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2001 | 11 | 6 | 1379-1386
Tytuł artykułu

The geometry of Darlington synthesis (in memory of W. Cauer)

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We revisit the classical problem of 'Darlington synthesis', or Darlington embedding. Although traditionally it is solved using analytic means, a more natural way to approach it is to use the geometric properties of a well-chosen Hankel map. The method yields surprising results. In the first place, it allows us to formulate necessary and sufficient conditions for the existence of the embedding in terms of systems properties of the transfer operation to be embedded. In addition, the approach allows us to extend the solution to situations where no analytical transform is available. The paper has a high review content, as all the results presented have been obtained during the last twenty years and have been published. However, we make a systematic attempt at formulating them in a geometric way, independent of an accidental parametrization. The benefit is clarity and generality.
Rocznik
Tom
11
Numer
6
Strony
1379-1386
Opis fizyczny
Daty
wydano
2001
Twórcy
  • DIMES, Faculty of Electrical Engineering, Delft University of Technology, Mekelweg 4, 2628 CD Delft, The Netherlands
Bibliografia
  • Anderson B.D.O. and Vongpanitlerd S. (1973): Network Analysis and Synthesis. — Englewood Cliffs: Prentice Hall.
  • Arov D.Z. (1971): On the Darlington method in the theory of dissipative systems. — Dokl. Akad. Nauk USSR, Vol.201, No.3, pp.559–562.
  • Belevitch V. (1968): Classical Network Theory. — San Francisco: Holden Day.
  • Cauer W. (1932): New theory and design of wave filters. — Physics, Vol.2, pp.242–267.
  • Delsarte P. and Genin Y. (1986): The split Levinson algorithm. — IEEE Trans. Acoust. Speech Sign. Process., Vol.34, No.19863, pp.470–478.
  • Dewilde P. (1971): Roomy scattering matrix synthesis. — Tech. Rep., Dept. of Mathematics, Univ. of California, Berkeley.
  • Dewilde P. (1976): Input-output description of roomy systems. — SIAM J. Contr. Optim., Vol.14, No.4, pp.712–736.
  • Dewilde P. (1999): Generalized Darlington synthesis. — IEEE Trans. Circ. Syst. – I: Fund. Theory Appl., Vol.45, No.1, pp.41–58.
  • Dewilde P. and van der Veen A.-J. (1998): Time-Varying Systems and Computations. — Dordrecht: Kluwer.
  • Fuhrmann P.A. (1981): Linear Systems and Operators in Hilbert Space. — New York: McGraw-Hill.
  • Helson H. (1964): Lectures on Invariant Subspaces. — New York: Academic Press.
  • Newcomb R. (1966): Linear Multiport Synthesis. — New York: McGraw Hill.
  • Masani P. and Wiener N. (1957): The prediction theory of multivariable stochastic processes. — Acta Math., Vol.98, No.1, pp.111–150.
  • Szegö G. (1920): Beitrage zur theorie der toeplitzen formen (ersten mitteilung). — Math. Zeit, Vol.6, No.2, pp.167–202.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv11i6p1379bwm
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