caa a22 4500 463247043 CHVBK 20180405153329.0 cr unu---uuuuu 170326e20070401xx s 000 0 eng 10.1007/s00041-006-6069-y doi (NATIONALLICENCE)springer-10.1007/s00041-006-6069-y Iterative Algorithms to Approximate Canonical Gabor Windows: Computational Aspects [Elektronische Daten] [A.J.E.M. Janssen, Peter L. Søndergaard] 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. Birkhauser Boston, 2007 Janssen A.J.E.M. Philips Research Laboratories WO-02, 5656AA Eindhoven, The Netherlands aut Søndergaard Peter L. Technical University of Denmark, Department of Mathematics, Building 303, 2800 Lyngby, Denmark aut Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/2(2007-04-01), 211-241 1069-5869 13:2<211 2007 13 41 https://doi.org/10.1007/s00041-006-6069-y text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00041-006-6069-y text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Janssen A.J.E.M. Philips Research Laboratories WO-02, 5656AA Eindhoven, The Netherlands aut NATIONALLICENCE 700 1- Søndergaard Peter L. Technical University of Denmark, Department of Mathematics, Building 303, 2800 Lyngby, Denmark aut NATIONALLICENCE 773 0- Journal of Fourier Analysis and Applications Birkhäuser-Verlag; www.birkhauser.com 13/2(2007-04-01), 211-241 1069-5869 13:2<211 2007 13 41 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer