Approximately dual Gabor frames and almost perfect reconstruction based on a class of window functions

Ole Christensen, Augustus J.E.M. Janssen, Hong Oh Kim, Rae Young Kim*

*Corresponding author for this work

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Abstract

It is a well-known problem in Gabor analysis how to construct explicitly given dual frames associated with a given frame. In this paper we will consider a class of window functions for which approximately dual windows can be calculated explicitly. The method makes it possible to get arbitrarily close to perfect reconstruction by allowing the modulation parameter to vary. Explicit estimates for the deviation from perfect reconstruction are provided for some of the standard functions in Gabor analysis, e.g., the Gaussian and the two-sided exponential function.

Original languageEnglish
JournalAdvances in Computational Mathematics
Volume44
Issue number5
Pages (from-to)1519-1535
ISSN1019-7168
DOIs
Publication statusPublished - 1 Oct 2018

Keywords

  • Almost perfect reconstruction
  • Approximately dual frames
  • Frames
  • Gaussian
  • Two-sided exponential

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