput. Sci.
Source	Scopus