2009, English, Article edition: Wavelet Packets of fractional Brownian motion: Asymptotic Analysis and Spectrum Estimation Atto, Abdourrahmane; Pastor, Dominique; Mercier, Grégoire

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Bookmark: http://trove.nla.gov.au/version/199445
Physical Description
  • text
Published
  • HAL - CCSD
  • 2009
Language
  • English

Edition details

Title
  • Wavelet Packets of fractional Brownian motion: Asymptotic Analysis and Spectrum Estimation
Author
  • Atto, Abdourrahmane
  • Pastor, Dominique
  • Mercier, Grégoire
Published
  • HAL - CCSD
  • 2009
Physical Description
  • text
Subjects
Notes
  • 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.
  • HAL:hal-00409479, version 1
  • HAL:http:/​/​hal.archives-ouvertes.fr/​hal-00409479/​en/​
Language
  • English
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