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

Abdourrahmane Atto (1) , Dominique Pastor (1, 2) , Grégoire Mercier (1, 2)

1 SC - Département Signal et Communications
2 Lab-STICC_TB_CID_TOMS

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.

Keywords: Spectral analysis.; Wavelet packet transforms; Fractional Brownian motion; Gray code; Spectral analysis

Domains: Information Theory [math.IT]; Information Theory [cs.IT]

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⟩