Journal of Fourier Analysis and Applications

, Volume 13, Issue 2, pp 211–241

Iterative Algorithms to Approximate Canonical Gabor Windows: Computational Aspects

Authors

    • Philips Research Laboratories WO-02
    • Technical University of Denmark, Department of Mathematics, Building 303
Open AccessArticle

DOI: 10.1007/s00041-006-6069-y

Cite this article as:
Janssen, A. & Søndergaard, P. J Fourier Anal Appl (2007) 13: 211. doi:10.1007/s00041-006-6069-y

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 γk, the frame operators S and Sk corresponding to (g, a, b) and (γk, 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 iterations, 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.

Copyright information

© Birkhauser Boston 2007