Best time localized trigonometric polynomials and wavelets
type: Item
instance of: scholarly article
title: Best time localized trigonometric polynomials and wavelets
zbMATH Open document ID: 1069.42001
author: Holger Rauhut
published in: Advances in Computational Mathematics
publication date: 2005-04-29T00:00:00Z
review text: As analogon to the Heisenberg uncertainty principle for \(L^2\)-functions, \textit{E. Breitenberger} [Found. Phys. 15, 353--364 (1983)] has introduced an uncertainty principle for \(2\pi\)-periodic functions which is formulated in terms of angular variance and frequency variance. The angular variance is a time localization measure for \(2\pi\)-periodic functions. In this paper, the author determines the minimum of the angular variance in the space \({\mathbb T}_n\) of all trigonometric polynomials of order \(\leq n\) and in the space \({\mathbb T}_m^n = {\mathbb T}_n \ominus {\mathbb T}_m\) \((1\leq m \leq n)\). Best time localized trigonometric polynomials are determined. Furthermore, trigonometric wavelets and wavelet packets are constructed with these trigonometric polynomials.
reviewed by: Manfred Tasche
Mathematics Subject Classification ID: 42A05
Mathematics Subject Classification ID: 42A10
Mathematics Subject Classification ID: 42C40
zbMATH DE Number: 2162392
zbMATH Keywords: uncertainty principle
zbMATH Keywords: time-frequency localization
zbMATH Keywords: trigonometric polynomials
zbMATH Keywords: trigonometric wavelets
zbMATH Keywords: angular variance
zbMATH Keywords: best time localization
MaRDI profile type: Publication
full work available at URL: s10444-005-7411-7
OpenAlex ID: W2064831415
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DOI: 10.1007/S10444-005-7411-7
description: scientific article; zbMATH DE number 2162392