### Abstract

Original language | English |
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Place of Publication | Lyngby |
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Publisher | Institut for Matematik, DTU |

Publication status | Published - 2006 |

Series | MAT Preprints |
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Number | 2006-2 |

### Cite this

*Iterative algorithms to approximate canonical Gabor windows: Computational aspects*. Lyngby: Institut for Matematik, DTU. MAT Preprints, No. 2006-2

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*Iterative algorithms to approximate canonical Gabor windows: Computational aspects*. MAT Preprints, no. 2006-2, Institut for Matematik, DTU, Lyngby.

**Iterative algorithms to approximate canonical Gabor windows: Computational aspects.** / Janssen, A.J.E.M; Søndergaard, Peter Lempel.

Research output: Book/Report › Report › Research

TY - RPRT

T1 - Iterative algorithms to approximate canonical Gabor windows: Computational aspects

AU - Janssen, A.J.E.M

AU - Søndergaard, Peter Lempel

PY - 2006

Y1 - 2006

N2 - In this paper 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}, the frame 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 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.

AB - In this paper 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}, the frame 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 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.

M3 - Report

BT - Iterative algorithms to approximate canonical Gabor windows: Computational aspects

PB - Institut for Matematik, DTU

CY - Lyngby

ER -