A quantitative Balian-Low theorem
Shahaf Nitzan, Jan-Fredrik Olsen
TL;DR
This paper provides a quantitative extension of the classical Balian-Low theorem, offering new bounds on the localization of functions generating Gabor Riesz bases on the integer lattice.
Contribution
It introduces a quantitative estimate that generalizes the Balian-Low theorem and related results, enhancing understanding of time-frequency localization constraints.
Findings
Derived a new quantitative bound for Gabor Riesz basis generators
Extended classical Balian-Low theorem to a broader, quantitative context
Provided insights into the limitations of simultaneous time and frequency localization
Abstract
We study functions generating Gabor Riesz bases on the integer lattice. The classical Balian-Low theorem restricts the simultaneous time and frequency localization of such functions. We obtain a quantitative estimate that extends both this result and other related theorems.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Digital Filter Design and Implementation · Image and Signal Denoising Methods