AI 中文总结
本文提出一种由相移高斯函数构成的更紧凑时频窗，用于引力波数据分析，其对称性使时频面积接近海森堡-加博尔极限，并推测达到WD小波窗的最小面积。
AI 中文摘要
时频（小波）域分析在引力波数据分析中的应用日益增多，这得益于其在处理非平稳噪声方面的优势。一种常用的选择是Wilson-Daubechies-Meyer（WDM）小波变换，其使用的窗函数在频率上非常紧凑，但在时间上则较为扩展。在本工作中，我们考虑了一种由相移高斯函数之和构成的替代窗函数。这种“高斯”窗在时频上更加对称，因此也更加紧凑。我们研究了该窗函数的性质及其对引力波分析的影响。我们解析计算了该窗的时频方差乘积，并进行了数值验证。对于对称情形，即窗在时间和频率上具有相同形式时，其构造达到了海森堡-加博尔不确定极限的约2.4%以内。我们推测，该高斯窗在任意WD小波窗中实现了最小时频面积。
英文摘要
Time-frequency (wavelet) domain analyses are seeing greater use for gravitational-wave data analysis due to the advantages they have in handling non-stationary noise. A popular choice is the Wilson-Daubechies-Meyer (WDM) wavelet transform, which uses a window function that is very compact in frequency, but more spread out in time. In this work, we consider an alternative window function that is built from a sum of phase-shifted Gaussians. This "Gaussian" window is more symmetric in time-frequency, and consequently more compact. We examine the properties of this window function and the implications it has for gravitational-wave analyses. We calculate the window's time-frequency variance product analytically and verify it numerically. For the symmetric case, where the window has the same form in time and frequency, the construction comes within $\sim2.4\%$ of saturating the Heisenberg-Gabor uncertainty limit. We conjecture that this Gaussian window achieves the minimum time-frequency area of any WD wavelet window.
Comments13 pages, 12 figures
