计算机工程与应用 ›› 2007, Vol. 43 ›› Issue (9): 72-75.

• 学术探讨 • 上一篇    下一篇

外在趋势对 1/f 噪声的影响及其消除方法

田泽 谢端 赵健 韩俊刚   

  1. 西北大学电子科学系
  • 收稿日期:2006-04-18 修回日期:1900-01-01 出版日期:2007-03-21 发布日期:2007-03-21
  • 通讯作者: 赵健

Trends in 1/f noise : effect and remedies

zhao jian   

  • Received:2006-04-18 Revised:1900-01-01 Online:2007-03-21 Published:2007-03-21
  • Contact: zhao jian

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

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