• DocumentCode
    1015977
  • Title

    The Zak transform and sampling theorems for wavelet subspaces

  • Author

    Janssen, Augustus J E M

  • Author_Institution
    Appl. Math. Group, Philips Res. Lab., Eindhoven, Netherlands
  • Volume
    41
  • Issue
    12
  • fYear
    1993
  • fDate
    12/1/1993 12:00:00 AM
  • Firstpage
    3360
  • Lastpage
    3364
  • Abstract
    The Zak transform is used for generalizing a sampling theorem of G. Waiter (see IEEE Trans. Informat. Theory, vol. 38, p. 881-884, 1992) for wavelet subspaces. Cardinal series based on signal samples f(a+n), n∈Z with a possibly unequal to 0 (Waiter´s case) are considered. The condition number of the sampling operator and worst-case aliasing errors are expressed in terms of Zak transforms of scaling function and wavelet. This shows that the stability of the resulting interpolation formula depends critically on a
  • Keywords
    interpolation; series (mathematics); signal processing; stability; wavelet transforms; Zak transform; cardinal series; interpolation formula; sampling operator; sampling theorem; sampling theorems; scaling function; signal samples; stability; wavelet subspaces; worst-case aliasing errors; Convergence; Discrete Fourier transforms; Fourier transforms; Interpolation; Mathematics; Sampling methods; Stability; Wavelet analysis; Wavelet transforms;
  • fLanguage
    English
  • Journal_Title
    Signal Processing, IEEE Transactions on
  • Publisher
    ieee
  • ISSN
    1053-587X
  • Type

    jour

  • DOI
    10.1109/78.258079
  • Filename
    258079