相关系数平稳过程时频分析方法

Time-Frequency Analysis of Correlation Coefficient Stationary Process

相关系数平稳过程是从非平稳过程中分离出的一类工程上常见且便于研究的随机过程,其均值和方差都可随时间变化,传统的平稳随机过程是它的一个特例。本文提出了相关系数AR(p),MA(q)和ARMA(p,q)序列的概念,建立了相关系数平稳过程的时频分析方法。该方法首先在时域进行全程分析,得到相关系数平稳过程的均值函数、方差函数和相关系数函数,然后可以对其进行傅里叶变换、短时傅里叶变换或小波变换,给出相关系数平稳过程的谱密度,同时提出了随机项谱密度和趋势项谱密度的概念。文中还讨论了线性系统对相关系数平稳过程输入的响应。

The correlation coefficient stationary process in which the mean and variance vary with time is familiar in engineering,and the traditional correlation function stationary process is just a special case of that.The method of timefrequency analysis and AR(p),MA(q) and ARMA(p, q) models of the correlation coefficient stationary process are presented in this paper.Its mean function, variance function and correlation coefficient function can be gained by the method in time domain.Thus the spectrum density of the correlation coefficient stationary process can be obtained by Fourier transform,shorttime Fourier transform or wavelet transform.The formulas for calculating the response of a linear system are derived when the input is a correlation coefficient stationary signal.In addition, the concepts of trend component spectrum density and random component spectrum density in random processes are also presented herein.The method has been used in the performance tests of aircraft and satellite successfully.It shows that a great number of specimens and time have been saved.