Iterative algorithms to approximate canonieal Gabor windows: Computational aspects

A. J. E. M. Janssen, Peter Lempel Søndergaard

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    Abstract

    In this article we investigate the computational aspects of some recently proposed iterative methods for approximating the canonical tight and canonical dual window of a Gabor frame (g, a, b). The iterations start with the window g while the iteration steps comprise the window g, the k(th) iterand gamma(k), theframe operators S and S-k corresponding to (g, a, b) and (gamma(k), a, b), respectively, and a number of scalars. The structure of the iteration step of the method is determined by the envisaged convergence order m of the method. We consider two strategies for scaling the terms in the iteration step: Norm scaling, where in each step the windows are normalized, and initial scaling where we only scale in the very beginning. Norm scaling leads to fast, but conditionally convergent methods, while initial scaling leads to unconditionally convergent methods, but with possibly, suboptimal convergence constants. The iteratious, initially formulated for time-continuous Gabor systems, are considered and tested in a discrete setting in which one passes to the appropriately sampled-and-periodized windows and frame operators. Furthermore, they are compared with respect to accuracy and efficiency, with other methods to approximate canonical windows associated with Gabor frames.
    Original languageEnglish
    JournalJournal of Fourier Analysis and Applications
    Volume13
    Issue number2
    Pages (from-to)211-241
    ISSN1069-5869
    DOIs
    Publication statusPublished - 2007

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