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Time-frequency shift invariance and the Amalgan Balian Low Theorem

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Type
Preprint
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Submission Date
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arXiv ID: 1410.7085
Source
arXiv
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Abstract

We consider smoothness properties of the generator of a principal Gabor space on the real line which is invariant under some additional translation-modulation pair. We prove that if a Gabor system on a lattice with rational density is a Riesz basis for its closed linear span, and if the closed linear span, a Gabor space, has any additional translation-modulation invariance, then its generator cannot decay well in time and in frequency simultaneously.

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