On the chirp decomposition of Weierstrass-Mandelbrot functions, and their time-frequency interpretation.
type: Item
instance of: scholarly article
title: On the chirp decomposition of Weierstrass-Mandelbrot functions, and their time-frequency interpretation.
zbMATH Open document ID: 1054.94002
DOI: 10.1016/S1063-5203(03)00047-2
author: Pierre Borgnat
author: Patrick Flandrin
published in: Applied and Computational Harmonic Analysis
publication date: 2003-11-16T00:00:00Z
review text: The authors provide a time-frequency interpretation of Weierstrass-Mandelbrot functions which puts emphasis on their possible decomposition on chirps, i.e. amplitude and frequency modulated signals of the form \(a(t)\exp\{i\psi(t)\}\) with \(\psi(t)=2\pi f\log t\), as an alternative to their standard Fourier-based representation. The authors consider examples of so-defined deterministic functions and their randomised variants and the relevant estimation problems.
Mathematics Subject Classification ID: 94A12
Mathematics Subject Classification ID: 28A80
Mathematics Subject Classification ID: 94A14
Mathematics Subject Classification ID: 26A27
zbMATH DE Number: 2003854
zbMATH Keywords: Weierstrass function
zbMATH Keywords: time-frequency
zbMATH Keywords: chirps
reviewed by: Ilya S. Molchanov
describes a project that uses: Matlab
describes a project that uses: Time-frequency Toolbox
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2003854