DISCUSSIONS ON SOME KEY PROBLEMS IN POWER SPECTRA ANALYSIS
功率谱分析中几个重要问题的讨论

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.