Title :
Some counterexamples in the theory of Weyl-Heisenberg frames
Author :
Janssen, A. J E M
Author_Institution :
Philips Res. Lab., Eindhoven, Netherlands
fDate :
3/1/1996 12:00:00 AM
Abstract :
We present an example of a positive function g with a positive Fourier transform gˆ and reasonable smoothness and decay properties such that (-1)nmexp(πitm)g(t-n), n, m∈Z 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)definiteness of its Weyl symbol
Keywords :
Fourier transforms; information theory; mathematical operators; time-frequency analysis; Weyl symbol; Weyl-Heisenberg frames; Zak transform; decay properties; definiteness; indefiniteness; positive Fourier transform; positive function; smoothness properties; time frequency analysis; Displays; Electronic switching systems; Fourier transforms; Smoothing methods; Time frequency analysis;
Journal_Title :
Information Theory, IEEE Transactions on
