基于谱密度的分形高斯噪声数据合成和估计

分形高斯噪声FGN是分形布朗运动的增量过程，广泛应用于自相似过程的建模分析。在众多的合成分形高斯噪声的方法中，研究了基于功率谱的FGN的生成算法，谱模拟方法和Paxson方法的特点以及联系．同时对基于功率谱的Hurst指数的估计方法，周期图法进行了讨论。仿真试验中，使用Paxson方法生成了FGN序列数据．试验结果表明生成的FGN具有很好的自相似性。应用周期图法估计了其Hurst指数，相比方差时间法，周期图法在估计长相关过程的参数方面能够提高精度。

Spectrum Density Application in Synthesis and Estimation for Fractional Gaussian Nioise

Fractional Gaussian Noise(FGN) is the increment process of fractional Brownian motion, they are widely used in modelling self-similar process. Among so many synthesis methods for FGN, there are the spectrum-based approaches, spectral simulation and Paxson method, which features and the relation between are explored in this paper. Morever the spectrum-based estimation for hurst exponent, periodogram, is researched. In simulation experiments, FGN series are made with Paxson method, demonstrating a good self-similarity. Their hurst exponents are caculated in periodogram, the results tell that periodogram is more suitable for evaluating the long range dependence(LRD)process.