基于小波变换的分形随机信号希尔伯特变换的波形估计(英文)

WAVEFORM ESTIMATION FOR HILBERT TRANSFORM OF FRACTAL STOCHASTIC SIGNALS USING WAVELET TRANSFORM

非平稳 1/ f类分形随机过程是一类重要的弱自相似随机过程 ,其典型例子是分形布朗运动 .作者考察了弱自相似过程的希尔伯特变换 ,证明了希尔伯特变换具有弱自相似不变性 .进而利用分形布朗运动的希尔伯特变换 ^BH(t)小波系数能量向低频集中的特性 ,采用最优门限方法实现 ^BH(t)

Those splendid characters of the Hilbert transform let the processes that taking wavelet transform after taking Hilbert transform for the statistic self similarity processes B H(t) become another processes, that firstly taking Hilbert transform for the wavelet function (t) and forming a new wavelet function ψ(t) , secondly taking the wavelet transform for B H(t). Then, the authors use the optimum threshold to estimate the 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.