Wavelet transform method of waveform estimation for Hilbert transform of fractional stochastic signals with noise

Abstract

In this paper, those splendid characters of the Hilbert transform let the processes that taking wavelet transform after taking Hilbert transform for the statistic self-similarity processes FBM [BH (t)] become another processes, that firstly taking Hilbert transform for the wavelet function φ (t) and forming a new wavelet function ψ (t), secondly taking the wavelet transform for BH (t). Then, we use the optimum threshold to estimate the BH. (t) embedded in additive white noise. Typical computer simulation results to demonstrate the viability and the effectiveness of the Hilbert transform in the signal's estimation of the statistic self-similarity process.