Abstract: Detrended fluctuation analysis has been used to quantify long-range power-law correla- tions in noise. However, recent studies have reported the susceptibility of DFA to trends, Trends such as linear, power-law and periodic trends have been found to give rise to crossovers in the log–log plots of the fluctuation function versus time scale and reflect spurious existence of more than a single scaling exponent at different time scales, These trends also prevent reliable estimation of the scaling exponent.In this paper, we propose a technique based on singular-value decomposition of the Toeplitz matrix to minimize the effect of rends superimposed on long-range correlated noise. Experimental results agree with the anticipant results well.

Key words: noise, Detrended Fluctuation Analysis, power-law correlation, singular-value

摘要： 噪声信号存在着长程的幂律相关性，对于平稳的噪声信号，经典的功率谱分析方法可以准确度量这种关联性，而对于非平稳噪声信号，功率谱法误差较大。近年来发展起来的去趋势分析法(Detrended Fluctuation Analysis)可以很好的弥补这种不足。但有研究发现，我们实测的噪声信号容易受到外界趋势的干扰，即使用去趋势分析法，也会产生错误。本文举出了几种典型的外界趋势（线性趋势、指数增长趋势、周期正弦趋势）对 噪声去趋势分析的影响，可以从中看到这种影响会给我们的分析带来很大的误差。为了消除这种影响，本文提出了一种新的计算方法：在去趋势分析之前，先用特征值分解的方法，从仿真信号中分离出外界的趋势，再应用去趋势法进行计算。应用此法后，实际计算结果与预期结果吻合的很好。

关键词: 噪声, 去趋势分析, 幂律关联性, 特征值分解