• DocumentCode
    761679
  • Title

    Some counterexamples in the theory of Weyl-Heisenberg frames

  • Author

    Janssen, A. J E M

  • Author_Institution
    Philips Res. Lab., Eindhoven, Netherlands
  • Volume
    42
  • Issue
    2
  • fYear
    1996
  • fDate
    3/1/1996 12:00:00 AM
  • Firstpage
    621
  • Lastpage
    623
  • Abstract
    We present an example of a positive function g with a positive Fourier transform gˆ and reasonable smoothness and decay properties such that (-1)nmexp(πitm)g(t-n), n, m∈Z does not constitute a frame for L2(R). We also give counterexamples for the statement that one can tell (in)definiteness of a Weyl-Heisenberg frame operator from (in)definiteness of its Weyl symbol
  • Keywords
    Fourier transforms; information theory; mathematical operators; time-frequency analysis; Weyl symbol; Weyl-Heisenberg frames; Zak transform; decay properties; definiteness; indefiniteness; positive Fourier transform; positive function; smoothness properties; time frequency analysis; Displays; Electronic switching systems; Fourier transforms; Smoothing methods; Time frequency analysis;
  • fLanguage
    English
  • Journal_Title
    Information Theory, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    0018-9448
  • Type

    jour

  • DOI
    10.1109/18.485730
  • Filename
    485730
    • Link To Document
    https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=761679