非平稳噪声建模：在引力波天文学中的应用
Modeling non-stationary noise: applications in gravitational wave astronomy
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中文总结 AI 辅助
研究引力波数据中测量噪声非平稳问题，引入通用框架，通过动态功率谱\(S(f,t)\)建模，构建噪声协方差矩阵的Gram因子模型，给出数据离散傅里叶和小波表示的闭式表达式并举例，推广了平稳功率谱。
中文摘要 AI 辅助
在理想世界中，引力波数据中的测量噪声是平稳且高斯的。但现实中这两个条件均不成立。本文引入一个通用框架，可通过动态功率谱\(S(f,t)\)以易于解释的方式对非平稳噪声进行建模。该构建是噪声协方差矩阵的Gram因子模型，其本质上是半正定的。此构建推广了常见的平稳功率谱\(S(f)\)。动态谱在任何基（包括频域、时域和时频小波域）中编码噪声协方差矩阵的属性。给出了数据离散傅里叶表示和离散Wilson-Daubechies小波表示的闭式表达式，二者均为Gram矩阵形式。还提供了示例，包括窗口函数引起的非平稳性、天基探测器对银河双星信号的调制响应以及其他更一般类型的非平稳性。
英文摘要
In an ideal world, the measurement noise in gravitational wave data would be stationary and Gaussian. In reality, neither of these conditions holds. Here a general framework is introduced that can be used to model non-stationary noise in an easily interpretable way, using a dynamic power spectrum $S(f,t)$. The construction is a Gram-factor model for the noise covariance matrix that is positive semi-definite by construction. This construction generalizes the familiar stationary power spectrum $S(f)$. The dynamic spectrum encodes the properties of the noise covariance matrix in any basis, including the frequency domain, time domain, and time-frequency wavelet domain. Closed form expressions are given for discrete Fourier representations of the data, and for discrete Wilson-Daubechies wavelet representations of the data. Both take the form of Gramian matrices. Examples are provided, including the non-stationarity caused by window functions, the modulated response to galactic binary signals for space-based detectors, and other, more general types of non-stationarity.
