An uncertainty principle for finite frames
type: Item
instance of: scholarly article
title: An uncertainty principle for finite frames
zbMATH Open document ID: 1203.42040
author: Anna Maeser
author: Mark C. Lammers
published in: Journal of Mathematical Analysis and Applications
publication date: 2010-10-22T00:00:00Z
review text: In this article the authors define an uncertainty principle for finite frames. They begin by developing a time-frequency localization measure for the entire frame using a difference operator. Then they prove that a subset of columns of the discrete Fourier transform matrix are optimal for minimizing this measure over all equal norm Parseval frames. This gives a sharp constant for the lower bound which is dependent on the dimension of the space and the number of elements in the frame. The authors also find a minimizer and bounds for the time-frequency measure in the case of Parseval frames which are not necessarily equal norm. Next they show that given any matrix whose columns form a frame, it is possible to generate a dual frame that minimizes the finite time-frequency measure. Finally, to illustrate this, the authors generate a random frame and compare the time-frequency localization of this dual with the canonical one.
Mathematics Subject Classification ID: 42C15
zbMATH DE Number: 5804456
zbMATH Keywords: frames
zbMATH Keywords: Gauss-Hermite differential equation
zbMATH Keywords: time-frequency dual
zbMATH Keywords: uncertainty principle
reviewed by: Magalí Anastasio
MaRDI profile type: Publication
full work available at URL: j.jmaa.2010.06.048
OpenAlex ID: W1994919943
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DOI: 10.1016/J.JMAA.2010.06.048
description: scientific article; zbMATH DE number 5804456