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 FMB[B{sub}H(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 B{sub}H(t). Then, we use the optimum threshold to estimate the B{sub}H(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.
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