Regular and irregular Gabor multipliers with application to psychoacoustic masking / Peter Balazs

• VerfasserIn: Balazs, Peter
• Place / Publishing House: 2005
• Year of Publication: 2005
• Language: English
• Classification: 31.35 - Harmonische Analyse; 31.47 - Operatortheorie; 31.76 - Numerische Mathematik; 31.80 - Angewandte Mathematik; 53.71 - Theoretische Nachrichtentechnik
• Physical Description: a-j, 303 Bl.; Ill., graph. Darst.
• Notes: Begutachter: Feichtinger, Georg ; Torresani, B.

ger: In this work the mathematical background for time-frequency masking filter is investigated. The concept of frame multiplier is introduced. The so-called Gabor multipliers are a current topic of research. Frame multipliers are a generalization of this type of operators to frames without further structure. Basic results, like the dependency of the operator on the symbol, are proved.<br />Irregular Gabor frames are investigated. In particular some results on irregular Gabor multipliers are proved like the continuous dependency of Gabor multipliers on the symbol, the lattice and the windows. An algorithm is presented for the approximation of arbitrary matrices by irregular Gabor multipliers and is compared to existing algorithms.<br />For application the finite-dimensional discrete case is important. In this work apart other topics also an idea is investigated how to approximately invert the Gabor frame operator (for regular lattices) in a numerically efficient way by using a double preconditioning scheme.<br />Finally a concept is presented how to implement a filter, which approximates the simultaneous and temporal masking known in psychoacoustics. As the linear frequency scale (in Hz) is not very well adapted to human perception, another is chosen (Bark), so this filtering can be seen as an irregular Gabor multiplier with adaptive symbol.