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Communication Dans Un Congrès Année : 2007

Spreading function representation of operators and Gabor multiplier approximation

Résumé

Modification of signals in the time-frequency domain are used in many applications. However, the modification is often restricted to be purely multiplicative. In this paper, it is shown that, in the continuous case, a quite general class of operators can be represented by a twisted convolution in the short-time Fourier transform domain. The discrete case of Gabor transforms turns out to be more intricate. A similar representation will however be derived by means of a special form for the operator's spreading function (twisted spline type function). The connection between STFT- and Gabor-multipliers, their spreading function and the twisted convolution representation will be investigated. A precise characterization of the best approximation and its existence is given for both cases. Finally, the concept of Gabor multipliers is generalized to better approximate ''overspread'' operators.
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Dates et versions

hal-00146274 , version 1 (14-05-2007)

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  • HAL Id : hal-00146274 , version 1

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Monika Dörfler, Bruno Torrésani. Spreading function representation of operators and Gabor multiplier approximation. SAMPTA'07, Sampling Theory and Applications, Jun 2007, Thessaloniki, Greece. ⟨hal-00146274⟩
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