关于功率谱密度与风速谱的注记

Notes on power spectrum density and wind-velocity PSD

探讨了随机过程中双边功率谱密度负频率引入的原因,实际的频谱函数应将负频率项与相应正频率项成对合并起来而直流分量保持不变,此即单边功率谱所表达的含义。对目前文献中给出的单边功率谱的表达式和单边功率谱与双边功率谱的关系式进行了修正,并对维纳-辛钦公式的变换形式也做了相应的修正,指出其修正前后在不同风速谱实际应用中的区别。算例证明了本文所给公式的正确性。

The reason that minus frequency appears in two-sided power spectrum density （PSD） of stochastic process is discussed. The actual frequency spectrum function should contains sum of minus and corresponding plus frequency component as well as the direct current part keeps invariable, and this is the underling meaning of one sided PSD. Both one-sided PSD formula and its relation with two-sided PSD given by the standard references are improved. Based upon the work above, the modification to the transformation of Winner-Khinehine formula is presented. Furthermore, the differences between modified and former formulae are pointed out for application in different wind-velocity PSD, and numerical results prove that the modified Winner-Khinehine formulae presented by the paper are correct.