Some counterexamples in the theory of Weyl-Heisenberg frames

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Abstract

We present an example of a positive function g with a positive Fourier transform <i and reasonable smoothness and decay properties such that (-1)nmexp(p'tm)g(t-n), n,m eZ does not constitute a frame for L2(R). We also give counterexamples for the statement that one can tell (in)definiteness of a Weyl-Heisenberg frame operator from (in)deflniteness of its Weyl symbol. Index Terms-Weyl-Heisenberg frame, Zak transform, Weyl symbol.
Original languageEnglish
Pages (from-to)621-623
Number of pages3
JournalIEEE Transactions on Information Theory
Volume42
Issue number2
DOIs
Publication statusPublished - 1996

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