Abstract
We discuss the linear independence of systems ofmvectors in n-dimensional complex vector spaces where the m vectors are time-frequency shifts of one generating vector. Such systems are called Gabor systems. When n is prime, we show that there exists an open, dense subset with full-measure of such generating vectors with the property that any subset of n vectors in the corresponding full Gabor system of n2 vectors is linearly independent. We derive consequences relevant to coding, operator identification and time-frequency analysis in general.
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Lawrence, J., Pfander, G. & Walnut, D. Linear Independence of Gabor Systems in Finite Dimensional Vector Spaces. J Fourier Anal Appl 11, 715–726 (2005). https://doi.org/10.1007/s00041-005-5017-6
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DOI: https://doi.org/10.1007/s00041-005-5017-6