Research

Discrete Gabor Analysis

Basic Description

This project line has the goal of finding efficient algorithms for signal processing applications. To apply the results of signal processing, Gabor or wavelet theory, the algorithms must be formulated for finite dimensional vectors. These discrete results are motivated by the continuous setting, but also often provide some insight. Furthermore, the efficient implementation of algorithms becomes important. For the consistency of these algorithms, it is useful to incorporate them into a maintained software package.

Subprojects

  • Double Preconditioning for Gabor Frames: This project develops a way to find an analysis-synthesis system with perfect reconstruction in a numerically efficient way using double preconditioning.
  • Perfect Reconstruction Overlap Add Method (PROLA): The classic overlap-add synthesis method is systematically compared to a new method motivated by frame theory.
  • Numerics of Block Matrices: In some applications in acoustics, it is apparent that block matrices are a powerful tool to find numerically efficient algorithms.
  • Practical Time Frequency Analysis: This project evaluates the usefulness of a time-frequency toolbox for acoustic applications and STx.

Partners

  • H.G. Feichtinger et al., NuHAG, Faculty of Mathematics, University of Vienna
  • B. Torrésani, Groupe de Traitement du Signal, Laboratoire d'Analyse Topologie et Probabilités, LATP/ CMI, Université de Provence, Marseille
  • P. Soendergaard, Department of Mathematics, Technical University of Denmark
  • J. Walker, Department of Mathematics, University of Wisconsin-Eau Claire

Publications

  • P. Balazs, H.G. Feichtinger, M. Hampejs, G. Kracher; "Double Preconditioning for Gabor Frames”; IEEE Transactions on Signal Processing, Vol. 54, No.12, December 2006 (2006), preprint
  • P. Balazs, H.G. Feichtinger, M. Hampejs, G. Kracher; "Double Preconditioning for the Gabor Frame Operator”; Proceedings ICASSP '06, May 14-19, Toulouse, DVD (2006)