SigSpec - I.傅里叶空间中的频率和相位分辨意义
SigSpec - I. Frequency- and Phase-Resolved Significance in Fourier Space
摘要：
在恒星光度学和光谱学的时间序列中识别低信噪比的频率，并精确测量它们的振幅比和峰宽，是星震学的关键目标。这些也是具有间隙的时间序列或其数据不是以恒定速率采样的挑战，即使使用现代离散傅里叶变换（DFT）软件也是如此。此外，Lomb和Scargle引入的误报概率是一种近似值，在数据间隔较长的时间序列中变得不太可靠。这里提出了一种严格的统计处理方法，用于确定DFT中峰值的显著性，称为SigSpec。SigSpec是基于一个概率的分析解决方案，即一个给定幅度的DFT峰值不会出现在一个非等间隔的数据集的白噪声。如果将频率和相位都纳入解中，则可以显式地导出由白噪声产生的幅度谱的潜在概率密度函数（PDF）。在本文中，我定义和评估一个无偏的统计估计，“频谱意义”，这取决于频率，幅度和相位的DFT，并考虑到时域采样。我还比较这个估计的结果，从其他成熟的技术，并证明SigSpec的有效性与地面和空间为基础的光度数据的几个例子，illustrring如何SigSpec处理噪声和时域采样的影响，在确定显着的频率。
英文摘要：
Identifying frequencies with low signal-to-noise ratios in time series of stellar photometry and spectroscopy, and measuring their amplitude ratios and peak widths accurately, are critical goals for asteroseismology. These are also challenges for time series with gaps or whose data are not sampled at a constant rate, even with modern Discrete Fourier Transform (DFT) software. Also the False-Alarm Probability introduced by Lomb and Scargle is an approximation which becomes less reliable in time series with longer data gaps. A rigorous statistical treatment of how to determine the significance of a peak in a DFT, called SigSpec, is presented here. SigSpec is based on an analytical solution of the probability that a DFT peak of a given amplitude does not arise from white noise in a non-equally spaced data set. The underlying Probability Density Function (PDF) of the amplitude spectrum generated by white noise can be derived explicitly if both frequency and phase are incorporated into the solution. In this paper, I define and evaluate an unbiased statistical estimator, the "spectral significance", which depends on frequency, amplitude, and phase in the DFT, and which takes into account the time-domain sampling. I also compare this estimator to results from other well established techniques and demonstrate the effectiveness of SigSpec with a few examples of ground- and space-based photometric data, illustratring how SigSpec deals with the effects of noise and time-domain sampling in determining significant frequencies.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
