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Sampling and reconstruction of operators

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Pfander, Götz E. ; Walnut, David:
Sampling and reconstruction of operators.
In: IEEE transactions on information theory : a journal devoted to the theoretical and experimental aspects of information transmission, processing, and utilization. Bd. 62 (Januar 2016) Heft 1. - S. 435-458.
ISSN 0018-9448

Kurzfassung/Abstract

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 theory of the sampling of operators in analogy with the classical theory of sampling of bandlimited functions. We define the notions of sampling set and sampling rate for operators and give necessary and sufficient conditions on the sampling rate that depend on the size and geometry of the bandlimiting set. We develop explicit reconstruction formulas for operator sampling that generalize reconstruction formulas for bandlimited functions. We give necessary and sufficient conditions on the bandlimiting set under which sampling of operators is possible by their action on a given periodically weighted delta train. We show that under mild geometric conditions on the bandlimiting set, classes of operators are bandlimited to an unknown set of area less than one-half permit sampling and reconstruction. We generalize two results of the Heckel and Bölcskei concerning sampling of operators with area not greater than one-half and less than one, respectively, by finding a larger class of operators to which they apply. Operators with bandlimited symbols have been used to model doubly dispersive communication channels with slowly time-varying impulse response. The results in this paper are rooted in work by Bello and Kailath in the 1960s.

Weitere Angaben

Publikationsform:Artikel
Schlagwörter:Bandlimined Kohn-Nirenberg symbols; spreading function; operator Paley-Wiener space; channel measurement; channel identification; operator identification; sampling of operators; Gabor analysis; symplectic matrices
Institutionen der Universität:Mathematisch-Geographische Fakultät > Mathematik > Lehrstuhl für Mathematik - Wissenschaftliches Rechnen/Informatik
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DOI / URN / ID: 10.1109/TIT.2015.2501646
Peer-Review-Journal:Ja
Titel an der KU entstanden:Nein
Eingestellt am:28. Aug 2017 14:07
Letzte Änderung:28. Aug 2017 14:07
URL zu dieser Anzeige:http://edoc.ku-eichstaett.de/20490/