IDEAS home Printed from https://ideas.repec.org/h/spr/sprchp/978-1-4757-2817-0_6.html

Isometric and Inner Operators

In: Time-Varying Systems and Computations

Author

Listed:
  • Patrick Dewilde

    (Delft University of Technology, DIMES)

  • Alle-Jan van der Veen

    (Delft University of Technology, DIMES)

Abstract

Lossless systems play an important role in the class of linear systems. They are causal systems which “conserve energy”. If energy is measured as the square of a quadratic norm ‖•‖, a lossless system transforms an input signal u with bounded energy ‖u‖ to an output signal y = uT which contains the same total energy: ‖u‖ = ‖y‖ In filter theory, scalar lossless systems are also known as allpass filters, with a flat amplitude spectrum but a variable phase. They have many interesting properties. One is that any passive rational filter may be realized as the partial response of a lossless filter. Another property is that lossless systems may be implemented in a locally lossless way as well, by using a state space realization in which every section is itself lossless. Such realizations do not amplify noise introduced at any point in the system, and they can be made robust with respect to parameter deviations as well.

Suggested Citation

  • Patrick Dewilde & Alle-Jan van der Veen, 1998. "Isometric and Inner Operators," Springer Books, in: Time-Varying Systems and Computations, chapter 6, pages 121-143, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-2817-0_6
    DOI: 10.1007/978-1-4757-2817-0_6
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a
    for a similarly titled item that would be available.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:sprchp:978-1-4757-2817-0_6. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.