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arXiv · 2001.08518

Data approximation with time-frequency invariant systems

D. Barbieri·C. Cabrelli·E. Hernández·U. Molter
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Abstract

In this paper we prove the existence of a time-frequency space that best approximates a given finite set of data. Here best approximation is in the least square sense, among all time-frequency spaces with no more than a prescribed number of generators. We provide a formula to construct the generators from the data and give the exact error of approximation. The setting is in the space of square integrable functions defined on a second countable LCA group and we use the Zak transform as the main tool.

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D. Barbieri, C. Cabrelli, E. Hernández, U. Molter. 2020-01-23. Data approximation with time-frequency invariant systems. https://arxiv.org/abs/2001.08518

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