Data approximation with time-frequency invariant systems
Functional Analysis
2020-01-24 v1 Classical Analysis and ODEs
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.
Keywords
Cite
@article{arxiv.2001.08518,
title = {Data approximation with time-frequency invariant systems},
author = {D. Barbieri and C. Cabrelli and E. Hernández and U. Molter},
journal= {arXiv preprint arXiv:2001.08518},
year = {2020}
}
Comments
11 pages