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Gabor analysis is playing an important role in time-frequency analysis for the last 60 years. The fundamental concept of Gabor frames has become a focus also in the finite dimensional setting. Here, we study which sets of discrete time frequency shifts admit a proper choice of window vector, so that they generate an orthonormal Gabor basis in the underlying finite dimensional vector space. We fully...
We study the recovery of operators with a bandlimited Kohn–Nirenberg symbol from the action of such operators on a weighted impulse train, a procedure we refer to as sampling of operators. Kailath, Bello, and later Kozek and the authors have shown that the sampling of operators is possible if the symbol of the operator is bandlimited to a set with area less than one. In this paper, we develop the...
Operator sampling considers the question of when operators of a given class can be distinguished by their action on a single probing signal. The fundamental result in this theory shows that the answer depends on the area of the support S of the so-called spreading function of the operator (i.e., the symplectic Fourier transform of its Kohn-Nirenberg symbol). |S| < 1 then identification is possible...
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