A simple statistical analysis of wavelet-based multifractal spectrum estimation

Author

Gonçalves, Paulo ; Riedi, Rudolf ; Baraniuk, Richard

Author_Institution

Inst. Nat. de Recherche en Inf. et Autom., Rocquencourt, France

Volume

1

fYear

1998

fDate

1-4 Nov. 1998

Firstpage

287

Abstract

The multifractal spectrum characterizes the scaling and singularity structures of signals and proves useful in numerous applications, from network traffic analysis to turbulence. Of great concern is the estimation of the spectrum from a finite data record. We derive asymptotic expressions for the bias and variance of a wavelet-based estimator for a fractional Brownian motion (fBm) process. Numerous numerical simulations demonstrate the accuracy and utility of our results.

Keywords

Brownian motion; fractals; parameter estimation; spectral analysis; statistical analysis; wavelet transforms; accuracy; asymptotic expressions; bias; discrete-time data sequence; finite data record; finite-length data sequence; fractional Brownian motion process; network traffic analysis; numerical simulations; scaling structure; singularity structure; statistical analysis; turbulence; variance; wavelet-based multifractal spectrum estimation; Application software; Brownian motion; Fractals; Motion estimation; Signal analysis; Spectral analysis; Statistical analysis; Wavelet analysis; Wavelet coefficients; Wavelet domain;

fLanguage

English

Publisher

ieee

Conference_Titel

Signals, Systems & Computers, 1998. Conference Record of the Thirty-Second Asilomar Conference on

Conference_Location

Pacific Grove, CA, USA

ISSN

1058-6393

Print_ISBN

0-7803-5148-7

Type

conf

DOI

10.1109/ACSSC.1998.750873

Filename

750873