功率谱分析中几个重要问题的讨论

本文从理论上推导了谱分析中最大后延M的取值,并且从理论和实际计算中得出了样本长度和其隐含周期之间的关系。只要抽样是平稳的,样本长度并非一定要求太长,仅略为超过其隐含周期的长度即可。但谱分析绝非是万能的。如果样本中仅含有两个波动,且当这两个波动的周期相差一个整数倍或更大时,这两个波动才可以通过谱分析分辨出,反之就会歪曲了其隐含周期。由此可见,在具体应用时,应作一些滤波和去掉趋势是必要的。因而这将对广大气象、地理科学工作者以及其它相邻学科的科研工作者具有重要的参考价值。

DISCUSSIONS ON SOME KEY PROBLEMS IN POWER SPECTRA ANALYSIS

The present paper include three aspects of question. (1) how to determine the value of Maximum Lag M in theory? (2) what is the reationship between the length of sample series N and the period T which is contained in this sample series? (3) how much is reliability of the period T which is disclosed by spectra analysis? The value of Maxmum Lag M is expected to be high if spectra unbiased estimation is considered. At the same time, however, this value is expected limited under the consideration of reduction variance of spectra estimation. It is advisable then that the value of Maximum Lag M be selected as 1/3 to 1/10 of the length of sample series N in both theory and practical calculations. Here lies the relationship between the length of sample series N and the period T which is contained in sample series with calculation and deduction. As long as the sample series is stable, sample series N needn't be too long, only a bit longer than the longest period T which is included in this sample series. Meanwhile, spectra analysis is not omnipotent. If one sample series has two waves, when one wave period is one times larger than another or much more, we can get these two wave periods with spectra analysis. Otherwise, there will appear "aliasing" and the attempt to get these two wave periods will be a failure. So it is necessary to filter and re-trend for sample series, before we use this spectra analysis. These speculations have great relevance to the research of meteorologists and other fields.