Ten lectures on wavelets
Adapted wavelet analysis from theory to software
Adapted wavelet analysis from theory to software
Central Limit theorems for wavelet packet decompositions of stationary random processes
IEEE Transactions on Signal Processing
IEEE Transactions on Information Theory
High-order wavelet packets and cumulant field analysis
IEEE Transactions on Information Theory
Asymptotic decorrelation of between-Scale Wavelet coefficients
IEEE Transactions on Information Theory
Noise Covariance Properties in Dual-Tree Wavelet Decompositions
IEEE Transactions on Information Theory
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This paper 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.