论文标题
关于进化功率频谱密度的估计
On the estimation of the evolutionary power spectral density
论文作者
论文摘要
从进化过程的样品中估算进化功率谱密度（EPSD）函数的两种流行光谱方法基于短期傅立叶变换（STFT）和连续的小波变换。两者都依赖于缓慢变化的调制或EPSD函数的概念，尽管估计的EPSD中“慢性”变化的效果的量化是难以捉摸的。在本研究中，我们建议在估计EPSD函数的背景下使用EPSD函数的衍生物来量化EPSD函数的平滑度。我们通过使用S变换和连续的小波变换来得出用于估计EPSD的方程式。这些方程与基于STFT得出的方程式使用。我们还通过使用这些转换（包括STFT）来得出相应的方程来评估估计的EPSD的残差。残差提供了一种在估计的上下文中识别或量化EPSD函数的“缓慢”变化的方法。派生的方程式和数值结果表明，残差取决于EPSD函数的衍生物，以及所采用的变换。
Two popular spectral-based approaches for estimating the evolutionary power spectral density (EPSD) function from the samples of the evolutionary process are based on the short-time Fourier transform (STFT) and the continuous wavelet transform. Both rely on the concept of slowly varying modulation or EPSD function, although the quantification of the effect of the 'slow' variation in the estimated EPSD is elusive. We propose, in the present study, to use the derivatives of the EPSD function to quantify the smoothness of the EPSD function in the context of estimating the EPSD function. We derive equations for estimating EPSD by using the S-transform and continuous wavelet transform. These equations are as simple to use as that derived based on STFT. We also derive the corresponding equations for assessing the residual for the estimated EPSD by using these transforms, including STFT. The residual provides an approach for identifying or quantifying, in the context of its estimation, the 'slow' variation of the EPSD function. The derived equations and numerical results indicate that the residual depends on both the derivatives of the EPSD function with respect to time and frequency as well as the adopted transform.
