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2007 | 17 | 2 | 143-156
Tytuł artykułu

Construction of sampling and interpolating sequences for multi-band signals. the two-band case

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Recently several papers have related the production of sampling and interpolating sequences for multi-band signals to the solution of certain kinds of Wiener-Hopf equations. Our approach is based on connections between exponential Riesz bases and the controllability of distributed parameter systems. For the case of two-band signals we derive an operator whose invertibility is equivalent to the existence of a sampling and interpolating sequence, and prove the invertibility of this operator.
Rocznik
Tom
17
Numer
2
Strony
143-156
Opis fizyczny
Daty
wydano
2007
otrzymano
2006-11-02
(nieznana)
2006-12-15
poprawiono
2007-02-22
Twórcy
  • Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775–6660, USA
  • Department of Mathematics and Statistics, University of Alaska Fairbanks, Fairbanks, AK 99775–6660, USA
  • Department of Electrical and Electronic Engineering, University of Melbourne, Melbourne Victoria 3010, Australia
Bibliografia
  • Antonevich A. (1996): Linear Functional Equations. Operator Approach.- Basel, Birkhauser.
  • Avdonin S. (1979): On Riesz bases from exponentials in L^2. - Vestnik Leningrad Univ. Math., Vol.7, pp. 203-211.
  • Avdonin S. and Ivanov S. (1995): Families of Exponentials. The Method of Moments in Controllability Problems for Distributed Parameter Systems.- New York: Cambridge University Press.
  • Avdonin S. and Moran W. (1999): Sampling and interpolation of functions with multi-band spectra and controllability problems, In: Optimal Control of Partial Differential Equations, (K.H. Hoffmann, G.Leugering and T.F., Eds.), Basel: Birkhauser, Vol.133, pp.43-51.
  • Beaty M. and Dodson M. (1989): Derivative sampling for multiband signals. - Numer. Funct. Anal. Optim., Vol.10, No.9-10, pp.875-898.
  • Beaty M. and Dodson M. (1993): The distribution of sampling rates for signals with equally wide, equally spaced spectral bands. - SIAM J. Appl. Math., Vol.53, No.3, pp.893-906.
  • Bezuglaya L. and Katsnelson V. (1993): The sampling theorem for functions with limed multi-band spectrum, I. - Z. Anal. Anwendungen, Vol.12, No.3, pp. 511-534.
  • Bottcher A., Karlovich Y. and Spitkovsky I. (2002): Convolution Operators and Factorization of Almost Periodic Matrix Functions. - Basel: Birkhauser.
  • Dodson M. and Silva A. (1989): An algorithm for optimal regular sampling. - Signal Process., Vol.17, No.2, pp.169-174.
  • Higgins J. (1996): Sampling Theory in Fourier and Signal Analysis: Foundations. - Oxford: Clarendon Press.
  • Hruščev S., Nikol'skii N. and Pavlov B. (1981): Unconditional bases of exponentials and reproducing kernels, In: Complex Analysis and Spectral Theory (V.P Havin and N.K. Nikol'ski, Eds.), Lecture Notes Math., Vol.864, pp. 214-335.
  • Katsnelson V. (1996): Sampling and interpolation for functions with multi-band spectrum: The mean-periodic continuation method, In: Wiener-Symposium (Grossbothen, 1994) Synerg. Syntropie Nichtlineare Syst., Vol.4, Leipzig: Verlag Wiss. Leipzig, pp.91-132,.
  • Kohlenberg A. (1953): Exact interpolation of band-limed functions.- J. Appl. Phys., Vol.24, No.12, pp.1432-1436.
  • Lyubarskii Y. and Seip K. (1997): Sampling and interpolating sequences for multiband-limed functions and exponential bases on disconnected sets.- J. Fourier Anal. Appl., Vol.3, No.5, pp.597-615.
  • Lyubarskii Y. and Spitkovsky I. (1996): Sampling and interpolation for a lacunary spectrum. - Proc. Royal. Soc. Edinburgh, Vol.126 A, No.1, pp.77-87.
  • Moran W. and Avdonin S. (1999): Sampling of multi-band signals. - Proc. 4-th Int. Congress Industrial and Applied Mathematics, Edinburgh, Scotland, pp.163-174.
  • Peterson K. (1983): Ergodic Theory. - Cambridge: Cambridge University Press.
  • Russell D. (1978): Controllability and stabilizability theory for linear partial differential equations. - SIAM Review, Vol.20, No.4, pp.639-739.
  • Seip K. (1995): A simple construction of exponential bases in L^2 of the union of several intervals. - Proc. Edinburgh Math. Soc.,Vol.38, No.1, pp.171-177.
  • Spitkovsky I. (2006): Personal communication
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv17i2p143bwm
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