关于非平稳过程处理的几个注解

Notes on processing non-stationary process

研究了非平稳的含义、非平稳随机过程的等效和幂律过程处理等几个问题.首先,阐述了非平稳存在两种理解,一种是针对确定性过程,另一种针对随机过程,二者分别适用于信号处理和随机动力学计算两种情形.其次,证明任何一个非平稳过程都可以用可数个调制非平稳过程来模拟或等效.然后,指出幂律过程为平稳过程,而非文献中所声明的非平稳过程.最后,论述了通过理想滤波器概念可以将幂律过程转变为各态历经过程.

Some topics, such as the implication of non-stati on ary, equivalence of non-stationary random process, and power law process, are st udied. Firstly, the 2 meanings of non-stationary are presented, one of which is base on the determinate signal, which applies to the case of signal processing, another on random process, which applies to random dynamics computation. Secondl y, it is proved that any non-stationary random process (NSRP) could be equivalen t to the sum of numerable modulating NSRP, which can be applied to simulating NSRP. Thirdly, it is shown that the power law process is not a genuine NSRP, wh ich contradicts to some literatures. Lastly, it is demonstrated that the power l aw process can be transformed to an ergodic process.