On the chirp decomposition of Weierstrass-Mandelbrot functions, and their time-frequency interpretation

被引：16

作者：

Borgnat, P ^{[1
]}

Flandrin, P ^{[1
]}

机构：

[1] Ecole Normale Super Lyon, CNRS, UMR 5672, Phys Lab, F-69364 Lyon 07, France

来源：

APPLIED AND COMPUTATIONAL HARMONIC ANALYSIS | 2003年 / 15卷 / 02期

关键词：

Weierstrass function; time-frequency; mellin; chirps;

D O I：

10.1016/S1063-5203(03)00047-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Weierstrass-Mandelbrot functions are given a time-frequency interpretation which puts emphasis on their possible decomposition on chirps as an alternative to their standard, Fourier-based, representation. Examples of deterministic functions are considered, as well as randomized versions for which the analysis is applied to empirical estimates of statistical quantities. (C) 2003 Elsevier Inc. All rights reserved.

引用

页码：134 / 146

页数：13

共 22 条

[1]

[Anonymous], TIME FREQUENCY TOOLB

[2]

[Anonymous], 1990, FRACTAL GEOMETRY

[3] IMPROVING THE READABILITY OF TIME-FREQUENCY AND TIME-SCALE REPRESENTATIONS BY THE REASSIGNMENT METHOD [J].

AUGER, F ;

FLANDRIN, P .

IEEE TRANSACTIONS ON SIGNAL PROCESSING, 1995, 43 (05) :1068-1089

[4] ON THE WEIERSTRASS-MANDELBROT FRACTAL FUNCTION [J].

BERRY, MV ;

LEWIS, ZV .

PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL AND PHYSICAL SCIENCES, 1980, 370 (1743) :459-484

[5]

Bertrand J., 1990, TRANSFORMS APPL HDB

[6] Stochastic discrete scale invariance [J].

Borgnat, P ;

Flandrin, P ;

Amblard, PO .

IEEE SIGNAL PROCESSING LETTERS, 2002, 9 (06) :181-184

[7]

BORGNAT P, 2002, THESIS ECOLE NORMALE

[8]

BORGNAT P, 2003, P INT C PHYS SIGN IM, P177

[9]

FLANDRIN P, 2001, SPIE, V4391

[10]

Flandrin P., 1999, TIME FREQUENCY TIME

← 1 2 3 →