Fischer R, Akay M
Biomedical Engineering Department, Rutgers University, Piscataway, NJ 08855, USA.
Ann Biomed Eng. 1996 Jul-Aug;24(4):537-43. doi: 10.1007/BF02648114.
Fractional Brownian motion (FBM) provides a useful model for many physical phenomena demonstrating long-term dependencies and l/f-type spectral behavior. In this model, only one parameter is necessary to describe the complexity of the data, H, the Hurst exponent. FBM is a nonstationary random function not well suited to traditional power spectral analysis however. In this paper we discuss alternative methods for the analysis of FBM, in the context of real-time biomedical signal processing. Regression-based methods utilizing the power spectral density (PSD), the discrete wavelet transform (DWT), and dispersive analysis (DA) are compared for estimation accuracy and precision on synthesized FBM datasets. The performance of a maximum likelihood estimator for H, theoretically the best possible estimator, are presented for reference. Of the regression-based methods, it is found that the estimates provided by the DWT method have better accuracy and precision for H > 0.5, but become biased for low values of H. The DA method is most accurate for H < 0.5 for a 256-point data window size. The PSD method was biased for both H < 0.5 and H > 0.5.
分数布朗运动（FBM）为许多呈现长期相关性和1/f型频谱行为的物理现象提供了一个有用的模型。在这个模型中，只需要一个参数来描述数据的复杂性，即Hurst指数H。然而，FBM是一种非平稳随机函数，不太适合传统的功率谱分析。在本文中，我们在实时生物医学信号处理的背景下讨论了分析FBM的替代方法。比较了基于回归的方法，这些方法利用功率谱密度（PSD）、离散小波变换（DWT）和色散分析（DA），以评估它们在合成FBM数据集上的估计准确性和精度。还给出了H的最大似然估计器的性能，理论上这是可能的最佳估计器，以供参考。在基于回归的方法中，发现对于H>0.5，DWT方法提供的估计具有更好的准确性和精度，但对于低值H会产生偏差。对于256点的数据窗口大小，DA方法在H<0.5时最准确。PSD方法在H<0.5和H>0.5时都会产生偏差。
