基于S变换的非平稳随机过程演变功率谱密度估计

提出了一种基于S变换的估计Priestley非平稳随机过程演变功率谱密度的方法。此方法的根本在于,相对于S变换的"变换核",Priestley非平稳随机过程的调制函数为慢变函数。因此,非平稳随机过程的S变换可视为相位修正后的另一非平稳随机过程。推导出了对应于特定频率点的S变换瞬时均方值和非平稳随机过程演变功率谱密度之间的关系式。将功率谱密度函数表达为有限个频率点的级数展开,通过求解一组代数方程,就能得到级数展开中每个频率点的时变系数,由此,可给出非平稳随机过程的演变功率谱密度。由于级数展开中的高斯形状函数不依赖于时间,因此,本文所提算法具有较高的计算效率。最后,给出了均匀调制和非均匀调制非平稳随机过程演变功率谱估计的算例。

Stockwell transform based power spectrum estimation of non-stationary stochastic process

The evolutionary power spectrum density (EPSD) of the non-stationary stochastic process is estimated via the Stockwell transform (S transform).The approach depends on the slowly varying pro-perty of the modulating function of the stochastic process, compared to the kernel of the S transform.This yields the phase-modified S transform of the process on a certain frequency can be viewed as a stochastic process with the EPSD given in terms of the EPSD of the original one.Further, an equation between the mean square value of the instantaneous S-transform and the EPSD of the process is derived.The solution of the equation is sought by representing the EPSD of the process as a sum of squared modulus of Gaussian shape functions of the S transform on the different frequency points, modulated by time-depended coefficients.Finally, the time-dependent coefficients can be determined by a linear algebra equation.Since the system matrix in the algebra equation only depends on the Gaussian shape function of the S transform, the algorithm shows high computational efficiency.Both the uniformly and non-uniformly modulated stochastic process is employed to demonstrate the accuracy of the proposed approach.