Linear independence of a finite set of time-frequency shifts

Abstract

This paper introduces an open conjecture in time-frequency analysis on the linear independence of a finite set of time-frequency shifts of a given L² function. Firstly, background and motivation for the conjecture are provided. Secondly, the main progress of this linear independence in the past twenty five years is reviewed. Finally, the partial results of the high dimensional case and other cases for the conjecture are briefly presented.

Key words： Time-frequency shift; Gabor frame; wavelet; linear independence

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China (Grant No. 61471410) and the Construction Fund for Subject Innovation Term of Wuhan Textile University (No. 201401023).

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