Frame Multiplier: Theory and Application in Acoustics (WWTF 2007)

This project ended in September 2011.

Media Coverage:


The final MulAc Meeting was in Vienna from 29th to 30th of August 2011.

The ARI Mulac Frame Meeting was held on Tuesday, June 15th 2010at ARI.

The MULAC Mid-term Meeting was held in Marseille from 12. to 13. April 2010. See the Registration-Webpage or the Program.

The FYMA Mulac seminar was held in Louvain-la-Neuve in the 11th of March, 2010. (Talks by Jean-Pierre Antoine, Jean-Pierre Gazeau, Diana Stoeva and Peter Balazs.)

The MULAC - Kick-Off Meeting took place at ARI in Vienna from September 23rd to 24th 2008.

This international, multi-disciplinary and team-oriented project allowed P. Balazs to form a small group 'Mathematics and Acoustical Signal Processing’ at the Acoustic Research Institute in cooperation with NuHAG Vienna (Hans G. Feichtinger),LMA (Richard Kronland-Martinet) and LATP Marseille (Bruno Torrésani) as well as the FYMA Louvain-la-Neuve (Jean-Pierre Antoine).

Within the institute the groups 'Audiological Acoustics' and 'Software Development' are involved.

This project is funded by the WWTF . It will run for 3,5 years and post-docs will be employed for six years total, as well as master students for 36 months total.

In December 2007 the Austrian Academy of Sciences was presenting 'mathematics in ...' as the topic of the month . This included 'mathematics at the Acoustics Research Institute', which describes this project.

General description

"Frame Multipliers” are a promising mathematical concept, which can be applied to retrieve desired information out of acoustic signals. P. Balazs introduced them by successfully generalizing existing time-variant filter approaches. This project aims to establish new results in the mathematical theory of frame multipliers, to integrate them in efficient digital signal processing algorithms and to make them available for use in 'real-world' acoustical applications. A multi-disciplinary and international cooperation has been established and will be extended in the project to create new significant impulses for the involved disciplines: mathematics, numerics, engineering, physics and cognitive sciences. Various acoustical applications like modelling of auditory perception, measurement of sound absorption coefficients and system identification of the head related transfer functions are included. The results of the project will allow their future integration into practical areas such as audio coding, noise abatement, sound quality design, virtual reality and hearing aids. 


Time-variant digital filtering algorithms have attracted more and more attention in numerous signal processing applications of today’s life. One approach to implement such filters is to use Gabor multipliers, which are currently an active and dynamic research field in mathematics. By generalizing this approach, P. Balazs has recently introduced the concept of frame multipliers.

Preliminary results of the preparatory research performed by the project partners already show a strong potential for both the theoretical development and the applicability in 'real-life' audio. Frame theory is a highly attractive discipline of mathematics, whose results have been proved to be particularly relevant for applications in digital signal processing. The project aims to exploit this strong link, as well as its use in acoustical applications. While Gabor multipliers have been investigated in the past, frame multipliers using specific frames with their high potential far beyond conventional applications still need research. 

The use of the theory of frame multipliers for acoustic applications and the mathematical investigation of (discrete) wavelet frame multipliers are innovations and seem to be highly promising. To investigate this potential to its fullest extent, an international cooperation based on joint research and vigorous knowledge exchange is considered to be essential. The international project team stands for strong links to international partner projects and for providing a solid basis for the solution of the scientific problems involved.

The project involves the following main topics:

  • mathematical investigation of analytical properties of frame multipliers
  • mathematical formulations of digital signal processing methods related to frame multipliers and systematic numerical validation.
  • implementation of digital signal processing algorithms in general purpose computer programs
  • applications to research fields in acoustics and associated areas.

The acoustical applications are expected to yield important benefits for the utilization in real life. The research results of the project’s application-oriented work packages [A1-A3] will allow the implementation of new methods for noise abatement, sound quality design, audio coding, virtual reality and hearing aids. At least one of the project’s developments is expected to be extended to a patentable method. The practical research work will include knowledge transfer between the different disciplines as well as an intensive exchange between the groups involved. The project is structured in the following work packages:

Theory of Frame Multipliers

Implementation and Application of Multipliers in Acoustics and Psychoacoustics

The research groups participating in the project have an international reputation for advanced research in their fields, as well as a record for successful interdisciplinary collaborations. The project will further benefit from synergetic effects of several ongoing international partner projects with different but related topics.



