Wavescan：引力波数据的多分辨率时频变换
Wavescan: Multiresolution Time-Frequency Transform of Gravitational-Wave Data
AI总结：
本文提出Wavescan时频变换，利用小波堆栈扫描多尺度功率，减少泄漏影响，增强时频局部化，用于识别引力波数据中的瞬态信号。
摘要：
识别嵌入在非平稳噪声中的瞬态信号，需要分析观测时间序列的时变频谱分量。信号功率的时频分布可以通过Gabor原子或小波来估计，这些原子或小波通过窗函数在时间和频率上局部化。这种分析受到海森堡-伽博不确定原理的约束，该原理限制了单个小波可实现的时频联合局部化能力。此外，由此产生的时频分布会受到时间和频谱泄漏的影响，从而限制了功率谱中尖锐或快速变化特征的识别。本文提出了一种时频变换，该变换使用一组小波堆栈来扫描多个尺度上的局部功率。在每个时频位置，从堆栈中选择受泄漏影响最小的小波，以获得功率的高分辨率局部化。由此产生的小波扫描（“wavescan”）通过增强时频局部化并减轻由时间和频谱泄漏引起的局部功率失真，扩展了传统的多分辨率分析。本文描述了wavescan框架的主要组成部分，包括时变频谱的估计、时频数据中瞬态信号的识别以及相应时域波形的重建。为了展示该方法的性能，将wavescan变换应用于来自LIGO探测器的引力波数据。
英文摘要：
Identifying transient signals embedded in non-stationary noise requires analyzing the time-dependent spectral components of the observed time series. The time-frequency distribution of the signal power can be estimated with Gabor atoms, or wavelets, localized in time and frequency by a window function. Such analysis is constrained by the Heisenberg-Gabor uncertainty principle, which limits the simultaneous time and frequency localization achievable with individual wavelets. Moreover, the resulting time-frequency distribution is subject to temporal and spectral leakage, limiting the identification of sharp or rapidly varying features in the power spectrum. This paper introduces a time-frequency transform that uses a stack of wavelets to scan local power across multiple scales. At each time-frequency location, a wavelet least affected by the leakage is selected from the stack to obtain high-resolution localization of power. The resulting wavelet scan ("wavescan") extends conventional multiresolution analysis by enhancing time-frequency localization and mitigating local power distortions caused by temporal and spectral leakage. The paper describes the principal components of the wavescan framework, including the estimation of the time-varying spectrum, identification of transient signals in the time-frequency data, and reconstruction of the corresponding time-domain waveforms. To demonstrate the performance of the method, the wavescan transform is applied to gravitational-wave data from the LIGO detectors.
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