### Basic Description:

Time-variant filters are gaining importance in today's signal processing applications. Gabor multipliers in particular are popular in current scientific investigations. These multipliers are a specialization of Bessel multipliers to Gabor frames. These operators are interesting in regard to both theory and application:

### Theory of Multipliers:

- Bessel and Frame Multipliers in Banach Spaces: In this project, the concept of frame multipliers should be generalized to work with Banach spaces.
- Theory of Wavelet Multipliers: The concept of multipliers can be easily extended to wavelet frames. The influence of the special structures of these sequences will be investigated.
- Basic Properties of Irregular Gabor Multipliers: Here multipliers for Gabor frames on irregular lattices are investigated.

### Application of Multipliers:

- Time Frequency Masking: Gabor Multiplier Models and Evaluation: The symbol for the Gabor multiplier is calculated adaptively and the resulting model incorporates both time and frequency masking components. The goal is to obtain an algorithm using 2-D convolution.
- Improving the Multiple Exponential Sweep Method (MESM) using Gabor Multipliers: The MESM is an efficient system identification method. Initial tests have shown that this method can be improved with a Gabor multiplier applied as a mask for the original sweep.
- Wavelet Multipliers and Their Application to Reflection Measurements: One method to calculate the absorption coefficient of a sound proof wall requires separation of the impulse responses of different reflections. They can be easily separated in a scalogram and they can be extracted using a wavelet multiplier.
- Mathematical Foundation of the Irrelevance Model: In this project, the theoretical foundation of the irrelevance algorithms implemented in STx is being developed.

### Partners:

- H.G. Feichtinger, K. Gröchenig et al., NuHAG, Faculty of Mathematics, University of Vienna
- R. Kronland-Martinet, S. Ytad, T. Necciari, Modélisation, Synthèse et Contrôle des Signaux Sonores et Musicaux of the LMA / CRNS Marseille
- S. Meunier, S. Savel, Acoustique perceptive et qualité de l’environnement sonore of the LMA / CRNS Marseille

### Publications:

- P. Balazs, B. Laback, G. Eckel, W. Deutsch, "Introducing Time-Frequency Sparsity by Removing Perceptually Irrelevant Components Using a Simple Model of Simultaneous Masking", IEEE Transactions on Audio, Speech and Language Processing, Vol. 17 (7) , in press (2009) , preprint
- P. Majdak, P. Balazs, B.Laback, "Multiple Exponential Sweep Method for Fast Measurement of Head Related Transfer Functions", Journal of the Acoustical Engineering Society , Vol. 55, No. 7/8, July/August 2007, Pages 623 - 637 (2007)

### Project-completion:

This project ended on 01.01.2010; most subprojects ended on 28.02.2008 and are incorporated into the 'High Potential'-Project of the WWTF, MULAC.