  • P. Majdak, P. Balazs, W. Kreuzer  and M. Dörfler, “A Time-Frequency Method for Increasing the Signal-To-Noise Ratio in System Identification with Exponential Sweeps”, ICASSP 2011, Prague, 2011 (accepted)
  • B. Laback, P. Balazs, T. Necciari, S. Savel,  S. Ystad, S. Meunier, R. Kronland-Martinet, "Additivity of auditory masking for short Gaussian-shaped sinusoids"The Journal of the Acoustical Society of America. to appear (2010)
  • P. Balazs, D. Stoeva, J. P. Antoine, "Classification of General Sequences by Frame-Related Operators", Sampling Theory in Signal and Image Processing (STSIP), to appear (2010)
  • Asghar Rahimi, “Multipliers of Generalized frames", Bulletin of Iranian mathematical society, vol. 35, pp. 97-109 (2009)
  • A. Rahimi, P. Balazs, "Multipliers for  p-Bessel sequences in Banach spaces", Integral Equations and Operator Theory, vol. 68, pp. 193-205 (2010)
  • P. Balazs, J.-P. Antoine, A. Grybos: Mutual relationship and first Numerical Properties"International Journal of Wavelets, Multiresolution and Information Processing vol. 8, pp. 109-132, 2010,  preprint
  • Monika Dörfler and Bruno Torrésani, "Representation of operators in the time-frequency domain and generalized Gabor multipliers", J. Fourier Anal. Appl., vol. 16, pp. 261-293 (2010)
  • 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. 18 (1) , pp. 34-49 (2010)
  • D. Stoeva and P. Balazs, “Weighted Frames and Frame Multipliers”, Proceedings of the International Conference UACEG2009: Science & Practice, 29-31 October 2009
  • P. Balazs, "Matrix Representation of Bounded Linear Operators By Bessel Sequences, Frames and Riesz Sequence",SampTA'09, 8th International Conference on Sampling and Applications, May 2009, Marseille, France
  • F. Jaillet, P. Balazs and M. Dörfler, "Nonstationary Gabor Frames", SampTA'09, 8th International Conference on Sampling and Applications, May 2009, Marseille, France
  • M. Dörfler, B. Torrésani : „Representation of operators by sampling in the time-frequency domain“, SampTA'09, 8th International Conference on Sampling and Applications, May 2009, Marseille, France
  • P. Balazs, “Matrix Representation of Bounded Linear Operators By Bessel Sequences, Frames and Riesz Sequence“,SampTA'09, 8th International Conference on Sampling and Applications, May 2009, Marseille, France


  • A. Olivero, B. Torrésani and R. Kronland-Martinet, "Estimation de multiplicateur de Gabor et algorithmes d'optimisation", Congrès Français d'Acoustique (2010)
  • A. Olivero, B. Torrésani and R. Kronland-Martinet, "A new method for Gabor multipliers estimation: application to sound morphing", EUSIPCO 2010
  • F. Jaillet, P. Balazs, M. Dörfler and N. Engelputzeder, "On the Structure of the Phase around the Zeros of the Short-Time Fourier Transform" ,NAG/DAGA 2009, International Conference on Acoustics, March 2009, Rotterdam, Nederland, pp. 1584-1587
  • M. Dörfler; P. Balazs amd F. Jaillet, “Removing Components from a Time-Frequency Representation” NAG/DAGA 2009, pp. 1596-1599
  • A. Olivero, L. Daudet, R. Kronland-Martinet and B. Torrésani,"Analyse et catégorisation de sons par multiplicateurs temps-fréquence", Proceedings of GRETSI'09, Dijon (France), September 2009
  • B. Laback, P. Balazs, G. Toupin, T. Necciari, S. Savel, S. Meunier, S. Ystad and R. Kronland-Martinet, "Additivity of auditory masking using Gaussian-shaped tones", Acoustics'08, Paris, 29.06.-04.07.2008 (03.07.2008)
  • Anaïk Olivero: "Expérimentation des multiplicateurs temps-échelle" (On the time-scale multipliers) Master thesis under the supervision of R. Kronland-Martinet and B. Torrésani, June 2008
  • Yohan Frutiger: "Multiplicateurs de Gabor pour les transformations sonores" (Gabor Multipliers for sound transformations) Master thesis under the supervision of R. Kronland-Martinet, June 2008