外在趋势对1/f噪声的影响及其消除方法

1/f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)可以很好地弥补这种不足。但有研究发现,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。论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1/f噪声去趋势分析的影响,可以从中看到这种影响会给分析带来很大的误差。为了消除这种影响,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得很好。

Trends in 1/f noise:effect and remedies

Detrended fluctuation analysis has been used to quantify long-range power-law correlations in 1/f 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.This paper proposes a technique based on singular-value decomposition of the Toeplitz matrix to minimize the effect of rends superimposed on long-range correlated 1/f noise.Experimental results agree with the anticipant results well.