Gabor multipliers: applied and theoretical aspects




Date(s) : 11/12/2014   iCal
10 h 00 min - 11 h 00 min

Gabor Multipliers are linear operators arising similar to Fourier multipliers: Given an input signal the Gabor expansions is obtained. After multiplication with a sequence of numbers the synthesis operator is applied. From an engineering point of view they are like actions of an audio-engineer who decides in a time-variant manner who the different frequency bands of a signal are amplified or damped. In the mathematical description one deals with function spaces, classes of operators, symbols etc.. For example, the question of best approximation of a given Hilbert Schmidt-operator by Gabor multipiers (in the Hilbert Schmidt norm) is translated into an approximation problem for spline-type functions (comparable to the question of approximating an L2-function on R by a cubic spline function). Gabor multipliers are easily implemented and even the theory of discrete Gabor multipliers provides a non-trivial and interesting chapter of linear algebra.

Hans Georg Feichtinger, Institute of Mathematics, University of Vienna

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