动态数据建模中时间序列采样间隔的研究

动态数据建模认为,平稳连续随机过程是白噪声激励相应的线性时不变连续时间系统的输出,为便于计算机处理,需要确定对连续随机过程进行采样的采样间隔,通常人们采用仙农采样定理来对待。文中阐述了对动态数据建模中时间序列采样的问题,用多项式插值的采样理论进行了研究,指出在动态数据建模中,若要使从连续时间随机过程到离散时间序列的统计特性得到保持,采样频率应大于系统最大极点自然频率的6倍。

The Study on Sampling Interval of Time Series in Dynamic Data Modeling

How to select the sampling interval of time series is an important problem in dynamic data modeling.In dynamic data modeling theory,a stationary stochastic continuous-time process is considered as the output of a linear time-invariant system forced by a white noise.In order to be processed by computer,the continuous-time random process must be sampled to obtain discrete time series,then the sampling rate or sampling interval will be chosen.In many literatures,the sampling rate to obtain time series is based on Shannon sampling theorem,but it's evidently not a low-pass band-limited signal case.In this paper,the sampling theorem of polynomials interpolation is used to study the problem of sampling rate for obtaining a time series in dynamic data modeling.It's shown that the sampling rate must be greater than 6 times of the biggest natural frequency of system poles,while the stochastic property is maintained from the continuous-time random process to discrete time series in dynamic data modeling.