Wavelet analysis and synthesis of fractional Brownian motion
- 1 March 1992
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Information Theory
- Vol. 38 (2) , 910-917
- https://doi.org/10.1109/18.119751
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
This publication has 18 references indexed in Scilit:
- Estimation of fractal signals from noisy measurements using waveletsIEEE Transactions on Signal Processing, 1992
- Fractal dimension estimators for fractional Brownian motionsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1991
- Multiscale signal detection in fractional Brownian motionPublished by SPIE-Intl Soc Optical Eng ,1990
- A Karhunen-Loeve-like expansion for 1/f processes via waveletsIEEE Transactions on Information Theory, 1990
- A theory for multiresolution signal decomposition: the wavelet representationPublished by Institute of Electrical and Electronics Engineers (IEEE) ,1989
- Approach to an irregular time series on the basis of the fractal theoryPhysica D: Nonlinear Phenomena, 1988
- Fractional Brownian Motion: A Maximum Likelihood Estimator and Its Application to Image TextureIEEE Transactions on Medical Imaging, 1986
- Fractal structure of the interplanetary magnetic fieldJournal of Geophysical Research, 1986
- Decomposition of Hardy Functions into Square Integrable Wavelets of Constant ShapeSIAM Journal on Mathematical Analysis, 1984
- 1/f noiseProceedings of the IEEE, 1982