Two results concerning chirps and 2-microlocal exponents prescription
type: Item
instance of: scholarly article
title: Two results concerning chirps and 2-microlocal exponents prescription
zbMATH Open document ID: 0930.42022
author: Bertrand Guiheneuf
author: Stéphane Jaffard
author: Jacques Lévy-Véhel
published in: Applied and Computational Harmonic Analysis
publication date: 2000-02-09T00:00:00Z
full work available at URL: Two results concerning chirps and 2-microlocal exponents prescription.pdf
review text: Harmonic analysis on the Heisenberg nilpotent Lie group is not only concerned with quantum physics but also with information transmission channels [\textit{W. Schempp}, ``Harmonic analysis on the Heisenberg nilpotent Lie group, with applications to signal theory'' (1986; Zbl 0632.43001)]. Due to the action of the metaplectic group, it allows to define chirp signals. In a more general parametrized setting, chirp signals can be used to provide information about the oscillatory behaviour of real-valued functions near a Hölder singularity that goes beyond the Hölder exponent characterization. The paper under review describes by means of two microlocalization techniques the local behaviour of such a function on the real line \(\mathbb{R}\). The parametrized description of the local behaviour is performed in terms of a combination of Hölder exponents as a measure of pointwise regularity and chirp exponents.
Mathematics Subject Classification ID: 42C40
Mathematics Subject Classification ID: 94A12
zbMATH DE Number: 1228533
zbMATH Keywords: wavelets
zbMATH Keywords: chirp signals
zbMATH Keywords: microlocalization techniques
zbMATH Keywords: Hölder exponents
zbMATH Keywords: chirp exponents
reviewed by: Walter Schempp
MaRDI profile type: Publication
OpenAlex ID: W2021558137
cites work: Oscillating singularities on Cantor sets: A grand-canonical multifractal formalism
cites work: Q3822600
cites work: Construction of continuous functions with prescribed local regularity
cites work: Pointwise smoothness, two-microlocalization and wavelet coefficients
cites work: Functions with prescribed Hölder exponent
cites work: Wavelet methods for pointwise regularity and local oscillations of functions
cites work: FRACTAL APPROACHES IN SIGNAL PROCESSING
DOI: 10.1006/ACHA.1997.0241
description: scientific article; zbMATH DE number 1228533