Effect of nonlinear filters on detrended fluctuation analysis
Effect of nonlinear filters on detrended fluctuation analysis
复制标题
DOI：
10.1103/physreve.71.011104
复制
发表时间：
2005-01-01
影响因子：
2.4
通讯作者：
Ivanov, PC
中科院分区：
文献类型：
--
作者：
Chen, Z;Hu, K;Ivanov, PC
在研究复杂的多组分物理和生理系统的动力学特性时，通常情况下，可测量系统的输出并不直接代表我们想要探测的数量，以了解潜在的机制。相反，输出信号通常是感兴趣量的线性或非线性函数。在这里，我们研究了各种线性和非线性变换如何影响信号的相关性和缩放特性，使用去趋势波动分析（DFA），该分析已被证明可以准确量化非平稳信号中的幂律相关性。具体来说，我们研究了三种类型的变换的效果：(i)线性(y(i)=ax(i) +b), （ii）非线性多项式(y(i)=ax（i)(k)）和（iii）非线性对数[y(i)=log(x(i)+Delta)]滤波器。我们比较了变换前后信号的相关性和标度特性。我们发现线性滤波器不会改变相关特性，而非线性多项式和对数滤波器的效果强烈依赖于(a)原始信号中的相关性强度，(b)多项式滤波器的功率k，以及(c)对数滤波器中的偏移量a。我们进一步应用DFA方法来研究三个解析函数的“表观”标度：(i)指数函数[exp(+/-x+a)], （ii）对数函数[log(x+a)]和（iii）幂律函数[(x+a)(lambda)]，它们经常在物理和生物过程中作为趋势遇到。虽然这三个函数具有不同的特征，但我们发现这三个函数的参数a值范围很广，其中DFA曲线的斜率是相同的。我们进一步注意到，对于一类其他解析函数所得到的DFA结果可以简化为这三种典型情况。我们系统地测试了DFA方法在三种滤波器和我们考虑的三种分析函数中对不同参数值的输出信号进行远程幂律相关性估计时的性能。
When investigating the dynamical properties of complex multiple-component physical and physiological systems, it is often the case that the measurable system's output does not directly represent the quantity we want to probe in order to understand the underlying mechanisms. Instead, the output signal is often a linear or nonlinear function of the quantity of interest. Here, we investigate how various linear and nonlinear transformations affect the correlation and scaling properties of a signal, using the detrended fluctuation analysis (DFA) which has been shown to accurately quantify power-law correlations in nonstationary signals. Specifically, we study the effect of three types of transforms: (i) linear (y(i) = ax(i)+b), (ii) nonlinear polynomial (y(i)=ax(i)(k)), and (iii) nonlinear logarithmic [y(i)=log(x(i)+Delta)] filters. We compare the correlation and scaling properties of signals before and after the transform. We find that linear filters do not change the correlation properties, while the effect of nonlinear polynomial and logarithmic filters strongly depends on (a) the strength of correlations in the original signal, (b) the power k of the polynomial filter, and (c) the offset A in the logarithmic filter. We further apply the DFA method to investigate the "apparent" scaling of three analytic functions: (i) exponential [exp(+/-x+a)], (ii) logarithmic [log(x+a)], and (iii) power law [(x+a)(lambda)], which are often encountered as trends in physical and biological processes. While these three functions have different characteristics, we find that there is a broad range of values for parameter a common for all three functions, where the slope of the DFA curves is identical. We further note that the DFA results obtained for a class of other analytic functions can be reduced to these three typical cases. We systematically test the performance of the DFA method when estimating long-range power-law correlations in the output signals for different parameter values in the three types of filters and the three analytic functions we consider.