Abstract
Our first goal in this paper is to investigate stationarization and asymptotic decorrelation for fractional Brownian motion (fBm) using wavelet packet transform. The wavelet packets are generated by the $N^{\mathrm{ th}}$ -order Daubechies scaling function and wavelet. To decorrelate the wavelet packet coefficients asymptotically, we take two strategies: fix $N$ and let absolute scale difference or absolute difference between time shifts get large; and fix scale level and time shift and let $N$ get large. Our second goal is to present the asymptotic properties of the entropy-like cost functional and denoising cost functional and their impact on the selection of best wavelet packet bases when used for fBm plus or not plus independent Gaussian white noise.
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