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This project consists of three subprojects:

### 1.1 Frame & Gabor Multiplier:

Recently Gabor Muiltipliers have been used to implement time-variant filtering as

*Gabor Filters*. This idea can be further generalized. To investigate the basic properties of such operators the concept of abstract, i.e. unstructured,*frames*is used. Such multipliers are operators, where a certain fixed mask, a so-called*symbol*, is applied to the coefficients of frame analysis , whereafter synthesis is done. The properties that can be found for this case can than be used for all kind of frames, for example regular and irregular Gabor frames, wavelet frames or auditory filterbanks.The basic definition of a frame multiplier follows:

As special case of such multipliers such operators for irregular Gabor system will be investigated and implemented. This corresponds to a irregular sampled Short-Time-Fourier-Transformation. As application an STFT correpsonding to the bark scale can be examined.

This mathematical and basic research-oriented project is important for many other projects like time-frequency-masking or system-identification.

#### References:

- O. Christensen,
*An Introduction To Frames And Riesz Bases*, Birkhäuser Boston (2003) - M. Dörfler,
*Gabor Analysis for a Class of Signals called Music*, Dissertation Univ. Wien (2002) - R.J. Duffin, A.C. Schaeffer,
*A Class of nonharmonic Fourier series*, Trans.Amer.Math.Soc., vol.72, pp. 341-366 (1952) - H. G. Feichtinger, K. Nowak,
*A First Survey of Gabor Multipliers*, in H. G. Feichtinger, T. Strohmer

#### Dokumente:

- Talk Frames and Frame Multiplier at the LMA, CNRS Marseille (Peter Balazs)

#### Kooperationen:

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