Wavelet Packets of fractional Brownian motion: Asymptotic Analysis and Spectrum Estimation - Archive ouverte HAL Access content directly
Journal Articles IEEE Transactions on Information Theory Year : 2009

Wavelet Packets of fractional Brownian motion: Asymptotic Analysis and Spectrum Estimation

(1) , (1, 2) , (1, 2)
1
2

Abstract

This work provides asymptotic properties of the autocorrelation functions of the wavelet packet coefficients of a fractional Brownian motion. It also discusses the convergence speed to the limit autocorrelation function, when the input random process is either a fractional Brownian motion or a wide-sense stationary second-order random process. The analysis concerns some families of wavelet paraunitary filters that converge almost everywhere to the Shannon paraunitary filters. From this analysis, we derive wavelet packet based spectrum estimation for fractional Brownian motions and wide-sense stationary random processes. Experimental tests show good results for estimating the spectrum of 1/f processes.
Fichier principal
Vignette du fichier
AsympFracBrownMotionWP_9_.pdf (270.51 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-00409479 , version 1 (08-08-2009)

Identifiers

Cite

Abdourrahmane Atto, Dominique Pastor, Grégoire Mercier. Wavelet Packets of fractional Brownian motion: Asymptotic Analysis and Spectrum Estimation. IEEE Transactions on Information Theory, 2009, 56 (9), pp.4741-4753. ⟨10.1109/TIT.2010.2053865⟩. ⟨hal-00409479⟩
140 View
234 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More