非平稳随机过程功率谱密度估计的小波方法

讨论了已有文献中基于一般非正交小波以及广义谐和小波的非平稳随机过程演变功率谱密度（Evolutionary Power Spectral Density, EPSD）估计的问题。在一种新的非平稳随机过程模型（局部平稳小波过程，Locally Stationary Wavelet process, LSW）的基础上，提出了一种新的估计非平稳随机过程时变功率谱密度的方法。所建议的新方法能与估计非平稳随机过程EPSD的经典方法统一起来，当以上两种方法均使用广义谐和小波时，二者退化为同一形式。为了验证所建议方法的有效性，给出了基于广义谐和小波的多变量均匀调制下非平稳随机地震动互/自功率谱估计的算例。并以汶川8.0级地震中某近场地及远场地上的地震加速度为例，计算得到了其能量在时－频域上的不同分布。

Power spectrum estimation of non-stationary processes via wavelet

Reviews on the Evolutionary Power Spectrum Density (EPSD) estimation of stochastic process via wavelets are presented in the paper. Based on a newly proposed Local Stationary Wavelet (LSW) model of non-stationary stochastic process, an approach of estimating the time-varying PSD is developed. The newly proposed approach can be explained in a unified perspective with the classic one. Both the approaches reduce to a same form when the general harmonic wavelet is applied. The auto/cross-EPSD of a multi-variant stochastic process is employed as a numerical example to demonstrate the efficiency of the approach. A real world situation, including both the near-field and far-field ground motions of the Wenchuan, China (05/12/2008), are applied as an example to show the applicability of the time-frequency analysis of the approach.