Wavelet analysis and synthesis of fractional Brownian motion

Author

Flandrin, P.

Author_Institution

LTS-ICPI, Lyon, France

Volume

38

Issue

2

fYear

1992

fDate

3/1/1992 12:00:00 AM

Firstpage

910

Lastpage

917

Abstract

Fractional Brownian motion (FBM) offers a convenient modeling for nonstationary stochastic processes with long-term dependencies and 1/f-type spectral behavior over wide ranges of frequencies. Statistical self-similarity is an essential feature of FBM and makes natural the use of wavelets for both its analysis and its synthesis. A detailed second-order analysis is carried out for wavelet coefficients of FBM. It reveals a stationary structure at each scale and a power-law behavior of the coefficients´ variance from which the fractal dimension of FBM can be estimated. Conditions for using orthonormal wavelet decompositions as approximate whitening filters are discussed, consequences of discretization are considered, and some connections between the wavelet point of view and previous approaches based on length measurements (analysis) or dyadic interpolation (synthesis) are briefly pointed out.<>

Keywords

Brownian motion; filtering and prediction theory; fractals; stochastic processes; transforms; 1/f-type spectral behavior; approximate whitening filters; discretization; dyadic interpolation; fractal dimension; fractional Brownian motion; length measurements; long-term dependencies; nonstationary stochastic processes; orthonormal wavelet decompositions; power-law behavior; self-similarity; stationary structure; wavelet analysis; wavelet synthesis; Brownian motion; Discrete wavelet transforms; Filters; Fractals; Frequency; Interpolation; Length measurement; Stochastic processes; Wavelet analysis; Wavelet coefficients;

fLanguage

English

Journal_Title

Information Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9448

Type

jour

DOI

10.1109/18.119751

Filename

119751